You will be provided with a reference and some statements. Please determine whether each statement is 'supported', 'unsupported', or 'unknown' with respect to the reference. Please note:
First, assess whether the reference contains any valid content. If the reference contains no valid information, such as a 'page not found' message, then all statements should be considered 'unknown'.
If the reference is valid, for a given statement: if the facts or data it contains can be found entirely or partially within the reference, it is considered 'supported' (data accepts rounding); if all facts and data in the statement cannot be found in the reference, it is considered 'unsupported'.

You should return the result in a JSON list format, where each item in the list contains the statement's index and the judgment result, for example:
[
    {
        "idx": 1,
        "result": "supported"
    },
    {
        "idx": 2,
        "result": "unsupported"
    }
]

Below are the reference and statements:
<reference>
Millisecond optical coherence and strong collective coupling in an integrated telecom rare-earth
photonic platform
Kah Jen Wo ,1, ∗ Pavel A. Dmitriev ,2, 3, † Karthik Dasigi ,2 Fumiya Hanamura ,2 and Steven Touzard

2, 4, ‡

1 Centre for Quantum Technologies, Singapore
2 Centre for Quantum Technologies, Queenstown 117543, Singapore
3 National University of Singapore, Department of Materials Science and Engineering, Singapore
4 National University of Singapore, Department of Physics, Singapore

arXiv:2608.08221v1 [quant-ph] 8 Aug 2026

(Dated: August 11, 2026)
Long-range quantum network nodes require the combination of strong light-matter coupling, long coherence
times and in situ spectral control at telecom wavelengths. The coherence of erbium in integrated devices is
held back by its hosts, which do not simultaneously provide the weakly magnetic nuclear-spin environment
and the well-defined substitutional sites found in coherence-optimised bulk crystals. Here we bring such an
optimised crystal onto a photonic chip, by bonding an Er3+ :CaWO4 host without an adhesive interlayer to a
high-𝑄 electro-optically tuneable thin-film lithium niobate microring resonator. At an effective temperature of
75mK and a field of only 0.2T, the bonded ensemble retains an effective homogeneous linewidth of 289 ± 34Hz
(𝑇M = 1.10 ± 0.13ms), with spectral diffusion proceeding at 86 ± 18Hz and saturating at 1.5 ± 0.2kHz. Electrooptically tuning the resonator through the erbium optical transition resolves an avoided crossing with a collective
cooperativity of 𝐶 = 6.7 ± 0.4. Exploiting superhyperfine coupling to the host’s 183 W nuclear spins, we store
and retrieve optical phase information over 5s with a visibility of 0.935 ± 0.015. Strong collective coupling,
millisecond coherence and in situ spectral tuning in a single device thus establish heterogeneous integration
leveraging coherence-optimised hosts as a route to scalable telecom quantum networks.

I.

INTRODUCTION

Scalable quantum networks require coherent interfaces between travelling optical photons and stationary matter systems [1–3]. Rare-earth ions in crystalline hosts are among the
most mature solid-state candidates, combining narrow optical
transitions with long-lived spin and shelving states [4–6], and
erbium is singular among them because its 4 I 15/2 ↔4 I 13/2 transition lies in the telecom C-band [7] and interfaces directly with
existing fibre networks. Deploying such interfaces at manufacturing scale requires combining erbium ensembles with
photonic circuits that confine the optical mode and provide in
situ tuneable resonators, thereby enhancing light–matter coupling and reducing the optical power required at millikelvin
temperatures.
This effort has seen substantial progress: integratedphotonics with direct erbium doping have demonstrated quantum memories, with atomic-frequency-comb (AFC) storage
of single-photon-level telecom pulses [8, 9] and efficient
resonator-enhanced storage of entangled photons with electrooptically routed retrieval [10]. However, the erbium coherence in these devices is limited by their choice of materials.
Each doped photonic material, such as silicon [11–14], silicon carbide [15], silicon nitride [16], thin-film lithium niobate
(TFLN) [17, 18], was adopted because it is available as large
wafers of thin-film on insulator with scalable fabrication techniques, and not because it suits erbium. These choices can
lead to a high level of magnetic noise, ill-defined substitution
sites or implantation damage. For example, although the effective homogeneous linewidth in erbium-doped TFLN reaches

∗ kjwo@u.nus.edu
† pavel.a.dmitriev@nus.edu.sg
‡ steven.touzard@nus.edu.sg

1.8kHz [19], in hosts where the spin bath environment causes
spectral diffusion and static spin broadening [20, 21], the storage time is currently limited to the 0.1-1µs range [9, 10].
In contrast, bulk rare-earth hosts offer a large coherence advantage over direct doping of photonic circuits. Er3+ :Y2 SiO5 ,
a host combining clear substitution sites with moderate magnetic noise, reaches 73Hz optical linewidths [22] and secondlong hyperfine coherence [23], but only near an extreme field
of 7T. Even though the optical effective linewidth itself can
be of order 100Hz at lower temperature and field [21, 24], the
100%-abundant 89 Y bath caps the spin coherence that underpins long-lived memories, and imposes superhyperfine structure obstructing precise spectral tailoring [21]. Optimised
hosts such as calcium tungstate (CaWO4 ) were predicted to
relax this constraint because their constituent nuclear spins are
dilute and weakly magnetic [20, 25]. Indeed, Er3+ :CaWO4
yields 23ms electron-spin coherence [26], week-long narrow
spectral holes [27], indistinguishable photons [28] and spinphoton entanglement from single erbium ions [29]. However,
because optimised hosts are not available as large thin films,
scalable memories built from them require heterogeneous integration. This route has already been explored for Er3+ :Y2 SiO5 ,
whose mechanical robustness and low refractive index make
it convenient to integrate. These heterogeneous integration attempts achieved resonator tuning but weak coupling in lithium
niobate [30], or strong coupling without resonator tuning in
silicon carbide [31]. For optimised hosts, heterogeneous integration has been attempted for CeO2 via deposition [32],
without reaching bulk-level coherence. Can the coherence of
erbium in optimised hosts be combined with the scalability of
integrated photonics?
Here we integrate Er3+ :CaWO4 with thin-film lithium niobate (TFLN) (Fig. 1a-e). We bond a 50ppm Er3+ :CaWO4
crystal directly to a high-𝑄 (pre-bonding 𝑄 int = 5 × 106 and
post-bonding 𝑄 int = 1 × 106 ), electro-optically tuneable mi-

a

Low noise Er3+ host
Er :CaWO4
3+

c

Bus waveguide

B

Fibre array

Ring resonator
Evanescent coupling

LiNbO3
SiO2

(i)

Si

(i)

TE0

(i)

Wire bond

(i)

Al
Substrate

100 µm

Electrode

b

Hydrogen bonds
δ+

Strong covalent bond formation
Minimal gap

Photonic integrated chip
Bus

Er3+:CaWO4

Ring resonator

e

Wire bonding pad

HO HO HO
OH OH OH

H 2O

δ-

Room temperature

d

1 µm

Post-bond annealing

100 nm

FIG. 1. Heterogeneously integrated photonic platform for strong light-matter coupling. a, Schematic of the heterogeneously integrated
platform. The photonic platform is thin-film lithium niobate (TFLN), with the SiO2 and Si layers forming its substrate. An external magnetic
field B is applied in the plane of the chip. A bus waveguide couples light in and out of the ring resonator via a pulley coupler, while aluminium
electrodes enable electro-optic tuning of the ring resonator. Inset: cross-section of the ring resonator with its single-mode profile evanescently
coupling to the Er3+ ions in the bonded CaWO4 . b, Schematic of the direct bonding procedure. At room temperature, hydrogen bonds form
at the Er3+ :CaWO4 –TFLN interface via surface activation (see Suppl). A subsequent post-bond anneal drives the formation of covalent bonds
with the release of H2 O [33]. c, Photograph of the experimental setup, with a zoomed-in view of the ring resonator. d, e, False-coloured
scanning electron microscope (SEM) images of the TFLN waveguides prior to direct bonding, showing the bus waveguide (orange) and ring
resonator (blue) with low sidewall roughness.

croring resonator without an adhesive interlayer (Fig. 1b),
placing the ions well within the evanescent field of the resonator mode (Fig. 1a; inset). The electro-optic effect of
TFLN enables spectral alignment of the resonator with a
spin-preserving optical transition at millikelvin temperatures,
where thermal and gas-condensation tuning are impractical.
Operating the device in a dilution refrigerator (Fig. 1c), we
measure an effective homogeneous linewidth of 289 ± 34Hz
(𝑇M = 1.10 ± 0.13ms) at 0.2T, with spectral diffusion proceeding at a rate 𝑅 = 86 ± 18Hz and saturating at an amplitude
ΓSD = 1.5 ± 0.2kHz. Tuning the resonator through the spinpreserving optical transition resolves an avoided crossing with
collective cooperativity 𝐶 = 6.7 ± 0.4. Superhyperfine coupling to host 183 W nuclear spins allows storage of optical
phases encoded in spectral gratings for 5s, retrieved with a
visibility of 0.935 ± 0.015. Strong collective coupling, millisecond optical coherence, slow spectral diffusion and electrooptic tuneability are thus obtained in one integrated device, establishing an optimal platform for scalable quantum networks.

II.
A.

RESULTS

High coherence and low spectral diffusion preserved in an
integrated chip

We characterise the optical coherence of the Er3+ ions using the bus waveguide, thereby probing the ions free from
resonator-induced Purcell modification, and from non-linear

effects due to strong collective coupling. The erbium dopant
is present in natural isotopic abundance, comprising both
the hyperfine-active 167 Er3+ isotope (𝐼 = 7/2, 22.9%) and
hyperfine-free even isotopes (𝐼 = 0, 77.1%). Of the four optical transitions (A–D) between the Kramers doublets (Fig. 2a),
we drive transition A (|↓⟩ 𝑍1 ↔|↓⟩𝑌1 ) in all experiments reported
in this work. This corresponds to a spin-preserving optical
transition, robust to magnetic noise.
To probe both the spectral diffusion and the homogeneous
linewidth, we employ the three-pulse photon echo (3PPE) technique (Fig. 2b) [34, 35]. The first two pulses, separated by time
𝜏12 , imprint a spectral population grating on the ensemble. After a waiting time 𝜏23 , a third pulse converts this grating back
into optical coherence, which rephases as an echo at a time 𝜏12
after the third pulse. For the measurement setup, see Suppl.
As long as 𝜏23 is less than the optical lifetime 𝑇1 = 6.5ms
(Suppl), the population grating is stored in the optical
transition and the decay of the echo intensity follows
𝐼3PPE ∝ exp (−4𝜋𝜏12 Γeff ), where Γeff is the effective linewidth.
This time-dependence is shown in Fig. 2c at the field of
|B| = 0.2T. In this regime, the effective linewidth remains
close to 260Hz Fig. 2d. For 𝜏23 ≫ 𝑇1 , the optical excited
state has fully decayed and the population grating is stored in
shelving states with much longer lifetimes (see Section II C).
At short 𝜏12 , the resulting echoes are modulated by electron
spin-echo envelope modulation (ESEEM) due to superhyperfine coupling [36]. At 𝜏12 > 20µs, we fit the decay of the intensity following the same model, from which we deduce Γeff .
We see that the effective linewidth rises around 𝜏23 = 1ms and

Page 2 out of 7

Energy

b

Y1
Y1

A
1532 nm

Intensity

a

D B

C

τ12

Z1
Z1

Norm. echo intensity I3PPE

c

100

|B| = 0.2 T

τ23

τ12

plateaus near 1kHz after 𝜏23 = 10ms verified up to 𝜏23 = 2s.
The evolution of the effective linewidth shown in Fig. 2d
matches the ubiquitous spectral diffusion model well, for
which Γeff = Γ0 + 21 ΓSD (𝑅𝜏12 + 1 − exp (−𝑅𝜏23 )) [34], where
Γ0 is the homogeneous linewidth, 𝑅 is the characteristic
rate at which neighbouring perturbers flip, and ΓSD is the
full-width half-maximum (FWHM) of the frequency distribution explored by Er3+ ions. We find that the homogeneous
linewidth is Γ0 = 254 ± 7Hz, the spectral diffusion rate is
𝑅 = 86 ± 18Hz, and the process saturates the linewidth at
ΓSD = 1.5 ± 0.2kHz. This spectral diffusion proceeds more
slowly than the optical lifetime (1/𝑅 = 11.6ms > 𝑇1 ), and
does not significantly affect the coherence of the optical transition. Indeed, the empirical coherence time calculated from
√
0
SD 𝑅
(−1 + (1 + Γ𝜋Γ
[34],
these parameters as 𝑇M = Γ2Γ
2 ))
0
SD 𝑅
gives
𝑇M = 1.10 ± 0.13ms,
which
is
close
to
1/𝜋Γ0 = 1.25 ± 0.03ms.
Correspondingly, the empirical
linewidth is Γ̃eff = 1/𝜋𝑇M = 289 ± 34Hz. In comparison, the
empirical linewidth at millikelvin temperatures with direct
doping is limited to 1.8kHz in TFLN [19] and 441kHz in
silicon carbide on insulator [15], and with heterogeneous
integration 1.3kHz for Er3+ :Y2 O3 on silicon [37] and 5kHz
for Er3+ :TiO2 on silicon nitride [16].
For different magnetic fields, the empirical coherence time
exceeds one millisecond between 0.2T and 0.6T, falling
sharply at lower fields and declining gradually at higher fields,
as shown in Fig. 2e. We attribute the fall at low fields to
the Er3+ electronic spin flip-flop interactions in the 𝑍1 manifold [34], and the decline at high fields to the one-phonon
direct process that involves an increased density of phonon
states whose energies are degenerate with the Zeeman splitting [22]. A fit combining both contributions (solid line) yields
an effective spin temperature 75mK (Suppl). This temperature
is limited by thermalisation and residual heating induced by
optical measurement pulses [38].

I3PPE
Time

1.0
0.5
0.0

10−1

0.0

0.1

10−2
0

Effective linewidth Γeff (kHz)

d

1
2
3
Rephasing time 2τ12 (ms)

2.0

4

|B| = 0.2 T

1.5
1

1.0

Γ0 + 2 ΓSD

0.5
Γ0
0.0
101

105
104
102
103
Waiting time τ23 (µs)

106

102

1.2

~

1.0
101

0.8
0.6

100

0.4
0.2

10−1

0.0
0.0

0.2
0.4
0.6
0.8
Magnetic field strength |B| (T)

1.0

Empirical coherence time TM (ms)

e

Empirical linewidth Γeff (kHz)

0.2
0.1 ms
4.1 ms
7.7 ms
0.1 s
1.0 s

FIG. 2. Spectral diffusion and coherence of Er3+ ions. a, Er3+
energy level structure in the presence of magnetic field, depicting four
distinct optical transitions (A–D) between the Kramers doublets of the
𝑍1 (4 I 15/2 ) and 𝑌1 (4 I 13/2 ) manifolds. Transition A (|↓⟩ 𝑍1 ↔|↓⟩𝑌1 )
is driven here. b, Pulse sequence for the three-pulse photon echo
(3PPE) measurement, defining the pulse separation 𝜏12 and waiting
time 𝜏23 [34]. c, Normalised echo intensity 𝐼3PPE as a function of
rephasing time 2𝜏12 , obtained for various waiting times 𝜏23 (different
markers) at |B| = 0.2T. Each curve is fitted to a spectral diffusion
model (solid line). Inset: Zoom-in on the shaded region revealing electron spin echo envelope modulation (ESEEM). d, Effective
linewidth Γeff as a function of waiting time 𝜏23 at |B| = 0.2T. The
curve is fitted to the same spectral diffusion model (solid line). Γ0 is
the homogeneous linewidth and ΓSD is the FWHM of the frequency
distribution explored by Er3+ ions. e, Empirical linewidth Γ̃eff (left
axis) and empirical coherence time 𝑇M (right axis) as a function of
magnetic field strength |B| up to 1T. Solid line: fit combining electronic spin flip-flop and one-phonon direct process contributions (see
Suppl), yielding a temperature of 75mK. The error bars represent
one-standard-deviation confidence intervals from least-square fits.

B.

Strong optical collective coupling with an integrated Er3+
ensemble

Having established millisecond optical coherence at telecom
wavelengths, we now demonstrate that the same integrated
platform achieves strong collective coupling between the ring
resonator and the Er3+ ensemble.
By electro-optically tuning the ring resonator across transition A, we map the optical field transmission as a function of
resonator-ensemble detuning (Fig. 3a). For all magnetic fields
between 0T and 1T, we observe a clear avoided crossing, which
is a spectroscopic signature of strong collective coupling. For
the extracted parameters across all magnetic fields, see Suppl.
We model this resonator-ensemble coupling with a Lorentzian
spectral distribution for the inhomogeneous broadening of the
Er3+ ensemble. This choice is physically justified by the strain
caused by dilute defects in rare-earth crystals [5, 39, 40], and
is consistent with prior observation [30].
For an inhomogeneously broadened ensemble with
linewidth Γinh coupled to a resonator of total linewidth 𝜅 tot ,
4𝐺 2
the collective cooperativity is defined as 𝐶 = 𝜅tot
Γinh , where 𝐺

Page 3 out of 7

is the collective coupling strength [41–43]. Fitting the transmission yields 𝐶 = 6.7 ± 0.4 with Γinh /2𝜋 = 332 ± 21MHz,
𝐺/2𝜋 = 331 ± 6MHz at zero field, and a loaded resonator linewidth of 𝜅tot /2𝜋 ≈ 200MHz.
At |B| = 1T,
we extract 𝐶 = 5.8 ± 0.8 with Γinh /2𝜋 = 387 ± 29MHz and
𝐺/2𝜋 = 353 ± 26MHz. One-dimensional slices across the
avoided crossings confirm the fit in both amplitude and phase
(Fig. 3b): (i) on resonance, the transmitted power splits into
two polariton branches accompanied by a sharp dispersive
phase feature, and (ii) both signatures vanish once the resonator is detuned.
In comparison, Er3+ :Y2 SiO5 direct bonded to a TFLN microring, reached 𝐶 = 0.36 [30], and 167 Er3+ :Y2 SiO5 on silicon
carbide microrings reached 𝐶 = 1.9 [31]. We attribute our improvement in cooperativity to annealed bonding and absence
of an adhesive layer. In TFLN integration, the electro-optic effect enables tuning compatible with millikelvin temperatures to
the spin-preserving transition A. Without this tuning capability, integrated memories rely on spin-flipping transitions that
can be tuned via magnetic field bias, at the cost of increased
sensitivity to magnetic noise.
a

1

1.0

C = 5.8

1T

Cavity detuning (GHz)

i

0

0T

0.0
−0.5

Phase (rad)

Norm. power

b

Fitted

Measured

−1
0.5

C = 6.7
Measured

−1

Fitted

0
1 −1
0
Probe detuning (GHz)

1

Norm. transmitted power

ii

0.4

1.0
0.5

i

ii

0.2
0.0

−0.2
−1

0
1
−1
0
Probe detuning (GHz)

1

FIG. 3. Strong collective light-matter coupling. a, Normalised
transmission spectrum of the ring resonator as it is electro-optically
tuned across the 𝑍1 ↔𝑌1 transition (transition A at finite field). An
avoided crossing is resolved at both |B| = 1T (top; 𝐶 = 5.8 ± 0.8)
and |B| = 0T (bottom; 𝐶 = 6.7 ± 0.4). The measured transmission
spectra are fitted to a coupled resonator–ensemble model assuming a
Lorentzian inhomogeneous broadening profile (see Suppl). b, Transmitted power (top) and phase response (bottom) when ring resonator
is on resonance (i; left) or detuned (ii; right) relative to transition A,
at |B| = 1T. Markers: measured data; solid lines: fit. The power and
phase response were acquired simultaneously using a phase-sensitive
heterodyne setup (see Suppl and Ref. [44]).

C.

Optical phase storage at seconds timescale

In Er3+ :CaWO4 , the 183 W isotope (𝐼 = 1/2, 14.3% natural abundance) provides access to ultra-long-lived shelving
states. The mechanism relies on superhyperfine coupling between the Er3+ electronic spin and the surrounding 183 W nuclear spins (Fig. 4a), which has been shown to enable spectral hole lifetimes on the order of minutes to hours [27].
We demonstrate this shelving timescale through an inversionrecovery measurement as shown in Fig. 4b: at a delay time
𝜏inv after an initial optical excitation to |↓⟩𝑌1 , we measure the
ground state population at the excitation frequency with a Hahn
echo sequence. The excited Er3+ ions relax through different channels with three well-separated timescales. The first
timescale involves the optical decay from the 𝑌1 to the 𝑍1 manifold with lifetime 𝑇1 = 6.34 ± 0.25ms (𝑇1 = 6.42 ± 0.25ms)
at 0.15T (0.2T) (measured independently via fluorescence
Suppl). The second timescale is the lifetime 𝑇Z = 126 ± 8ms
(𝑇Z = 45 ± 7ms) of the upper Zeeman sublevel |↑⟩ 𝑍1 at 0.15T
(0.2T). At longer delays, the intensity of the recovered echo
continuously increases for delays up to 10,000s. We fit this
increase with a stretched exponential with a stretching factor
of 0.5, which suggests a timescale beyond 1,000s (a better estimate would require observing a clear plateau). We attribute
this third timescale 𝑇W ≫ 𝑇Z to the flips of the tungsten 183 W
nuclear spins, which are coupled to erbium ions via superhyperfine interaction [27] and can serve as long-lived shelving
states.
These shelving states are critical for many quantum memory protocols such as the atomic frequency comb (AFC). In
AFCs, the phase information of time-bin qubits is typically
measured using the interference pattern through a dual-comb
interferometer [31, 46]. A similar capability is available for an
optical phase using the 3PPE sequence shown in Fig. 4c. The
3PPE protocol is analogous to an AFC for which the finesse
of the comb is intrinsically insufficient for efficient quantum
storage [47]. An initial preparation pulse first excites a frequency band within the inhomogeneous line. After a delay
𝜏12 , two write pulses, separated by 𝜏d , create a pair of spectral
population gratings within this band. The relative phase Δ𝜙
between the write pulses is thereby encoded into the frequency
offset between these two gratings. After a time 𝜏23 , two read
pulses separated by 𝜏d convert the spectral population gratings back into optical coherence, generating three echoes. If
the period of both population gratings and their relative frequency offset is preserved, the central echo displays consistent
interference between the retrieved pulses encoding the original
phase information Δ𝜙. The delay time 𝜏d = 6.15µs is chosen
for robustness against the phase drift of our 2kHz linewidth
source laser. For the pulse parameters, see Suppl.
We observe high contrast interference for delays up to
𝜏23 = 5s as shown in Fig. 4d. We quantify this contrast using
the visibility 𝑉 = (𝐼max − 𝐼min )/(𝐼max + 𝐼min ), where 𝐼max and
𝐼min are the integrated intensities of the central interfered echo
for constructive and destructive interference, respectively. The
visibility remains constant across all investigated storage times
with an average value 𝑉 = 0.935 ± 0.015, as shown in Fig. 4e.
This confirms that the relative encoded optical phase is not

Page 4 out of 7

Energy

W

Z1

TZ

t =0

d
Z1

0.75

Y1

τinv

Norm.
Intensity

Norm. echo intensity Iinv

TW

W

Z1

1.00

Prepare

Intensity

T1

b

c

Er3+ — 183W
superhyperfine
interaction

Y1

Iinv

0.5
0.0

τH τH

0.50

e

0.25

0.20 T

108

Δϕ = 0

τ23

τd

τ23 = 2 ms
Δϕ = π

3×

Retrieval

τ12

τd τd

t

τ23 = 5 s

−2

0
2
−2
0
Time t − 2τ12 − τ23 − 3τd (µs)

103

105
104
106
Waiting time τ23 (μs)

2

1.0

0.0

1010
Norm. intensity

104
106
Delay τinv (µs)

τd

Read

0.5

0.15 T

0.00
102

1.0

τ12

Write
Δϕ

Visibility V

a

FIG. 4. Optical phase storage. a, Decay mechanisms of Er3+ ions populated in the |↓⟩𝑌1 state following optical excitation. b, Inversionrecovery echo intensity 𝐼inv as a function of waiting time 𝜏inv between the first pulse (see inset for sequence) and the subsequent Hahn echo
sequence with time 𝜏H at different fields (markers). The echo intensities are normalised to their common plateau at 𝑇1 , 𝑇Z < 𝜏inv < 𝑇W . Lines:
fit to a triple exponential 𝐼inv ∝ [1 − ( 𝑝 1 exp (−𝜏inv /𝑇1 ) + 𝑝 Z exp (−𝜏inv /𝑇Z ) + 𝑝 W exp (−(𝜏inv /𝑇W ) 1/2 ))] 2 , from which 𝑇1 , 𝑇Z , and 𝑇W are
extracted. The dashed line section indicates estimate for the ultra long-lived states. Arrows indicate the echo features corresponding to each
of the three decay channels shown in a: optical (𝑇1 ), electronic spin (𝑇Z ), and nuclear spin (𝑇W ), from left to right. c, The pulse sequence
for optical phase storage protocol, based on the 3PPE sequence [45]. A preparation pulse is followed by two write pulses after a delay 𝜏12 .
The write pulses are separated by 𝜏d and carry a relative phase Δ𝜙. After a time 𝜏23 , two read pulses retrieve the stored relative phase as an
interference pattern of the emitted echoes. d, Emitted echoes for an input pulse pair with relative phase Δ𝜙 = 0 (constructive interference,
green) and Δ𝜙 = 𝜋 (destructive interference, orange), at delays 𝜏23 = 2ms (left) and 𝜏23 = 5s (right) at |B| = 0.2T. The traces for 𝜏23 = 5s are
scaled up by a factor of 3× for clarity. e, Visibility 𝑉 of the retrieved interference pattern as a function of waiting time 𝜏23 .

scrambled by the spectral diffusion process. It also validates
that the 183 W nuclear spins act as shelving states.

III.

DISCUSSION AND CONCLUSION

We have integrated an erbium host optimised for coherence
into scalable photonics without apparent coherence trade-off.
Bonding an Er3+ :CaWO4 crystal directly to a high-𝑄 thin-film
lithium niobate microring places the ions in the evanescent
field of the resonator, where their optical coherence is preserved.
Electro-optic control of the resonator allows the coupling to
be measured on the highly coherent spin-preserving transition
on which a quantum memory would operate, whereas neither
thermal nor gas-condensation tuning is practical at millikelvin
temperatures. We find a collective cooperativity of 𝐶 = 6.7 in
an ensemble whose optical coherence extends to the millisecond scale. The device therefore simultaneously offers strong
collective coupling, bulk-level optical coherence and on-chip
resonator tuning.
The optical transition frequency is stable over long times,
as it varies more slowly than the optical lifetime and remains
within 1kHz from its original value even after seconds. We
attribute this stability to the sparse bath of nuclear spins in
CaWO4 and to the high crystallinity of the host. This stability is paramount for quantum memory protocols based on
spectral-hole burning such as AFC [48]. Sustaining a sub-

kilohertz effective linewidth over the preparation time of an
AFC makes kilohertz tooth spacings plausible, corresponding to delays two orders of magnitude beyond the microsecond
range demonstrated so far [9, 10]. Our demonstration of 3PPEbased interference provides a necessary primitive towards this
goal. Preparing a high-efficiency AFC and operating it on
quantum signals remains to be demonstrated.
The tight mode confinement of our integrated photonics lowers the optical power needed to drive the Er3+ ions and makes
millikelvin operation possible. At this operating temperature,
a field as small as 0.2T polarises the electronic spins and suppresses spin flip-flops, leading to our narrow optical effective
linewidth. Compared to the multi-tesla fields required to reach
comparable effective linewidths at higher temperature [22, 23],
here a permanent magnet would suffice to operate our devices
as a scalable quantum network node.
The combination of high cooperativity and optical coherence also enables efficient echo-based quantum memories [49, 50]. In our device, the cooperativity 𝐶 = 6.7 indicates
that the collective coupling of the erbium ensemble to the resonator far exceeds its coupling to the environment. The same
architecture can be designed to operate in the overcoupled
regime, enabling a high-efficiency impedance-matched quantum memory with 𝐶 = 1 [43, 51]. Identifying and removing
the loss introduced by bonding would provide a straightforward path towards further improvements in efficiency. Such
an echo-based memory would allow on-demand storage of
order millisecond, limited by the optical effective linewidth.

Page 5 out of 7

Our rare-earth host also provides a route towards far longer
storage, through hyperfine shelving in erbium enriched in
the 167 Er isotope. The dilute nuclear spin background, together with the zero first-order-Zeeman points identified in
CaWO4 [52], should lift the hyperfine coherence restriction
of about a second previously measured in 167 Er3+ :Y2 SiO5 at
7T [23]. Together with the low temperatures that integrated
devices enable, this platform opens a path towards spin-wave
quantum storage on the minute timescales. The platform thus
supports a long-term programme, from high-efficiency nodes
for metropolitan quantum networks to the far longer storage
that intercontinental and satellite links require.

of Sydney – National University of Singapore 2026 Ignition
Grants, and from E6Nanofab facilities. K.J.W. and K.D. acknowledge the support of the Singapore National Quantum
Scholarship Scheme (NQSS).

COMPETING INTERESTS

The authors declare no competing interests.

AUTHOR CONTRIBUTIONS
ACKNOWLEDGEMENTS

We thank Jian-Rui Soh, Mikhael Sayat, John Bartholomew,
and Miloš Rančić for helpful discussions. This research is supported by the Ministry of Education, Singapore, the National
Research Foundation, Singapore, under grants ID NRFF142022-0002 and CRP33-2025-0072, and through the National
Quantum Office, hosted in A*STAR, under its Centre for
Quantum Technologies Funding Initiative (S24Q2d0009). We
also acknowledge the funding support from The University

[1] H. J. Kimble, The quantum internet, Nature 453, 1023 (2008).
[2] N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, Quantum repeaters based on atomic ensembles and linear optics, Reviews of Modern Physics 83, 33 (2011).
[3] S. Wehner, D. Elkouss, and R. Hanson, Quantum internet: A vision for the road ahead, Science 362, 10.1126/science.aam9288
(2018).
[4] W. Tittel, M. Afzelius, T. Chaneliére, R. Cone, S. Kröll, S. Moiseev, and M. Sellars, Photon–echo quantum memory in solid
state systems, Laser & Photonics Reviews 4, 244 (2010).
[5] C. Thiel, T. Böttger, and R. Cone, Rare-earth-doped materials for applications in quantum information storage and signal
processing, Journal of Luminescence 131, 353 (2011).
[6] M. Afzelius, N. Gisin, and H. de Riedmatten, Quantum memory
for photons, Physics Today 68, 42 (2015).
[7] G. H. Dieke, Spectra and energy levels of rare earth ions in
crystals, edited by H. M. Crosswhite and H. Crosswhite (Interscience Publishers, New York, 1968).
[8] S. Dutta, Y. Zhao, U. Saha, D. Farfurnik, E. A. Goldschmidt,
and E. Waks, An Atomic Frequency Comb Memory in RareEarth-Doped Thin-Film Lithium Niobate, ACS Photonics 10,
1104 (2023).
[9] P. Barya, D. Chen, A. Prabhu, L. Heller, E. Chow, H. Kim,
J. Akin, V. Niaouris, J. Zhang, A. M. Dibos, P. Wang, and E. A.
Goldschmidt, Telecom quantum memory over one microsecond
in nanophotonic lithium niobate (2026).
[10] C. Yang, H. Guo, Y.-Y. An, Q. He, C. Lu, Z. Jiang, Y.-Q. Lu,
S. Zhu, and X.-S. Ma, Programmable cavity-enhanced telecom
quantum memory in thin-film lithium niobate (2026).
[11] L. Weiss, A. Gritsch, B. Merkel, and A. Reiserer, Erbium
dopants in nanophotonic silicon waveguides, Optica 8, 40
(2021).

K.J.W. carried out the measurements and developed the direct bonding procedure. P.A.D. fabricated and packaged the
TFLN samples and assisted in developing the direct bonding procedure. K.J.W., P.A.D. and K.D. designed the cryogenic measurement setup. K.D. developed the setup for the
heterodyne measurements, assisted with nanofabrication and
measurements. F.H. assisted with measurements and data interpretation. S.T. developed the concept, coordinated the work
and assisted with data interpretation. All authors participated
in the writing and reviewing of the manuscript.

[12] A. Gritsch, L. Weiss, J. Früh, S. Rinner, and A. Reiserer, Narrow
Optical Transitions in Erbium-Implanted Silicon Waveguides,
Physical Review X 12, 041009 (2022).
[13] S. Rinner, F. Burger, A. Gritsch, J. Schmitt, and A. Reiserer, Erbium emitters in commercially fabricated nanophotonic silicon
waveguides, Nanophotonics 12, 3455 (2023).
[14] I. R. Berkman, A. Lyasota, G. G. de Boo, J. G. Bartholomew,
S. Q. Lim, B. C. Johnson, J. C. McCallum, B.-B. Xu, S. Xie,
N. V. Abrosimov, H.-J. Pohl, R. L. Ahlefeldt, M. J. Sellars,
C. Yin, and S. Rogge, Long optical and electron spin coherence
times for erbium ions in silicon, npj Quantum Information 11,
66 (2025).
[15] A. Lyasota, J. Bader, S. Q. Lim, B. C. Johnson, J. C. McCallum, Q. Li, S. Rogge, and S. Castelletto, Narrow magnetooptical transitions of erbium implanted into silicon carbide-oninsulator, Communications Materials 7, 10.1038/s43246-02601154-5 (2026).
[16] S. Gupta, R. M. Pettit, A. Sundaresh, V. Niaouris, S. DeckoffJones, D. P. Crowley, L. G. Carpenter, A. M. Dibos, M. K.
Singh, and S. E. Sullivan, Erbium quantum memory platform
with long optical coherence via back-end-of-line deposition
on foundry-fabricated photonics, Physical Review Applied 24,
10.1103/xj8y-b6sl (2025).
[17] S. Wang, L. Yang, R. Cheng, Y. Xu, M. Shen, R. L. Cone,
C. W. Thiel, and H. X. Tang, Incorporation of erbium ions into
thin-film lithium niobate integrated photonics, Applied Physics
Letters 116, 10.1063/1.5142631 (2020).
[18] S. Dutta, E. A. Goldschmidt, S. Barik, U. Saha, and E. Waks,
Integrated Photonic Platform for Rare-Earth Ions in Thin Film
Lithium Niobate, Nano Letters 20, 741 (2020).
[19] S. Wang, L. Yang, M. Shen, W. Fu, Y. Xu, R. L. Cone, C. W.
Thiel, and H. X. Tang, Er:LiNbO3 with High Optical Coherence
Enabling Optical Thickness Control, Physical Review Applied

Page 6 out of 7

18, 014069 (2022).
[20] S. Kanai, F. J. Heremans, H. Seo, G. Wolfowicz, C. P. Anderson,
S. E. Sullivan, M. Onizhuk, G. Galli, D. D. Awschalom, and
H. Ohno, Generalized scaling of spin qubit coherence in over
12,000 host materials, Proceedings of the National Academy of
Sciences 119, 10.1073/pnas.2121808119 (2022).
[21] M. Guo, Q. Li, Z. Xu, S. Liu, F. Wang, and M. Zhong, Decoherence characterization and quantum memory design in
167 Er3+ :Y SiO , Frontiers of Physics 21, 033201 (2026).
2
5
[22] T. Böttger, C. W. Thiel, R. L. Cone, and Y. Sun, Effects of magnetic field orientation on optical decoherence in Er3+ :Y2 SiO5 ,
Phys. Rev. B 79, 115104 (2009).
[23] M. Rančić, M. P. Hedges, R. L. Ahlefeldt, and M. J. Sellars, Coherence time of over a second in a telecom-compatible quantum
memory storage material, Nature Physics 14, 50 (2017).
[24] R. Fukumori, Y. Huang, J. Yang, H. Zhang, and T. Zhong, Subkilohertz optical homogeneous linewidth and dephasing mechanisms in Er3+ :Y2 O3 ceramics, Physical Review B 101, 214202
(2020).
[25] A. M. Ferrenti, N. P. de Leon, J. D. Thompson, and R. J. Cava,
Identifying candidate hosts for quantum defects via data mining,
npj Computational Materials 6, 10.1038/s41524-020-00391-7
(2020).
[26] M. Le Dantec, M. Rančić, S. Lin, E. Billaud, V. Ranjan, D. Flanigan, S. Bertaina, T. Chanelière, P. Goldner, A. Erb, R. B. Liu,
D. Estève, D. Vion, E. Flurin, and P. Bertet, Twenty-three–
millisecond electron spin coherence of erbium ions in a naturalabundance crystal, Science Advances 7, 10.1126/sciadv.abj9786
(2021).
[27] Z. Wang, S. Lin, M. Le Dantec, M. Rančić, P. Goldner,
S. Bertaina, T. Chaneliere, R. Liu, D. Esteve, D. Vion, E. Flurin,
and P. Bertet, Week-long-lifetime microwave spectral holes in an
erbium-doped scheelite crystal at millikelvin temperature, Nature Communications 16, 10.1038/s41467-025-64087-6 (2025).
[28] S. Ourari, Ł. Dusanowski, S. P. Horvath, M. T. Uysal, C. M.
Phenicie, P. Stevenson, M. Raha, S. Chen, R. J. Cava, N. P.
de Leon, and J. D. Thompson, Indistinguishable telecom band
photons from a single Er ion in the solid state, Nature 620, 977
(2023).
[29] M. T. Uysal, Ł. Dusanowski, H. Xu, S. P. Horvath, S. Ourari,
R. J. Cava, N. P. de Leon, and J. D. Thompson, Spin-Photon
Entanglement of a Single Er3+ Ion in the Telecom Band, Physical
Review X 15, 011071 (2025).
[30] L. Yang, M. Shen, Y. Xu, J. Xie, and H. X. Tang, Photonic
integration of Er3+ :Y2 SiO5 with thin-film lithium niobate by
flip chip bonding, Optics Express 29, 15497 (2021).
[31] A. Kolar, I. Chin, C. Fong, D. M. Lukin, M. A. Guidry, M. Palei,
J. Vučković, and T. Zhong, Integrated photon-memory entanglement generation using dual photonic resonators (2026).
[32] J. Zhang, G. D. Grant, I. Masiulionis, M. T. Solomon, J. C.
Marcks, J. K. Bindra, J. Niklas, A. M. Dibos, O. G. Poluektov,
F. J. Heremans, S. Guha, and D. D. Awschalom, Optical and
spin coherence of er spin qubits in epitaxial cerium dioxide
on silicon, npj Quantum Information 10, 10.1038/s41534-02400903-z (2024).
[33] Q. Kang, H. Yan, F. Niu, K. Liu, T. Suga, and C. Wang,
Inp/linbo3 covalent heterointerface construction via an asymmetric plasma activation strategy for hybrid integrated quantum
systems, ACS Applied Materials & Interfaces 16, 48502 (2024),
pMID: 39193874.
[34] T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, Optical decoherence and spectral diffusion at 1.5 µm in Er3+ :Y2 SiO5 versus
magnetic field, temperature, and Er3+ concentration, Phys. Rev.

B 73, 075101 (2006).
[35] M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser
Spectroscopy (Academic Press, New York, 1988).
[36] S. Probst, G. Zhang, M. Rančić, V. Ranjan, M. Le Dantec, Z. Zhang, B. Albanese, A. Doll, R. B. Liu, J. Morton,
T. Chanelière, P. Goldner, D. Vion, D. Esteve, and P. Bertet, Hyperfine spectroscopy in a quantum-limited spectrometer, Magnetic Resonance 1, 315 (2020).
[37] S. Gupta, Y. Huang, S. Liu, Y. Pei, Q. Gao, S. Yang, N. Tomm,
R. J. Warburton, and T. Zhong, Dual epitaxial telecom spinphoton interfaces with long-lived coherence, Nature Communications 16, 9814 (2025).
[38] J. Rochman, T. Xie, J. G. Bartholomew, K. C. Schwab, and
A. Faraon, Microwave-to-optical transduction with erbium ions
coupled to planar photonic and superconducting resonators, Nature Communications 14, 10.1038/s41467-023-36799-0 (2023).
[39] T. Böttger, Y. Sun, C. W. Thiel, and R. L. Cone, Spectroscopy
and dynamics of Er3+ :Y2 SiO5 at 1.5 µm, Phys. Rev. B 74,
075107 (2006).
[40] D. L. Orth and J. L. Skinner, Lattice model of inhomogeneous
broadening in crystals: Correlation of frequency distributions
for different transitions, The Journal of Physical Chemistry 98,
7342 (1994).
[41] I. Diniz, S. Portolan, R. Ferreira, J. M. Gérard, P. Bertet, and
A. Auffèves, Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum
memories, Physical Review A 84, 063810 (2011).
[42] A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen,
Photon storage in Λ-type optically dense atomic media. i. cavity
model, Physical Review A 76, 033804 (2007).
[43] M. Afzelius and C. Simon, Impedance-matched cavity quantum
memory, Physical Review A 82, 022310 (2010).
[44] K. Dasigi, P. A. Dmitriev, K. J. Wo, F. Hanamura, L. Kong,
and S. Touzard, Quantum-limited optical vector analysis, IEEE
Transactions on Instrumentation and Measurement , 1 (2026).
[45] M. U. Staudt, S. R. Hastings-Simon, M. Nilsson, M. Afzelius,
V. Scarani, R. Ricken, H. Suche, W. Sohler, W. Tittel, and
N. Gisin, Fidelity of an optical memory based on stimulated
photon echoes, Physical Review Letters 98, 113601 (2007).
[46] D.-C. Liu, P.-Y. Li, T.-X. Zhu, L. Zheng, J.-Y. Huang, Z.-Q.
Zhou, C.-F. Li, and G.-C. Guo, On-demand storage of photonic
qubits at telecom wavelengths, Physical Review Letters 129,
210501 (2022).
[47] M. Bonarota, J. Ruggiero, J. L. L. Gouët, and T. Chanelière, Efficiency optimization for atomic frequency comb storage, Physical
Review A 81, 033803 (2010).
[48] M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, Multimode quantum memory based on atomic frequency combs,
Physical Review A 79, 052329 (2009).
[49] V. Damon, M. Bonarota, A. Louchet-Chauvet, T. Chanelière,
and J.-L. Le Gouët, Revival of silenced echo and quantum memory for light, New Journal of Physics 13, 093031 (2011).
[50] L. A Williamson and J. J Longdell, Cavity enhanced rephased
amplified spontaneous emission, New Journal of Physics 16,
073046 (2014).
[51] S. A. Moiseev, S. N. Andrianov, and F. F. Gubaidullin, Efficient multimode quantum memory based on photon echo in an
optimal qed cavity, Physical Review A 82, 022311 (2010).
[52] L. Marsh, Y. Yikai, C. Mattiroli, M. T. Sayat, Ð. M. Trí, H. M.
Rønnow, J. J. Longdell, and J.-R. Soh, Nuclear quadrupole interaction and zero first-order zeeman transitions of 167 Er3+ in
CaWO4 , Physical Review B 113, 10.1103/pg5m-hk2n (2026).

Page 7 out of 7

Supplementary Information: Millisecond optical coherence and strong collective coupling in an
integrated telecom rare-earth photonic platform
Kah Jen Wo ,1, ∗ Pavel A. Dmitriev ,1, 2, † Karthik Dasigi ,1 Fumiya Hanamura ,1 and Steven Touzard

1, 3, ‡

1 Centre for Quantum Technologies, Queenstown 117543, Singapore
2 National University of Singapore, Department of Materials Science and Engineering, Singapore
3 National University of Singapore, Department of Physics, Singapore

CONTENTS

SUPPLEMENTARY NOTE 1. Sample preparation: Photonic circuit design considerations

2

SUPPLEMENTARY NOTE 2. Sample preparation: Thin-film lithium niobate fabrication

3

SUPPLEMENTARY NOTE 3. Sample preparation: Direct bonding

6

SUPPLEMENTARY NOTE 4. Experimental setup in the dilution refrigerator

7

SUPPLEMENTARY NOTE 5. Measurement setups

8

SUPPLEMENTARY NOTE 6. Thermal expansion contrast analysis and bond strength characterisation

9

SUPPLEMENTARY NOTE 7. Collective cooperativity estimation

10

SUPPLEMENTARY NOTE 8. Magnetic field dependence of inhomogeneous broadening and 𝒈-factor

12

SUPPLEMENTARY NOTE 9. Spectral diffusion and coherence

13

SUPPLEMENTARY NOTE 10. Optical lifetime 𝑻1

14

SUPPLEMENTARY NOTE 11. Inversion echo fit parameters

15

SUPPLEMENTARY NOTE 12. Optical phase storage pulse parameters

15

SUPPLEMENTARY NOTE 13. Erbium coherence and coupling in literature

16

∗ kjwo@u.nus.edu

† pavel.a.dmitriev@nus.edu.sg
‡ steven.touzard@nus.edu.sg

SUPPLEMENTARY NOTE 1.

SAMPLE PREPARATION: PHOTONIC CIRCUIT DESIGN CONSIDERATIONS

We designed our thin film lithium niobate (TFLN) photonic circuits for high-𝑄, single-mode operation while bonded to
calcium tungstate (CaWO4 ). Since adding CaWO4 on top of the TFLN waveguide decreases the index contrast and reduces mode
confinement, radiative losses due to bending is a major limiting factor to the geometry of the resonator. Our optimised design for
the ring resonator has a width of 4µm and radius of 250µm, which, while supporting many modes before bonding, is effectively
single-mode after bonding to CaWO4 .
Outside of the ring resonator and the pulley coupler, all waveguide bends were defined as Euler bends [1] to minimise mode
mismatch and bending losses.
Fabrication limitations were taken into account when designing the ring to bus waveguide coupler and grating couplers for
the optical fibres. Lithium niobate waveguide fabrication is generally limited by sidewall roughness causing scattering losses, so
when designing resonators, care needs to be taken when choosing between a deeper etch for better mode confinement but higher
sidewall losses, or a shallower etch with lower sidewall losses and lower confinement (higher radiative bending losses) [2]. Our
best results were with a 250nm deep etch of a 500nm lithium niobate film. Because our fabrication process is limited to sidewall
angles of about 60°, we are limited to a minimum spacing between features of 250nm, which requires a further buffer owing to
redeposition affecting nearby structures.
For coupling the ring to the bus waveguide, we opted for a pulley coupler design, where coupling strength can be controlled
by both the gap between the ring and bus waveguides and by the wrapping angle of the pulley coupler. Our chosen gap for
best control over coupling within fabrication limits was 1.1µm. For our wrapping angle of the pulley coupler, we chose 30°.
For best control of the coupling, we decreased the width of the bus waveguide width relative to the ring resonator to match the
group velocity of the fundamental TE0 mode in the resonator and in the bus waveguide [3]. This also provides additional mode
selectivity by decreasing coupling to all other modes.
For the grating coupler, optimising for maximum transmission at the Er3+ :CaWO4 |↓⟩ 𝑍1 ↔ |↓⟩𝑌1 optical transition near
1532.63nm yielded a grating pitch of 964nm with a fill factor of 21%, meaning 202nm wide ridges with a gap of 764nm.
The shape of the grating was chosen to linearly expand over 600µm from the bus waveguide width to 15µm to preserve the modes
in the waveguide (i.e., minimise mode hybridisation) while expanding them to better match the modes of the optical fibres.
When designing the electrodes for electro-optic tuning of the resonator, we needed to take several factors into account [4–6].
First, the electrodes need to be aligned to the 𝑟 33 electro-optic component of lithium niobate, in-plane in our X-cut TFLN
samples. We limit the pulley coupler wrapping angle and align the electrodes so that we maximise the electro-optic tuning.
Next, we maximised the length of the resonator covered by electrodes, without affecting the coupling region and to minimise the
edge-to-edge gap between the electrodes to increase field strength, while not introducing additional losses to the optical mode and
leaving enough leeway for fabrication imperfections, with the final value we settled for being 15µm. Lastly, we chose an electrode
thickness of 150nm to ensure most of the electric field passes through the rib waveguide, while still being compatible with our
bonding process. Since our measurement process did not involve fast tuning of the resonator, capacitance of the electrodes was
not considered in the design process.

4 µm
150 nm

964 nm

600µm

250 nm

R

25

0µ
m

60º

15µm

15 µm

202 nm

4 µm

30º
1.1µm

4µm 4µm

1.26µm

Supplementary Figure 1. Dimensions of photonic circuit. Schematic top view of ring resonator, pulley coupler, electrodes and tapered
grating coupler. Insets, clockwise from top left: Cross-sectional view of resonator and electrodes, close up view of grating coupler, close up
view of ring resonator and pulley coupler, close up view of electrodes and ring resonator.

Page 2 out of 18

SUPPLEMENTARY NOTE 2.

SAMPLE PREPARATION: THIN-FILM LITHIUM NIOBATE FABRICATION

Samples were fabricated out of 500nm X-cut thin-film lithium niobate on insulator (LNOI) chips, purchased from NANOLN.
Patterning was done using hydrogen silsesquioxane (HSQ) resist with electron beam lithography (EBL) for the ring resonator and
waveguides and photolithography for the electrodes and bonding mesa. A total of four lithography steps were used to create the
final chip. To align the lithography masks, we first added marks at the corners of the chip using a bilayer AZ1512 / LOR-5A resist
stack, e-beam deposition of a 100nm Ti layer and subsequent lift-off in Remover PG. Titanium was chosen because it provides
enough contrast for EBL alignment, yet can be easily removed with hydrofluoric acid (HF), which is used during one of the final
cleaning steps in the fabrication process.
Most of the complexity of the nanofabrication process lay in the development of lithium niobate (LN) patterning and etching.
The final step of the fabrication process involves direct bonding of an erbium-doped Er3+ :CaWO4 to the finished LNOI photonic
chip (Supplementary Note 3). Therefore, it is important to retain as much unetched LN as possible to increase the bonding
area and bond strength. We grew a 600nm layer of SiO2 using PECVD to use as a hard mask during the subsequent etching
of LN. Next, we defined trenches in the SiO2 for the waveguides and electrodes. We wrote the trench pattern using AZ1512
photoresist with a AR 300-80 new adhesion promotion layer, exposed by 405nm light and developed by MIF319 developer and
then transferred the pattern to the SiO2 by a wet chemical etch using 1% w/w HF, taking care not to overetch to prevent damage
to the LN layer by the HF [7].
Next, we wrote the waveguides and rings with EBL using HSQ (FOx-16) resist. A 600nm-thick layer of HSQ was spin coated
onto the chips to create a sufficiently thick mask for reactive ion etching (RIE). Exposure was done using EBL with a total dose of
2000µC/cm2 for the rings and waveguides, and 1800µC/cm2 for the denser grating coupler features. The pattern was developed
using 25% w/w Tetramethylammonium Hydroxide (TMAH) to ensure high contrast and well-defined nanogaps especially in the
grating couplers and ring to bus waveguide coupling region [8, 9]. Special care was taken when writing the rings themselves in
EBL: we made sure that the rings fit into one exposure field to eliminate any stitching errors that would contribute to scattering
losses. Additionally, the whole exposure was split into 4 passes with slight offsets (physical stage movement compensated by
beam deflection within the write field) to smooth out any staircasing caused by the discrete nature of the EBL patterning process,
especially when approximating smooth curved lines. Moreover, proximity effect correction was crucial as it accounts for electron
backscattering due to the thick resist layer and the largely non-conductive LNOI chip.
Following the patterning, we etched the LN using induction-coupled plasma reactive ion etching (ICP RIE). LN is notoriously
difficult to etch using RIE because standard fluorine- or chlorine-based plasmas either leave behind insoluble residues or drastically
increase surface roughness, making pure argon plasma the best option for high-quality etching [10]. A pure argon plasma etch,
being a pure physical etch, leads to redeposition of the etched material [11]. The physical nature of the etch process also limits the
etch selectivity, in our case never going above 1.2:1 (LN : SiO2 ), hence the requirements for thick masks. Optimisation of the RIE
power and pressure can decrease the amount of redeposited material [12–14], but cannot completely solve the problem. Thus,
the remaining redeposited material needs to be removed with a post-etch cleaning process. SC-1 solution (Deionised water :
Ammonium Hydroxide : Hydrogen Peroxide) is currently one of the most commonly used cleaning agents to remove redeposited
LN from the chip [11, 12, 15, 16]. Varying concentrations, temperatures and durations have been proposed for cleaning, and in
our case a 2:1:1 v/v concentration at room temperature for 1 hour yielded the best results in removing redeposited material. Care
must be taken not to use overly aggressive SC-1 conditions, since it will also attack the unetched LN itself – and has been used
as a stand-alone wet etchant of LN [17]. Additional steps in the cleaning process involved using HF to strip the oxide hardmasks
and piranha solution to clear any organic contaminants. Another consideration for RIE etch parameters is the effect of RIE power
on the resulting sidewall angles, where higher RIE power generally produces more vertical sidewalls [14], but in our case would
lead to the deterioration of the hard mask and worse overall etch outcomes. Our optimal conditions (150W RF and 1500W ICP,
40sccm Ar at 2mTorr) resulted in 60° sidewalls with a 50nm/min etch rate and we etched our waveguides to a depth of 250nm
(controlled by ellipsometric measurements before and after the etch process) in a single continuous etch.
The NANOLN fabrication process to create LNOI wafers itself introduces defects into the LN layer and additional defects are
introduced during the argon etch and post-etch wet chemical processing. These defects can be repaired by an annealing process.
After transferring the ring patterns to the LN and cleaning any redeposition residues, we anneal our chips for 1 hour at 520°C in
a pure oxygen atmosphere – repairing any deep defects from the helium implantation during the NANOLN fabrication process and
new surface defects introduced by our own processing, while the oxygen atmosphere prevents lithium depletion in the surface
layer [16, 18–24].
Finally, we added electrodes to the rings for electro-optic tuneability again using a bilayer AZ1512 / LOR-5A resist stack,
e-beam deposition of a Ti/Al (10nm / 150nm) electrode layer and subsequent lift-off in Remover PG. We chose aluminium over
gold for the electrode material to prevent formation of intermetallic compounds with the aluminium wires used for wirebonding
during the final packaging step, which might affect the structural stability of the bonds during thermal cycling [25].
The detailed fabrication process flows for the samples are presented in Supplementary Table 1. Corresponding schematics are
shown in Supplementary Figure 2.

Page 3 out of 18

Fabrication flow. 1. Alignment marks

Fabrication flow. 3. Ring resonator

1. Wash (Acetone / Isopropyl Alcohol (IPA) / Deionised water (DI)).

1. Wash (Acetone / IPA / DI / MIF319 / DI).
2. Bake for 5 minutes at 140°C.

2. Bake for 5 minutes at 140°C.
3. Spin coat LOR-5A, 60s, 4000 RPM.
4. Bake for 2 minutes at 180°C.

3. Spin coat FOx-16 HSQ resist, 60s, 2500 RPM.
4. Bake for 5 min at 80°C.
5. Expose, EBL at 2 nA with a total dose of

5. Spin coat AZ1512, 60s, 4000 RPM.
6. Bake for 60s at 100°C.
7. Expose, 405nm with a dose of 50µC/cm2 .

2000µC/cm2 .
6. Develop 25% w/w TMAH for 17 s.
7. Develop MIF319 for 60s.

8. Develop in MIF319 (2.5% TMAH) for 90s at room
temperature (RT).
9. DI stop.

8. DI stop.
9. Etch using ICP RIE, Argon 40sccm, 2mTorr, 1500W
ICP / 150W RF.

10. Deposit 100nm Ti using e-Beam evaporator.
11. Lift-off using Remover PG at RT for 24 h.
12. DI stop.

10. Strip Ti, HSQ and SiO2 in 1% HF for 10 min.
11. Clean using 3:1 v/v Piranha solution (96% Sulphuric
Acid : 30% Hydrogen Peroxide) for 30 min, no ex-

13. Wash (Acetone / IPA / DI).

ternal heating.
12. Clean using 2:1:1 v/v/v SC-1 solution (DI : 30%
Ammonium Hydroxide : 30% Hydrogen Peroxide)
for 60 min, no external heating.
13. DI stop.
14. Anneal at 520°C in a pure Oxygen atmosphere for
1 h.

Fabrication flow. 2. Bonding mesa

Fabrication flow. 4. Electrodes

1. Wash (Acetone / IPA / DI).
2. Bake for 5 minutes at 140°C.

1. Wash (Acetone / Isopropyl Alcohol (IPA) / Deionised water (DI)).

3. Deposit 600nm of SiO2 using PECVD, 300°C, N2 O
460sccm, SiH4 3sccm, 20W RF.
4. Spin coat AR 300-80 new, 60s, 6000 RPM.

2. Bake for 5 minutes at 140°C.
3. Spin coat LOR-5A, 60s, 4000 RPM.
4. Bake for 2 minutes at 180°C.

5. Bake for 2 minutes at 180°C.
6. Spin coat AZ1512, 60s, 4000 RPM.
7. Bake 90s at 115°C.

5. Spin coat AZ1512, 60s, 4000 RPM.
6. Bake for 60s at 100°C.
7. Expose, 405nm with a dose of 50µC/cm2 .

8. Expose, 405nm with a dose of 75µC/cm2 .
9. Develop in MIF319 for 30s at RT.
10. Etch SiO2 in 1% w/w Hydrofluoric Acid (HF) for

8. Develop in MIF319 (2.5% TMAH) for 90s at room
temperature (RT).
9. DI stop.

10 min.
11. DI stop.
12. Strip resist in Remover PG at RT for 24 h.

10. Deposit 10nm Ti and 150nm Al using e-Beam evaporator.
11. Lift-off using Remover PG at RT for 24 h.
12. DI stop.
13. Wash (Acetone / IPA / DI).
14. Bake for 5 minutes at 180°C.

Supplementary Table 1. Thin-film lithium niobate nanofabrication flows. Summary of the thin-film lithium niobate fabrication workflow,
divided into four modules: alignment mark definition, bonding mesa preparation, ring resonator patterning and electrode deposition.

Page 4 out of 18

a

b

Marks

c

Trench

Waveguides

Spin coat LOR-5A

PECVD SiO2

Spin coat HSQ

Spin coat AZ1512

Spin coat
AZ1512 /w AR 300-80 new

Expose and Develop

Expose and Develop

d

Electrodes

Spin coat LOR-5A

Spin coat AZ1512

Ar ICP-RIE

Expose and Develop

Clean and Anneal

Deposit Ti/Al

Expose and Develop

Deposit Titanium

Wet Etch

Lift-off
Lift-off

Resist Strip

LiNbO3

Si

AZ1512

HSQ

SiO2

LOR-5A

Ti

Al

AR 300-80 new

Supplementary Figure 2. Thin-film lithium niobate nanofabrication flow schematic. Schematic cross-sectional illustration of the four
lithography steps used to fabricate the TFLN photonic chip. a, Alignment marks: a bilayer LOR-5A/AZ1512 resist stack is patterned via
405nm photolithography, followed by e-beam evaporation of 100nm Ti and lift-off. b, Bonding mesa and trench definition: a 600nm PECVD
SiO2 hard mask layer is deposited and then defined by photolithography and wet etching in 1% HF to define trenches for the waveguides
and electrodes. c, Waveguide and ring resonator patterning: HSQ (FOx-16) resist is exposed by electron beam lithography, developed in
25% TMAH, and the pattern is transferred into the LN layer by Ar ICP-RIE dry etching. Post-etch cleaning (SC-1 and piranha) removes
redeposited material, followed by annealing at 520°C in O2 to repair etch-induced and implantation defects. d, Electrode fabrication: a bilayer
LOR-5A/AZ1512 resist stack is patterned via 405nm photolithography, followed by e-beam evaporation of Ti/Al (10nm/150nm) and lift-off to
form the electrodes for electro-optic tuning.

Page 5 out of 18

SUPPLEMENTARY NOTE 3.

SAMPLE PREPARATION: DIRECT BONDING

Successful direct bonding requires that the root-mean-square (RMS) surface roughness of both bonding interfaces remains
below 1nm. To meet this requirement, we used an 8.5×8.5×0.5mm3 50ppm Er3+ :CaWO4 chip (SurfaceNet GmbH) that
was epi-polished on both sides. While only a single polished surface is required for bonding, this dual-sided polish provides
optical transparency through the chip, a feature critical for verifying bond integrity and microring resonator coverage via optical
microscopy. The surface of a representative, as-received sample was characterised with a Bruker Dimension Icon atomic force
microscope (AFM), yielding an RMS surface roughness below 1nm (see Supplementary Figure 3a). Similarly, a representative
patterned LNOI chip was characterised and also found to have an RMS surface roughness below 1nm (see Supplementary
Figure 3b). As the characterisation was performed in a standard laboratory setting rather than a cleanroom, this value represents
a conservative upper bound on the intrinsic material roughness, inclusive of any potential surface particulates.
To allow the crystal host to fit onto the patterned photonic chip (see Supplementary Figure 3a), the crystal host was mechanically
diced to ∼8.5×6.5mm2 with an Accretech SS20 dicer. The diced Er3+ :CaWO4 together with the patterned photonic chip were
then cleaned with ultrasonication in acetone for approximately 5 minutes, followed by another 5 minutes of ultrasonication in
isopropyl alcohol in a class-10 cleanroom. Contact with the bonding interfaces of the Er3+ :CaWO4 chip and the photonic chip
was minimised by using a polytetrafluoroethylene (PTFE) wafer rack that allows the chips to be slotted in vertically during the
ultrasonication bath. After the ultrasonication cleaning, the chips were rinsed with deionised water and blow dried with a nitrogen
gun.
We prepared two samples using different bonding agents: main sample and sample b. The main sample, whose results are
presented in the main text, was bonded using deionised (DI) water, while sample b was bonded using 30% (w/w) ammonium
hydroxide (NH4 OH) in water. This method is based on Ref. [26]. Apart from the choice of bonding agent, the bonding procedure
was identical for both samples and proceeded as follows.
The photonic chip was placed with the bonding interface facing upwards on a flat surface in a class-100 cleanroom. A
microdroplet of the bonding agent (DI water or NH4 OH, as appropriate) was placed near the ring resonators by eye using a
PTFE tweezer that had been dipped into the corresponding liquid. The tweezers themselves were cleaned with isopropyl alcohol
ultrasonication prior to this step, and during the placement of the microdroplet, the tweezers never physically touched the photonic
chip. After the droplet was placed, the Er3+ :CaWO4 was flipped and placed gently onto the droplet. Without any externally
applied force, the liquid was allowed to evaporate, and direct bonding between the Er3+ :CaWO4 and the photonic chip formed.
The chips were handled exclusively using polyetheretherketone (PEEK) tweezers, which we found to minimise chipping of the

5
05
4 3
y (µm 2 1
)
0

c

LNOI photonic integrated chip
σz = 0.5005 nm

4
3
)
2
1 x (µm
0

5

15
10
5
05
4 3
y (µm 2 1
)
0

Photonic integrated chip

e
d

Grating coupler

Norm. power

z (nm)

10

b

Er3+:CaWO4
σz = 0.3873 nm
z (nm)

a

20 μm

4
3
)
2
1 x (µm
0

5

1

0

Before bonding
After bonding

Phase

π
0

-π
−0.5
0.0
0.5
Frequency offset (GHz)

2 mm

Supplementary Figure 3. Bonding surface characterisation and bonded photonic integrated chip. a, b, Atomic force microscope scans
of a Er3+ :CaWO4 crystal surface (root-mean-square roughness 𝜎z = 0.3873nm) and the bonding interface of a patterned thin-film lithium
niobate-on-insulator photonic integrated chip (𝜎z = 0.5005nm) respectively. Both values satisfy the sub-nanometre roughness requirement for
direct bonding. c, Top-down optical microscope image of the thin-film lithium niobate photonic integrated chip bonded with Er3+ :CaWO4 . The
nanophotonic structures corresponding to the ring resonator characterised in the main text (main sample) are outlined in dashed orange lines,
and the grating couplers in dashed blue lines. d, Zoomed-in optical microscope image of a grating coupler on the same chip. e, Normalised
power and phase response of a ring resonator device measured before and after bonding with our heterodyne setup (see Supplementary Note
5), showing that the ring quality factor required for high collective cooperativity 𝐶 is preserved (see Supplementary Note 7).

Page 6 out of 18

Er3+ :CaWO4 crystal compared to ceramic or metal tweezers.
The bonded stack was stored at room temperature in a nitrogen desiccator for 24 hours to allow for full evaporation of the bonding
agent and for the bonds to strengthen. The bonded stack was then annealed on a hotplate at 100°C under atmospheric conditions.
sample b was annealed for approximately 12 hours and loaded first into the dilution refrigerator, serving as the pathfinder device
on which the measurement protocols and thermalisation procedures were developed and optimised. main sample remained on the
hotplate during this period, accumulating an anneal time of approximately 1 month; shear-test measurements on a control sample
and thermal cycling of sample b confirmed that the shorter anneal produces bond strengths sufficient for repeated cooldowns to
millikelvin temperatures (see Supplementary Note 6). The experience gained with sample b informed the thermalisation and
mounting procedures used for main sample, which is the primary device reported in the main text. After passively cooling back
down to room temperature, main sample was ready to be loaded into our Bluefors LD400 dilution refrigerator (see Supplementary
Note 4). For a quantitative study of the bonding strength using shear test, see Supplementary Note 6. The optical microscope
image in Supplementary Figure 3c corresponds to main sample.
We characterised the ring resonator using our heterodyne setup (see Supplementary Note 5), and observed that the intrinsic
quality factor 𝑄 int decreased after bonding. In particular, we measured a ring resonator (on sample b) at wavelength ∼1532.6nm
near the |↓⟩ 𝑍1 ↔ |↓⟩𝑌1 optical transition, and obtained 𝑄 int ≈ 8million before bonding and 𝑄 int ≈ 2million after bonding at room
temperature and atmospheric conditions (see Supplementary Figure 3e). We attribute the decrease of the intrinsic quality factor
to increased participation of the optical mode with defects near the bonding interface or in the crystal, as well as mechanical stress
arising from thermal-expansion mismatch, leading to additional losses. In addition, over the course of cooling both main sample
and sample b down to ∼4K in our Bluefors LD400 dilution refrigerator, we observed a non-monotonic behaviour in the intrinsic
quality factor of the bare ring resonator, which we attribute to slippage of the Er3+ :CaWO4 that is on top of the ring resonator
(see Supplementary Note 6). Despite the decrease in intrinsic quality factor, we show that in Supplementary Note 7 we can still
achieve collective cooperativity 𝐶 > 1. At temperatures lower than ∼4K, the intrinsic quality factor stabilises at ∼1 million for
main sample and ∼2 million for sample b.

SUPPLEMENTARY NOTE 4.

EXPERIMENTAL SETUP IN THE DILUTION REFRIGERATOR

To couple telecom C-band light into our Bluefors LD400 dilution refrigerator, we employed SMF-28 single mode fibres
(Corning). These were connected via mating sleeves at the mixing chamber to a fibre array unit for coupling to the on-chip
grating couplers (see Supplementary Figure 4). To minimise the passive thermal load on the mixing chamber and enable operation
a
Fiber optic mating sleeves

Electrical connections for
nanopositioners and electro-optic tuning
Fiber array

Mixing chamber flange

Wire bond

b

Fibre array holder

Nanopositioner array

Printed circuit board

Wire bonding pad

Photonic integrated chip

Er3+:CaWO4

Supplementary Figure 4. Experimental setup in a dilution refrigerator. a, Photograph of the photonic integrated chip at the mixing
chamber flange of a Bluefors LD400 dilution refrigerator, showing the fibre array holder, nanopositioner array, fibre optic mating sleeves, and
electrical connections. b, Close-up photograph of the photonic integrated chip mounted on a printed circuit board, showing the fibre array for
optical coupling to photonic integrated chip, the bonded Er3+ :CaWO4 crystal, and aluminium wire bonds for electro-optic tuning.

Page 7 out of 18

at base temperature, the pigtails of the fibre array were shortened to the required length by splicing with a Fujikura 45S splicer.
The fibre array was then bonded to a copper holder using the low-outgassing UV-cured Norland Optical Adhesive NOA 88.
To enable in situ optimal fibre-to-chip alignment at cryogenic temperatures, the chip was mounted on an Attocube piezo-based
nanopositioner array ANPx101 (2×), and ANPz102 (1×). The integrity of the fibre array assembly has been validated through
five full thermal cycles from room temperature to the cryostat’s base temperature, without degradation in alignment stability or
coupling efficiency (∼15.3% efficiency per facet).
To fix the integrated photonic chip in place so that it does not slip during position adjustments, we applied Apiezon N grease
to the copper sample holder that is on the nanopositioner array before affixing the integrated photonic chip onto it. We chose this
grease due to its ability to maintain good thermal conductivity at cryogenic environments. To control the electro-optic tuning of
the ring resonator, we used a Westbond 7674E to wire bond the chip to a Rogers RO4350B printed circuit board (PCB) with
aluminium wires. This PCB was chosen for its high thermal conductivity. The footprint of the setup was designed such that it fits
within the bore of an American Magnetics Inc. 3-dimensional vector magnet. All copper used in our experimental setup is
oxygen-free (C101) to maximise thermal conductivity and minimise outgassing.

SUPPLEMENTARY NOTE 5.

MEASUREMENT SETUPS

We perform optical vector analysis using a free-running Mach-Zehnder interferometer setup based on Ref. [27] which enables
phase-sensitive detection, as shown in Supplementary Figure 5a. To acquire the complex transmission over a wavelength range,
a

Laser source

b

Heterodyne detection setup

Fluorescence / transmission detection setup

Local oscillator arm

Laser source
AOM

Signal arm

Pulse
sequencer

VOA

Electrode
control

Electrode
control

Pulse
sequencer

AOM

VOA

EOM

Oscilloscope

Oscilloscope

Photodiode

50:50 beamsplitter

EOM

Electro-optic modulator

Balanced photodetection

Optical signal

DC source

Device under test

AOM

Acousto-optic modulator

Cryogenic environment

Electrical signal

AC source

Polarization controller

VOA

Variable optical attenuator

Only in time-bin experiment

SNSPD

Supplementary Figure 5. Optical measurement setups. a, Heterodyne detection setup based on a free-running Mach-Zehnder interferometer
for optical vector analysis. The laser output is split by a 50:50 beamsplitter into a local oscillator (LO) arm and a signal arm. The signal arm
is frequency-shifted by an acousto-optic modulator (AOM) and attenuated by a variable optical attenuator (VOA) before passing through the
device under test (DUT) inside the cryogenic environment. The transmitted signal is recombined with the LO arm at a balanced photodetector,
and the resulting electronic signal is recorded on an oscilloscope. An electro-optic modulator (EOM) and polarisation controllers are included
in the signal path for the coherent storage and retrieval experiment. b, Fluorescence and transmission detection setup. The laser output passes
through an AOM and VOA before being routed to the DUT in the cryogenic environment. Transmitted or fluorescence signals are detected by
superconducting nanowire single-photon detectors (SNSPDs) and read out on an oscilloscope. A pulse sequencer controls the timing of optical
pulse gating and data acquisition in both configurations. Electrode control provides electrical biasing of the DUT via a DC source.

which is required for collective cooperativity extraction, we use Santec TSL-570 as our laser source, which enables fast
wavelength sweep. A wavelength sweep rate of 100nm/s is chosen such that phase fluctuations due to vibrations and thermal
fluctuations in the optical fibres are negligible over a wavelength range of interest. This signal is then split 50:50 into the local
oscillator (LO) arm and signal arm. The signal in signal arm is detuned by an acousto-optic modulator (AOM) at +200MHz,
then passes through the device under test (DUT) before being detected at the balanced photodetector along with the LO arm. The
AOM used is SGTF200-1550-1T-1D. To control the input power, we use a Santec OVA-100 variable optical attenuator (VOA)
Page 8 out of 18

to attenuate the signal going into the DUT. The balanced photodetector (Wieserlabs WL-BPD1GA) converts optical signal into
electronic signal, which is then acquired through a TeledyneLecroy 610Z oscilloscope. This electronic signal can then be
demodulated either in software or in hardware, to extract the amplitude and phase components of the complex transmission.
Polarisation controllers were added in between components to match polarisation and maximise overall coupling efficiency. For
Er3+ coherence, spectral diffusion, and inversion echo measurements, instead of a scanning laser, the laser source is replaced by an
ultra-low noise, narrow linewidth, single-frequency Precilaser FL-SF-1533-S laser. Its linewidth as reported by Precilaser
is <2kHz at 100µs integration. The pulse sequencer (ArTiQ 2238 MCX-TTL) gates the AOM to form optical pulses required for
the three-pulse photon echo (3PPE) measurement. To shift the phase of individual AOM-gated pulses in our coherent interference
experiment, an exail MPX-LN-0.1 electro-optic modulator (EOM) is used.
To measure the fluorescence of the Er3+ ion ensemble, we excite the ensemble via an AOM-gated optical pulse, and measure
the fluorescence using a Single Quantum SSPD-1550-70-80 superconducting nanowire single photon detector (SNSPD)
mounted on the 4K flange of our Bluefors LD400 dilution refrigerator. The SNSPD signals were counted and averaged on a
TeledyneLecroy 610Z oscilloscope. The measurement schematic is shown in Supplementary Figure 5b. The extracted optical
𝑇1 is later validated with inversion-recovery echo measurement.
SUPPLEMENTARY NOTE 6.

THERMAL EXPANSION CONTRAST ANALYSIS AND BOND STRENGTH
CHARACTERISATION

To determine the appropriate CaWO4 crystal orientation for integration with LNOI that is robust to temperature changes due
to post-bond annealing, we employ a numerical analysis using the multilayer strain framework from Ref. [28], which captures
three distinct contributions to the thermally induced strain: (i) the intrinsic thermal contraction of each individual material, (ii)
the in-plane constraint imposed by coefficient of thermal expansion (CTE)-mismatched layers bonded in a common stack, and
(iii) the additional deformation arising from curvature of the composite structure due to asymmetric thermal stresses. Using this
ℓ𝑖
𝑖
model, in which each layer has a thickness ℓ and width 𝑤, the strain in the 𝑖-th layer is given by 𝜀 𝑖 = 𝛼𝑖 Δ𝑇 + E𝐹𝑖 A
+ 2R
, where
𝑖
for each layer, 𝛼𝑖 is the CTE, 𝐹𝑖 the thermally-induced axial force, E𝑖 the Young’s modulus, and A𝑖 = ℓ𝑖 𝑤 𝑖 the cross-sectional
area. Δ𝑇 is the temperature difference and R the radius of common curvature. We note that this model does not take into account
any slippage of layers, and that elastic material response is obeyed throughout, with stress and strain related through the Hooke’s
law 𝜎 = E𝜀. By solving for the following system of linear equations for 4 layers: CaWO4 –LiNbO3 –SiO2 –Si
Í4
(S6.1)
𝑖=1 𝐹𝑖 = 0,
Í4
Í4
𝑖=1 E𝑖 𝐼𝑖
,
(S6.2)
𝑖=1 ℎ𝑖 𝐹𝑖 =
R
ℓ𝑗
𝐹 𝑗+1
ℓ 𝑗+1
𝐹𝑗
+
= 𝛼 𝑗+1 Δ𝑇 +
−
,
(S6.3)
𝛼 𝑗 Δ𝑇 +
E 𝑗 A 𝑗 2R
E 𝑗+1 A 𝑗+1
2R
we determine the total strain 𝜀 𝑖 in each layer. When no external force is assumed, the sum of thermally-induced axial forces is
given by Eq. (S6.1). The moments due to those forces follows Eq. (S6.2), where 𝐼𝑖 = ℓ𝑖3 𝑤 𝑖 /12 is the area moment of inertia, and
ℎ𝑖 is the distance from the bottom of the stack to the centre of the 𝑖-th layer. The continuity of strain at each interface 𝑗 = 1, ..., 3
yields Eq. (S6.3). The thicknesses in our bonded stack are ℓCaWO4 = 500µm, ℓLN = 500nm, ℓSiO2 = 4.7µm, and ℓSi = 525µm.
The Young’s moduli and CTEs are given in Supplementary Table 2. For simplicity, the widths in the numerical analysis were set
to 8mm.
The stress in the CaWO4 layer is shown in Supplementary Figure 6a. We observed no significant difference of stress in CaWO4
along the extraordinary versus ordinary axes of LiNbO3 , which indicates that the stress contribution is dominated by the much
thicker SiO2 +Si substrate. Our analysis shows that by taking the 𝑐-cut CaWO4 (i.e., 𝑎- and 𝑏-axes are in-plane), we minimise
the stress that is thermally-induced in it.
Material

Si

SiO2

LN,e

LN,o

CaWO4 ,𝑐

CaWO4 ,𝑎

E (GPa)

130 [29]

75 [30]

199 [28, 31]

173 [28, 31]

108 [32]

137a [32]

𝛼 (10 −6 K −1 )

2.6 [33]

1 [30]

3.4 [34]

13.4 [34]

13.4b [35]

7.9b [35]

a The maximum value in the 𝑎𝑏-plane was taken to estimate the upper bound of the thermally-induced multilayer stress.
b Calculated with lattice parameter at 100-295K from Ref. [35].

Supplementary Table 2. Mechanical and thermal parameters used in the numerical analysis of thermally induced stress. Here, E denotes
Young’s modulus, and 𝛼 denotes the coefficient of thermal expansion (CTE). (e,o) denotes the parameter values parallel to the extraordinaryand ordinary-axes of lithium niobate. (𝑎,𝑐) denotes the parameter values parallel to the 𝑎- and 𝑐-axes of calcium tungstate.

Page 9 out of 18

Stress in CaWO4 σ (MPa)

a

500
400
300
200

Shear tip

100
0
300

d

5

40

4

30

3
2

c

After shear test

d
Distance (mm)

Load (kgf)

ΔT (K)

200

6

50

10

SAMPLE B after 4 thermal cycles

Sample backstop
100

60

20

e

Bonded stack

0

b

Before shear test

c

CaWO4-a | LNOI-o
CaWO4-a | LNOI-e
CaWO4-c | LNOI-o
CaWO4-c | LNOI-e

1

0

0
0

20

40

60 80 100 120 140
Time (s)

Supplementary Figure 6. Theoretical thermal stress and experimental shear testing of bonded CaWO4 on LNOI. a, Calculated thermal
stress, 𝜎, in the CaWO4 layer as a function of temperature change Δ𝑇 for different crystal cut combinations. Note that the theoretical curves
for X-cut and Z-cut LNOI overlap almost perfectly for both cuts of the CaWO4 orientations. b, Experimental load and displacement curves
as a function of time during a destructive shear test of an undoped CaWO4 chip bonded to an unpatterned LNOI substrate. The green and
pink arrows (labelled c and d) indicate the time points corresponding to the photographs in the subsequent panels. c, d, Photographs of the
experimental setup c, before and d, after the shear test. To provide a visual scale, the undoped CaWO4 measures 10×10mm2 . The sample
backstop ensures the LNOI substrate remains stationary under high lateral loads. e, Photograph of sample b after 4 thermal cycles, showing
that the Er3+ :CaWO4 is still bonded to the underlying photonic integrated chip.

To experimentally gauge the strength of our bonded stack comprising an undoped 10×10mm2 𝑐-cut 1-side epi-polished
CaWO4 crystal bonded to an unpatterned LNOI chip, we performed a destructive shear test on it at room temperature using a
Nordson DAGE 4000 bond tester, as shown in Supplementary Figure 6b-d. The bond tester uses a shear tip positioned above
the LNOI chip but below the CaWO4 chip. The shear tip moves at a set rate of 25µm/s to push only against the CaWO4 , while
the whole bonded stack is held in place by the sample backstop (Supplementary Figure 6c). Our test reveals that the maximum
load sustained is 54.54kgf, which converts to a maximum shear stress of 7.9MPa.
Note that sample b’s characterised ring resonator intrinsic quality factor remained at approximately 2 million during its initial
thermal cycles, enabling the high-cooperativity measurements presented in Supplementary Note 7.

SUPPLEMENTARY NOTE 7.

COLLECTIVE COOPERATIVITY ESTIMATION

To estimate the collective cooperativity of our Er3+ :CaWO4 -on-TFLN platform, we first evaluate the participation 𝑃 of electric
field energy of the waveguide’s optical TE0 mode in the Er3+ :CaWO4 crystal, defined as [36]
↔

∫
𝑃=

CaWO4

∫

E∗ (®
𝑟 ) · 𝜖 (®
𝑟 ) · E(®
𝑟 ) d𝑉
↔

E∗ (®
𝑟 ) · 𝜖 (®
𝑟 ) · E(®
𝑟 ) d𝑉

,

(S7.4)

↔

where 𝜖 is the permittivity tensor. Supplementary Figure 7a shows the simulated 𝑃 as a function of the bend radius 𝑟 bend
for 50% etched 500nm X-cut LNOI waveguide with top width 𝑤 top = 4µm and 60° sidewall angle, corresponding to the ring
resonator geometry of the device characterised in the main text, i.e., main sample. Directly above the waveguide in the
simulation geometry is a 𝑐-cut CaWO4 . A 4µm top width ensures fundamental-mode TE0 operation by suppressing higherorder modes in the Er3+ :CaWO4 -on-TFLN ring resonator. Mode propagation along the extraordinary and ordinary axes of
the LiNbO3 were simulated separately, denoted by 𝑘 ∥e and 𝑘 ∥o, respectively. For the simulation, the refractive index values
𝑛CaWO4 ,𝑎 = 1.8842, 𝑛CaWO4 ,𝑐 = 1.8984, 𝑛LiNbO3 ,o = 2.2117, 𝑛LiNbO3 ,e = 2.1381, and 𝑛SiO2 = 1.4442 were used at simulation
wavelength 𝜆sim = 1532.63nm.
Page 10 out of 18

b
wtop = 4 µm

40
30

k || o

20

k || e

10
0
20

100

180
260
rbend (µm)

340

420

Mode volume Vmode (µm2)

Particpation factor P (%)

a 50

1.2
1.0

k || o

0.8

rbend = 250 µm

1.0

0.6

k || e

0.6

0.4

wtop = 4 µm

0.2

20

100

180
260
rbend (µm)

340

420

Supplementary Figure 7.
Simulated Er3+ :CaWO4 participation and mode volume. a, The simulated participation factor 𝑃 of the
fundamental TE0 mode as a function of waveguide bend radius 𝑟 bend for top width 𝑤 top = 4µm. Mode propagation along the extraordinary
and ordinary axes of the lithium niobate are simulated, denoted by 𝑘 ∥e and 𝑘 ∥o, respectively. b, The corresponding simulated mode volume
𝑉mode . The dashed lines indicate corresponding values for straight waveguide. The insets show the normalised energy density mode profiles
for 𝑟 bend = 250µm.

To provide
physical intuition for the spatial scale of the light-matter coupling, we additionally plot the mode volume
∫
↔

𝑉mode =

E∗ ( 𝑟® ) · 𝜖 ( 𝑟® ) ·E( 𝑟® ) d𝑉
↔

max(E∗ ( 𝑟® ) · 𝜖 ( 𝑟® ) ·E( 𝑟® ) )

in Supplementary Figure 7b. This shows that the mode volume remains under 1µm2 , confirm-

ing that the guided mode is tightly confined compared to free space approaches. This tight confinement, combined with the
strong participation in the CaWO4 , ensures efficient coupling between the ring resonator photons and the near-surface ensemble
of Er3+ ions, which directly enters the collective cooperativity through the collective coupling strength defined as [36]
√︂
𝑃𝜌𝜔
𝜇
𝐺=
,
(S7.5)
𝑛mode 2𝜖0 ℏ
where 𝜇 is the transition dipole moment, 𝜌 the Er3+ ion density, 𝜖0 the vacuum permittivity, ℏ the reduced Planck constant, and
𝑛mode the effective refractive index of the optical resonator mode.
To estimate the transition dipole moment 𝜇 for the 𝑍1 ↔𝑌1 transition, we first calculate the oscillator strength given by [37, 38]
∫
𝑚𝑒 𝑐 1 𝑛
𝑓 = 4𝜋𝜖0 2
𝛼(𝜈) d𝜈,
(S7.6)
𝜋𝑒 𝜌 𝜒𝐿2
where 𝛼(𝜈) is the absorption coefficient as a function of frequency 𝜈 = 𝜔/2𝜋, 𝑒 the electron charge, 𝑚 𝑒 the electron mass, and
𝑛 is the refractive index of the material in which the Er3+ ion ensemble resides. In our case, 𝑛 = 𝑛CaWO4 ,𝑎 = 1.8842. The real
cavity model has been found suitable for substitutional ions [39], and therefore we take 𝜒𝐿 = 3𝑛2 /(2𝑛2 + 1). Given the 50ppm
dopant concentration of the Er3+ :CaWO4 , its ion density is calculated to be 𝜌 = 6.4 × 1023 m−3 .
The absorption coefficient here is given by 𝛼(𝜈) = −2.3 log (| 𝐴(𝜈)| 2 /max | 𝐴(𝜈)| 2 )/(𝑃𝐿) [40, §8.2.2.4], where 𝐿 = 7850µm
is the optical length of the bus waveguide which is estimated based on the bonding area in Supplementary Figure 3c,
and 𝐴(𝜈) is the complex transmission. The participation factors of the bus waveguide are simulated to 𝑃 𝑘 ∥e = 14.8%
and 𝑃 𝑘 ∥o = 23.5% for 𝑟 bend → ∞, which is a good approximation since the bend radii of the bus waveguide are large
enough. By taking the weighted average of these participation factors based on the bus waveguide geometry, we approximate
𝑃 = (𝐿 𝑘 ∥o /𝐿)𝑃 𝑘 ∥o + (1 − 𝐿 𝑘 ∥o /𝐿)𝑃 𝑘 ∥e = 15.6%, with the length parallel to TFLN’s ordinary axis taken to be 𝐿 𝑘 ∥o = 680µm.
Taking 𝛼(𝜈) at zero field, as shown in Supplementary
Figure 8a, we obtained 𝑓 = 2.2 × 10−7 . The transition dipole moment is
√︁
related to the oscillator strength through 𝜇 = ℏ𝑒 2 𝑓 /(2𝑚 𝑒 𝜔) [37, 38, 41]. Substituting the obtained oscillator strength into the
expression we get 𝜇 = 1.6 × 10−32 C·m.
Having established the transition dipole moment value, we now proceed to estimating the collective cooperativity of Er3+ ions
coupled to the ring resonator. Since the geometry of the resonator is a ring, the effective participation factor can be approximated
as the average between 𝑘 ∥e and 𝑘 ∥o values such that 𝑃 = (𝑃 𝑘 ∥e + 𝑃 𝑘 ∥o )/2. The resonator characterised in the main text has a bend
radius 𝑟 bend = 250µm, which corresponds to 𝑃 = 17.2%. The corresponding effective indices of the TE0 mode found from the
simulation are 𝑛mode,𝑘 ∥e = 2.0311 and 𝑛mode,𝑘 ∥o = 1.9722. Taking its average, we obtain 𝑛mode = 2.0017. Finally, by substituting
above values into Eq. (S7.5), we obtain 𝐺 estimated /2𝜋 = 314MHz, which leads to collective cooperativity 𝐶estimated = 6.0 ± 0.5
for 𝜅 tot and Γinh values at |B| = 0T in Supplementary Table 3. Note that the eigenmode simulations in this section were done with
a commercial software: Ansys Lumerical.
To determine the experimental collective cooperativity, we approximate inhomogeneous optical transition of the Er3+ ensemble
by a Lorentzian spectral distribution. We compared this choice against a Gaussian profile and found that the Lorentzian profile
consistently provided better agreement with the measured transmission data. We also found no significant difference in the
Page 11 out of 18

collective cooperativities using the Gaussian inhomogeneous broadening model. The choice of Lorentzian profile is also
consistent with previous REI spectroscopy [42], REI resonator-ensemble modelling [36], and is expected in rare-earth crystals
with dilute defects [43, 44]. Using the Lorentzian model, the complex transmission of the ring resonator at angular frequency
𝜔cav in the presence of Er3+ ions at frequency 𝜔ions is given by [45]
𝐴 =1−

𝑖𝜅 ext

(S7.7)

,
2

𝐺
(𝜔 − 𝜔cav ) + 𝑖𝜅 tot /2 − 𝜔− 𝜔ions
+𝑖Γinh /2

where 𝜔 is the probe angular frequency, 𝜅 tot = 𝜅 int + 𝜅ext the total linewidth of the resonator and Γinh the inhomogeneous
broadening linewidth of the Er3+ ions. By fitting the complex transmission to Eq. (S7.7), we extract collective cooperativities
through 𝜅 tot , Γinh and 𝐺 for various magnetic fields (Supplementary Table 3). To reliably extract the experimental collective
cooperativity, we separately determine the intrinsic 𝜅int and extrinsic linewidths 𝜅ext of the ring resonator with detuning ≫Γinh ,𝐺.
This allows us to fix 𝜅tot fit to Eq. (S7.7) with only two free parameters: Γinh and 𝐺. Because the laser is swept repeatedly
with an interval between sweeps shorter than the shelving-state lifetimes, the ensemble is probed in an optically pumped steady
state whose depletion depends on magnetic field through both the shelving branching ratios and their lifetimes; the extracted 𝐺
is therefore a lower bound on its intrinsic value. For more information about the inhomogeneous broadening of the Er3+ ions
coupled to the ring resonator versus bus waveguide, see Supplementary Note 8.
We now compare the experimentally determined collective cooperativity with our theoretical estimate. From the fit to our
main sample zero-field transmission data Supplementary Table 3, we extract a collective cooperativity 𝐶 = 6.66 ± 0.42. This
value is comparable with the predicted value of 𝐶estimated = 6.0 ± 0.5, which was calculated based on the simulated mode
properties and the oscillator strength derived from bus waveguide absorption.
To validate the reproducibility of our platform, we also characterised a pathfinder device, sample b, which featured a ring
with a smaller bend radius (𝑟 bend = 140µm). The following data were obtained during its initial thermal cycles, prior to the
𝑄 int -factor degradation discussed in Supplementary Note 6. By fitting the complex transmission to Eq. (S7.7), we determined a
collective cooperativity of 𝐶 = 9.06 ± 0.96. The parameters extracted from this fit are detailed in Supplementary Table 3. The
low inhomogeneous broadening observed for this device Γinh is consistent with the restricted sampling with reduced strain and
𝑔-factor variation (see Supplementary Note 8).

SUPPLEMENTARY NOTE 8.

MAGNETIC FIELD DEPENDENCE OF INHOMOGENEOUS BROADENING AND 𝒈-FACTOR

The absorbance of the |↓⟩ 𝑍1 ↔|↓⟩𝑌1 transition of the Er3+ ions coupled to the bus waveguide was acquired using our heterodyne
detection setup (see Supplementary Note 5), and fitted to a Lorentzian profile to extract the inhomogeneous broadening linewidth
Γinh for various magnetic field strengths |B|, as shown by the orange markers in Supplementary Figure 8a. We overlay in
blue markers the inhomogeneous broadening linewidths of Er3+ ions coupled only to the ring resonator, found from fitting our
2

𝜅ext /2𝜋 (MHz)

𝜅int /2𝜋 (MHz)

Γinh /2𝜋 (MHz)

𝐺/2𝜋 (MHz)

4𝐺
𝐶 = 𝜅tot
Γinh

𝜆ions (nm)

0.0T

39.12 ± 0.46

158.68 ± 8.44

331.79 ± 20.94

330.57 ± 5.67

6.66 ± 0.42

1532.6350

0.1T

31.38 ± 0.24

153.01 ± 2.72

195.00 ± 10.22

211.00 ± 2.60

4.95 ± 0.25

1532.6305

0.4T

36.55 ± 0.17

155.43 ± 3.18

226.22 ± 10.75

231.34 ± 2.56

4.93 ± 0.20

1532.6201

1.0T

36.96 ± 0.29

186.97 ± 7.65

386.58 ± 29.49

353.49 ± 25.87

5.77 ± 0.77

1532.6197

Sample b (0T)a 93.69 ± 1.71

75.23 ± 14.27

264.40 ± 13.30

318.02 ± 3.51

9.06 ± 0.96

1532.6346

Condition
Main sample

a Data for sample b (𝑟
bend = 140µm) during its initial thermal cycles. Nominal mixing chamber temperature was ∼20mK. See Supplementary Note 6 for

discussion of its 𝑄int -factor degradation.

Supplementary Table 3. Fitted and measured parameters of the resonator-coupled Er3+ ion ensemble. The table details parameters for
the main sample at various magnetic field strengths and includes comparative data from sample b at zero field. The centre wavelength 𝜆ions
corresponds to |↓⟩ 𝑍1 ↔|↓⟩𝑌1 transition frequency of the resonator-coupled ions, which is additionally shifted relative to the bus-waveguidecoupled ions due to the DC electric field applied for electro-optic tuning (up to 600V). The resonator linewidths 𝜅int and 𝜅 ext were determined
independently with the resonator detuned by ≫𝐺 from the Er3+ transition and held fixed during subsequent fits. The inhomogeneous broadening
linewidth Γinh and collective coupling strength 𝐺 were obtained as free parameters by fitting the complex transmission to the coupled-resonator
model Eq. (S7.7), which assumes a Lorentzian inhomogeneous profile. The collective cooperativity 𝐶 is derived from the fitted parameters
with standard error propagation. All uncertainties represent one-standard-deviation confidence intervals from least-squares fits. Measurements
for main sample were performed at a nominal mixing chamber temperature ∼8mK.

Page 12 out of 18

Bus

−2 0 2 −2 0 2
(ω−ωion)/2π (GHz)

600

Resonator

400

|A|2

30
25

|B| (T)

20

1532.6
1532.5 λ (nm)
1532.4

1

Γinh (MHz)

800

b

1T

0T

ΔωY / 2π (GHz)

a

1000

Absorbance

measured complex transmission to Eq. (S7.7). At higher magnetic field strengths, the inhomogeneous broadening linewidth
increases, which we attribute to a spatially varying 𝑔-factor across the crystal and spatially varying magnetic field: different ions
experience slightly different local environments, leading to a distribution of Zeeman shifts that broadens the ensemble linewidth.
The overlaid resonator data reveals that at |B| = 0T, there is already a decrease in inhomogeneous broadening by coupling to Er3+
ions in a relatively small region compared to the ions coupled to the bus waveguide. At non-zero magnetic fields, the suppression
effect is magnified further, confirming a spatially varying local environment experienced by the Er3+ ion ensemble.

15
gY = 7.41 ± 0.01

10

200
0.0

0.2

0.4
0.6
|B| (T)

0.8

1.0

1

0.10

0.15

|B| (T)

0.20

0.25

Supplementary Figure 8. Magnetic field dependence of inhomogeneous broadening linewidth and Zeeman splitting of 𝒀1 manifold.
a, Inhomogeneous broadening linewidth Γinh as a function of magnetic field strength |B| for Er3+ ions coupled to the bus waveguide (orange)
and to the ring resonator (blue). The inset plots show absorbance spectra at |B| = 0T and 1T for bus waveguide coupled ions. b, Zeeman
splitting Δ𝜔𝑌1 /2𝜋 of the 𝑌1 excited-state Kramers doublet as a function of |B|, with a linear fit yielding an effective 𝑔-factor 𝑔𝑌1 = 7.41 ± 0.01.
Inset: transmission spectra at corresponding magnetic fields showing the progressive Zeeman splitting.

To characterise the 𝑔-factor corresponding to the electronic transition |↓⟩𝑌1 ↔|↑⟩𝑌1 which we denote as 𝑔𝑌1 , we perform a linear
fit to the frequency difference Δ𝜔𝑌1 between the |↓⟩ 𝑍1 ↔|↓⟩𝑌1 and |↓⟩ 𝑍1 ↔|↑⟩𝑌1 transitions as shown in Supplementary Figure 8b.
From this we extract 𝑔𝑌1 = 7.41 ± 0.01, which agrees well with Ref. [46].

SUPPLEMENTARY NOTE 9.

SPECTRAL DIFFUSION AND COHERENCE

To investigate spectral diffusion of Er3+ ions, we employ the 3-pulse photon echo (3PPE) or stimulated photon echo experiment,
where the delay between the first two pulses is 𝜏12 , and the delay between the second and third pulses is 𝜏23 . The delays are measured
from the centre of each pulse. The intensity of the stimulated photon echo as a function of 𝜏12 is given by 𝐼3PPE ∝ exp (−4𝜋𝜏12 Γeff )
[47], where Γeff is the effective linewidth. It is modelled as a function of 𝜏12 and 𝜏23 through the following relation [47]
1
Γeff = Γ0 + ΓSD (𝑅𝜏12 + 1 − exp (−𝑅𝜏23 )),
2

(S9.8)

where Γ0 is the homogeneous linewidth as if there were no spectral diffusion, 𝑅 the rate of spectral diffusion, and ΓSD the linewidth
of spectral diffusion. For this measurement, all optical pulses had a duration of 150ns and a power of 0.3mW at the cryostat
input, and the resulting echoes were averaged at the intensity level over 50 – 170 acquisitions with repetition time 100ms. The
stimulated echo intensity is given by
𝐼3PPE = 𝐼0 exp (−4𝜋𝜏12 Γeff ),

(S9.9)

where 𝜏23 dependence is absorbed into the constant 𝐼0 . To extract the theoretical effective linewidth Γeff as a function of 𝜏23 as
shown in the main text, we fitted the echo decay using Eq. (S9.8).
To study the effective coherence time of the Er3+ ions in our system, it is instructive to consider 𝜏23 = 0 where the 3PPE
measurement becomes equivalent to the two-pulse photon echo (2PPE) or Hahn echo measurement. The empirical effective
coherence time 𝑇M at 𝜏23 = 0 extracted from the spectral diffusion parameters can be written as [43, 47]
!
√︂
2Γ0
ΓSD 𝑅
𝑇M =
−1+ 1+
,
(S9.10)
ΓSD 𝑅
𝜋Γ02
The corresponding empirical effective homogeneous linewidth is then
Γ̃eff =

1
.
𝜋𝑇M

Page 13 out of 18

(S9.11)

To obtain each data point in the empirical coherence time versus magnetic field strength plot in the main text, we substitute
into Eq. (S9.10) the Γ0 and ΓSD 𝑅 values obtained from fitting Γeff ≊ Γ0 + 12 ΓSD 𝑅𝜏23 (Supplementary Table 4). For the linear
approximation to hold, we fit to data for 𝜏23 < 2𝑇1 . The values of 𝑅 and ΓSD quoted separately in the main text are instead
obtained from the full model, Eq. (S9.8), fitted over the entire range of 𝜏23 ; their product, 0.13 ± 0.03kHz2 , agrees with the
linearised determination at |B| = 0.2T within one standard deviation. Note that the homogeneous linewidth at zero-field was
done with 2PPE measurement. The empirical effective coherence times are then converted into homogeneous linewidths through
Eq. (S9.11).
As a magnetic field is introduced, the effective homogeneous linewidth of the Er3+ ions drops due to the suppression of electronic
spin flip-flop interactions, which contributes to the homogeneous linewidth according to the Boltzmann distribution [47]
 𝑔 𝜇 𝐵
𝑔 𝜇 𝐵
eff B
eff B
ΔΓff = 𝛼ff exp −
sech
,
2𝑘B𝑇
2𝑘B𝑇

(S9.12)

where 𝛼ff is a coefficient describing the strength of the spin flip-flop processes, 𝑔eff is the effective 𝑔-factor of the electronic
spin state, 𝜇B the Bohr magneton, 𝑘B the Boltzmann constant, and 𝑇 the temperature. In addition to the suppression of flip-flop
interactions, we observed another mechanism causing an increase in homogeneous linewidth at higher magnetic field strengths.
We attribute this increase in homogeneous linewidth to the one-phonon direct process, which involves the absorption/emission
of a single phonon from the resonant electronic spin transition. This linewidth contribution due to the direct process has the
form [48]
𝑔 𝜇 𝐵
eff B
ΔΓD = 𝛼D 𝑔eff3 𝐵5 coth
,
(S9.13)
2𝑘B𝑇
where 𝛼D describes the strength of the one-phonon direct process. The complete contribution to the effective linewidth as a
function of magnetic field |B| is then
Γ̃eff = Γeff,0 + ΔΓff + ΔΓD ,

(S9.14)

where Γeff,0 is the effective linewidth from magnetic field-independent contributions. Using this model (Eq. (S9.14)), we find
excellent agreement, with Γeff,0 = 295 ± 1Hz, 𝛼ff = 71 ± (1 × 10−3 ) kHz, 𝛼D 𝑔eff3 = 160 ± 5HzT−5 , and 𝑔eff 𝜇B /𝑘B𝑇 = 75 ± 1T−1 .
By taking 𝑔-factor of the 𝑍1 manifold to be 𝑔 𝑍1 = 8.38 [49], we find that the effective spin temperature of our system is
𝑇 = 75 ± 1mK.
|B| (T)

0.1

0.15

0.2

0.25

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Γ0 (Hz)

319
±9

268
±5

258
±7

268
±4

261
±5

266
±4

267
±4

269
±4

274
±5

318
±5

364
±5

388
±7

ΓSD 𝑅 (kHz2 )

0.258
±0.039

0.097
±0.016

0.104
±0.010

0.107
±0.010

0.106
±0.010

0.119
±0.012

0.126
±0.011

0.154
±0.014

0.163
±0.014

0.172
±0.016

0.176
±0.022

0.284
±0.022

𝜆ions (+1532nm)

0.6297

0.6275

0.6256

0.6237

0.6221

0.6197

0.6177

0.6168

0.6162

0.6168

0.6176

0.6192

Supplementary Table 4. Fitted and measured spectral diffusion parameters of the Er3+ ensemble at various magnetic field strengths
for 𝑅𝜏23 ≪1. The centre wavelength 𝜆ions corresponds to |↓⟩ 𝑍1 ↔|↓⟩𝑌1 transition frequency of the bus waveguide-coupled ions. The spectral
diffusion-independent linewidth Γ0 and spectral diffusion product ΓSD 𝑅 were obtained as free parameters by fitting to Γeff ≊ Γ0 + 12 ΓSD 𝑅𝜏23
where we have taken 𝑅𝜏23 ≪1 in Eq. (S9.8). All uncertainties represent one-standard-deviation confidence intervals from least-squares fits.
Measurements were performed at a nominal mixing chamber temperature of ∼8mK.

SUPPLEMENTARY NOTE 10.

OPTICAL LIFETIME 𝑻1

The bare relaxation time 𝑇1 of the Er3+ ions not coupled to the ring resonator shows no systematic dependence on the applied
magnetic field strength over the range investigated |B| ∈ [0T, 1T], as shown by the green markers in Supplementary Figure 9a.
We calculate the average bare relaxation time 𝑇1 = 6.47 ± 0.03ms across all measured magnetic field strengths. When the ring
resonator is brought to the 𝑍1 ↔𝑌1 transition frequency at zero field, the coupled system forms polaritons (hybridised light-matter
states) as shown in the inset of Supplementary Figure 9a at wavelengths 1532.6324nm and 1532.6374nm. These polaritons
are each detuned from Er3+ centre wavelength by ∼𝐺. The fluorescence decay data corresponding to the lower and upper
polaritons are shown in orange and purple colours, respectively, in Supplementary Figure 9b. Single-exponential fits yield
𝑇1 = 4.53 ± 0.21ms for the lower polariton and 𝑇1 = 4.78 ± 0.24ms for the upper polariton.
Page 14 out of 18

a

b

8

|B| = 0 T

λions

λ (nm)

1532.6375
1532.6350
1532.6325
0

2
0
0.0

0.2

Counts

4

Counts

T1 (ms)

6

10 20 30
Time (ms)

0.4
0.6
|B| (T)

0.8

1.0

0

10

20
30
Time (ms)

40

50

Supplementary Figure 9. Relaxation time 𝑻1 of Er3+ ions. a, Optical lifetime 𝑇1 as a function of applied magnetic field strength |B| for bare
Er3+ ions not coupled to the ring resonator (green) and for ions coupled to the ring resonator at the lower (orange) and upper (purple) polariton
branches. The bare ions lifetime shows no systematic dependence on |B|. Inset: two-dimensional fluorescence map showing the polariton
mode structure near the |↓⟩ 𝑍1 ↔|↓⟩𝑌1 transition. b, Fluorescence decay curves at |B| = 0T for the same lower and upper polaritons as in a,
together with single-exponential fits (solid lines).

SUPPLEMENTARY NOTE 11.

INVERSION ECHO FIT PARAMETERS

An initial pulse of length 600ns excites the population; after a variable delay 𝜏inv , a Hahn echo sequence with delay 𝜏H = 42µs
and pulse length 150ns reads out the population remaining at the initial excitation frequency. The fractional stretching factor of
0.5 used in the stretched exponential for 𝑇W can be seen as a distribution of characteristic relaxation rates [50, 51].
|B|

𝑝1

𝑝Z

𝑝W

𝑇Z

𝑇W

0.15T

0.360 ± 0.009

0.276 ± 0.008

0.364 ± 0.006

126 ± 8ms

1070 ± 129s

0.2T

0.578 ± 0.024

0.205 ± 0.020

0.217 ± 0.017

45 ± 7ms

1056 ± 539s

Supplementary Table 5.
Inversion echo fitted parameters and lifetimes.
The parameters were obtained by fitting to
𝐼inv ∝ [1 − ( 𝑝 1 exp (−𝜏inv /𝑇1 ) + 𝑝 Z exp (−𝜏inv /𝑇Z ) + 𝑝 W exp (−(𝜏inv /𝑇W ) 1/2 ))] 2 . The optical 𝑇1 was fixed to values obtained from an independent fluorescence measurement. Note that 𝑝 W does not reflect the true branching factor because no clear plateau of the intensity of the
recovered echo at measured time delays was observed.

SUPPLEMENTARY NOTE 12.

OPTICAL PHASE STORAGE PULSE PARAMETERS

The power of the optical pulses used here is 24µW at the cryostat input, and the resulting echoes were averaged at the intensity
level over 600 acquisitions with repetition time 200ms. The pulse lengths are 150ns long and the delay is 𝜏12 = 6.15µs.

Page 15 out of 18

SUPPLEMENTARY NOTE 13.

Platform

ERBIUM COHERENCE AND COUPLING IN LITERATURE

𝑪

𝑻

𝑩

0.36
1.9
—

4K
7 mK
mK

—

sub-K 433 mT 5 kHz (𝑇2 = 64 µs)

—
0.54

3.6 K
4.5 K

𝚪eff

Spectral diffusion

Heterogeneously Integrated
Er3+ :Y2 SiO5 on TFLN ring [36]
Er3+ :Y2 SiO5 on SiC ring [52]
Er3+ :CaWO4 + Si resonator (single
ion) [53]
Er3+ :TiO2 on SiN nanophotonic
waveguides [54]
Er3+ :CeO2 epitaxial on Si [55]
𝛼-Si on Er3+ :Y2 SiO5 [56]

This work: Er3+ :CaWO4 bonded to 4.9 − 6.7 75 mK
TFLN (main sample)

—
—
1.238 T —
60 mT 31 kHz (𝑇2 = 10.2 µs)

None 440 kHz (𝑇2 = 0.72 µs)
None —
0.2 T

289 ± 34 Hz (Γ0 = 254 ± 7 Hz)

—
—
63 kHz long-term
27 kHz within 4 ms
—
—
𝚪SD = 1.5 kHz, 𝑅 = 86 Hz, verified
to 2 s

Implanted and doped waveguides
Er3+ :LiNbO3 SmartCut,
ridge
waveguides + microrings [57]
Er implanted,
SiC-on-insulator
film [58]
Er implanted, Si waveguides [59]
Er implanted, commercial Si waveguides [60]
Er3+ :LiNbO3 SmartCut [61]
Er3+ :LiNbO3 SmartCut [62]

—

20 mK

0.55 T 1.8 kHz (𝑇2 = 180 µs)

—

20 mKa

None 441 kHz

Present with stretched exponential,
not quantified (2PPE only)
—

—
—

8K
2K

None ≲10 kHz
≤9 T <30 kHz

—
—

—

30 mK

1.5 T

3.5 kHz

0.39b

260 mK

2T

3.4 kHz (𝑇2 = 93 µs)

Present with stretched exponential,
not quantified
Present with stretched exponential,
not quantified

—
—
—
—
—

20 mK ∼11 mT <70 kHz
100 mK 0.2 T 100 Hz
1.5 K
7 T 73 Hz
mK
0.7 T 580 ± 20 Hz
7 mK 0.09 T ∼8 kHz effective

Bulk
Er in isotopically enriched Si [63]
167 Er3+ :Y SiO [64]
2
5
Er3+ :Y2 SiO5 [65]
Er3+ :Y2 O3 [66]
Er-doped silica fibre [67]

—
ΓSD = 880 ∼ 1010 Hz
Negligible
∼1 kHz at 100 µs and ∼2 kHz over ms
ΓSD = 38 kHz, 𝑅 = 1 kHz, TLS suppressed below 100 mK

a The authors infer a sample temperature ≳0.5 K from the absence of Zeeman-branch depopulation at 400 mT.
b Effective cooperativity that governs their atomic frequency comb storage efficiency.

Supplementary Table 6. Optical coherence and light–matter coupling across erbium photonic platforms.

SUPPLEMENTARY REFERENCES
[1] M. Bahadori, M. Nikdast, Q. Cheng, and K. Bergman, Universal design of waveguide bends in silicon-on-insulator photonics platform,
Journal of Lightwave Technology 37, 3044 (2019).
[2] Y. Gao, F. Lei, M. Girardi, Z. Ye, R. Van Laer, V. Torres-Company, and J. Schröder, Compact lithium niobate microring resonators in the
ultrahigh q/v regime, Optics Letters 48, 3949 (2023).
[3] D. Dai and J. E. Bowers, Novel ultra-short and ultra-broadband polarization beam splitter based on a bent directional coupler, Optics
express 19, 18614 (2011).
[4] M. Li, J. Ling, Y. He, U. A. Javid, S. Xue, and Q. Lin, Lithium niobate photonic-crystal electro-optic modulator, Nature communications
11, 4123 (2020).
[5] C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Lončar, Nanophotonic lithium niobate electro-optic modulators, Optics express 26,
1547 (2018).
[6] A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Electro–optically tunable microring resonators in lithium niobate,
Nature photonics 1, 407 (2007).
[7] S. Yu, H. Kang, X. Shen, Y. Xue, W. Wan, C. Zou, B. Chen, and J. Lu, Poling-assisted hydrofluoric acid wet etching of thin-film lithium
niobate, Optics Letters 49, 854 (2024).

Page 16 out of 18

[8] P. B. Deotare, Nanobeam cavities for reconfigurable photonics (Harvard University, 2012).
[9] J. T.-H. Choy, Nanophotonic structures for coupling to quantum emitters in the visible (Harvard University, 2013).
[10] C. Shen, C. Wang, Y. Zhu, J. Wu, Y. Chen, Z. Li, K. Huang, X. Zhao, S. Song, J. Zhang, et al., A comparative study of dry-etching
nanophotonic devices on a linbo3-on-insulator material platform, in 4th Optics Young Scientist Summit (OYSS 2020), Vol. 11781 (SPIE,
2021) pp. 212–217.
[11] C. Kumar, N. N. Klimov, and P. S. Kuo, Optimization of waveguide fabrication processes in lithium-niobate-on-insulator platform, AIP
advances 14 (2024).
[12] H.-S. Kim, G. Kim, T. Slusar, J. Kim, J. Park, J. Park, H. Hwang, W. Noh, H. Lee, M.-K. Seo, K. Moon, and J. J. Ju, Fabrication of
low-loss symmetrical rib waveguides based on x-cut lithium niobate on insulator for integrated quantum photonics, ETRI Journal 46, 783
(2024), https://onlinelibrary.wiley.com/doi/pdf/10.4218/etrĳ.2024-0137.
[13] F. Kaufmann, G. Finco, A. Maeder, and R. Grange, Redeposition-free inductively-coupled plasma etching of lithium niobate for integrated
photonics, Nanophotonics 12, 1601 (2023), https://onlinelibrary.wiley.com/doi/pdf/10.1515/nanoph-2022-0676.
[14] S. Yang, Y. Li, J. Xu, M. Wang, L. Wu, X. Quan, M. Liu, L. Fu, and X. Cheng, Low loss ridge-waveguide grating couplers in lithium
niobate on insulator, Optical Materials Express 11, 1366 (2021).
[15] G. Ulliac, V. Calero, A. Ndao, F. Baida, and M.-P. Bernal, Argon plasma inductively coupled plasma reactive ion etching study for smooth
sidewall thin film lithium niobate waveguide application, Optical Materials 53, 1 (2016).
[16] J. C. Holzgrafe, Cavity electro-optics in thin-film lithium niobate, PhD Thesis, Harvard University (2022).
[17] R. Zhuang, J. He, Y. Qi, and Y. Li, High-q thin-film lithium niobate microrings fabricated with wet etching, Advanced Materials 35,
2208113 (2023).
[18] A. Shams Ansari, Integrated lithium niobate photonics and applications, Ph.D. thesis (2022).
[19] M. Leidinger, K. Buse, and I. Breunig, Influence of dry-oxygen-annealing on the residual absorption of lithium niobate crystals in the
spectral range from 500 to 2900 nanometers, Opt. Mater. Express 6, 264 (2016).
[20] A. Shams-Ansari, G. Huang, L. He, Z. Li, J. Holzgrafe, M. Jankowski, M. Churaev, P. Kharel, R. Cheng, D. Zhu, N. Sinclair, B. Desiatov,
M. Zhang, T. J. Kippenberg, and M. Lončar, Reduced material loss in thin-film lithium niobate waveguides, APL Photonics 7, 081301
(2022).
[21] M. Zhang, C. Wang, Y. Hu, A. Shams-Ansari, T. Ren, S. Fan, and M. Lončar, Electronically programmable photonic molecule, Nature
Photonics 13, 36 (2019).
[22] B. Desiatov, A. Shams-Ansari, M. Zhang, C. Wang, and M. Lončar, Ultra-low-loss integrated visible photonics using thin-film lithium
niobate, Optica 6, 380 (2019).
[23] A. Shams-Ansari, M. Yu, Z. Chen, C. Reimer, M. Zhang, N. Picquè, and M. Lončar, Thin-film lithium-niobate electro-optic platform for
spectrally tailored dual-comb spectroscopy, Communications Physics 5, 88 (2022).
[24] A. V. Sosunov, I. V. Petukhov, V. Kichigin, R. S. Ponomarev, A. A. Mololkin, and M. Kuneva, The impact of various factors on the surface
of x-cut lithium niobate and properties of proton-exchanged waveguides, Ferroelectrics 618, 1300 (2024).
[25] K. Xu, W. Zhang, J. Luo, H. Yu, H. Yuan, B. Wang, and D. Wu, Evolution mechanism of interfacial multi-layer intermetallic compounds
and failure behavior in the al–au wire bonding, Journal of Materials Research and Technology 32, 2843 (2024).
[26] Q. Kang, H. Yan, F. Niu, K. Liu, T. Suga, and C. Wang, Inp/linbo3 covalent heterointerface construction via an asymmetric plasma
activation strategy for hybrid integrated quantum systems, ACS Applied Materials & Interfaces 16, 48502 (2024), pMID: 39193874.
[27] K. Dasigi, P. A. Dmitriev, K. J. Wo, F. Hanamura, L. Kong, and S. Touzard, Quantum-limited optical vector analysis, IEEE Transactions
on Instrumentation and Measurement , 1 (2026).
[28] P. Weigel and S. Mookherjea, Reducing the thermal stress in a heterogeneous material stack for large-area hybrid optical silicon-lithium
niobate waveguide micro-chips, Optical Materials 66, 605 (2017).
[29] M. A. Hopcroft, W. D. Nix, and T. W. Kenny, What is the young’s modulus of silicon?, Journal of Microelectromechanical Systems 19,
229 (2010).
[30] J.-H. Zhao, T. Ryan, P. S. Ho, A. J. McKerrow, and W.-Y. Shih, Measurement of elastic modulus, poisson ratio, and coefficient of thermal
expansion of on-wafer submicron films, Journal of Applied Physics 85, 6421 (1999).
[31] R. S. Weis and T. K. Gaylord, Lithium niobate: Summary of physical properties and crystal structure, Applied Physics A Solids and
Surfaces 37, 191 (1985).
[32] V. A. Gorodtsov, V. G. Tkachenko, and D. S. Lisovenko, Extreme values of young’s modulus of tetragonal crystals, Mechanics of Materials
154, 103724 (2021).
[33] C. A. Swenson, Recommended values for the thermal expansivity of silicon from 0 to 1000 k, Journal of Physical and Chemical Reference
Data 12, 179 (1983).
[34] F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De Nicola, Measurement of the thermal expansion coefficients
of ferroelectric crystals by a moiré interferometer, Optics Communications 277, 14 (2007).
[35] A. Senyshyn, M. Hoelzel, T. Hansen, L. Vasylechko, V. Mikhailik, H. Kraus, and H. Ehrenberg, Thermal structural properties of calcium
tungstate, Journal of Applied Crystallography 44, 319 (2011).
[36] L. Yang, M. Shen, Y. Xu, J. Xie, and H. X. Tang, Photonic integration of Er3+ :Y2 SiO5 with thin-film lithium niobate by flip chip bonding,
Optics Express 29, 15497 (2021).
[37] B. D. Bartolo, Optical interactions in solids (Wiley, New York, 1968).
[38] B. Henderson and G. F. Imbusch., Optical spectroscopy of inorganic solids (Oxford University Press, Oxford, 2006).
[39] K. Dolgaleva and R. W. Boyd, Local-field effects in nanostructured photonic materials, Advances in Optics and Photonics 4, 1 (2012).
[40] G. Liu and B. Jacquier, Spectroscopic Properties of Rare Earths in Optical Materials (Springer Berlin Heidelberg, 2005).
[41] T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and
A. Faraon, Optically addressing single rare-earth ions in a nanophotonic cavity, Physical Review Letters 121, 183603 (2018).
[42] T. Böttger, Y. Sun, C. W. Thiel, and R. L. Cone, Spectroscopy and dynamics of Er3+ :Y2 SiO5 at 1.5 µm, Phys. Rev. B 74, 075107 (2006).

Page 17 out of 18

[43] C. Thiel, T. Böttger, and R. Cone, Rare-earth-doped materials for applications in quantum information storage and signal processing,
Journal of Luminescence 131, 353 (2011).
[44] D. L. Orth and J. L. Skinner, Lattice model of inhomogeneous broadening in crystals: Correlation of frequency distributions for different
transitions, The Journal of Physical Chemistry 98, 7342 (1994).
[45] I. Diniz, S. Portolan, R. Ferreira, J. M. Gérard, P. Bertet, and A. Auffèves, Strongly coupling a cavity to inhomogeneous ensembles of
emitters: Potential for long-lived solid-state quantum memories, Physical Review A 84, 063810 (2011).
[46] F. Becker, S. KC, L. J. J. Sauerzopf, T. Schneider, L. Risinger, C. Schmid, and K. Müller, Zeeman spectroscopy of vacancy-chargecompensated Er3+ sites in CaWO4 under vector magnetic fields, Physical Review Materials 10, 10.1103/mkpd-9r5p (2026).
[47] T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, Optical decoherence and spectral diffusion at 1.5 µm in Er3+ :Y2 SiO5 versus magnetic
field, temperature, and Er3+ concentration, Phys. Rev. B 73, 075101 (2006).
[48] A. Abragam and B. Bleaney, Electron paramagnetic resonance of transition ions (Oxford University Press, London, 1970).
[49] M. Le Dantec, M. Rančić, S. Lin, E. Billaud, V. Ranjan, D. Flanigan, S. Bertaina, T. Chanelière, P. Goldner, A. Erb, R. B. Liu, D. Estève,
D. Vion, E. Flurin, and P. Bertet, Twenty-three–millisecond electron spin coherence of erbium ions in a natural-abundance crystal, Science
Advances 7, 10.1126/sciadv.abj9786 (2021).
[50] M. Berberan-Santos, E. Bodunov, and B. Valeur, Mathematical functions for the analysis of luminescence decays with underlying
distributions 1. kohlrausch decay function (stretched exponential), Chemical Physics 315, 171 (2005).
[51] Z. Wang, S. Lin, M. Le Dantec, M. Rančić, P. Goldner, S. Bertaina, T. Chaneliere, R. Liu, D. Esteve, D. Vion, E. Flurin, and P. Bertet,
Week-long-lifetime microwave spectral holes in an erbium-doped scheelite crystal at millikelvin temperature, Nature Communications 16,
10.1038/s41467-025-64087-6 (2025).
[52] A. Kolar, I. Chin, C. Fong, D. M. Lukin, M. A. Guidry, M. Palei, J. Vučković, and T. Zhong, Integrated photon-memory entanglement
generation using dual photonic resonators (2026).
[53] S. Ourari, Ł. Dusanowski, S. P. Horvath, M. T. Uysal, C. M. Phenicie, P. Stevenson, M. Raha, S. Chen, R. J. Cava, N. P. de Leon, and
J. D. Thompson, Indistinguishable telecom band photons from a single Er ion in the solid state, Nature 620, 977 (2023).
[54] S. Gupta, R. M. Pettit, A. Sundaresh, V. Niaouris, S. Deckoff-Jones, D. P. Crowley, L. G. Carpenter, A. M. Dibos, M. K. Singh, and S. E.
Sullivan, Erbium quantum memory platform with long optical coherence via back-end-of-line deposition on foundry-fabricated photonics,
Physical Review Applied 24, 10.1103/xj8y-b6sl (2025).
[55] J. Zhang, G. D. Grant, I. Masiulionis, M. T. Solomon, J. C. Marcks, J. K. Bindra, J. Niklas, A. M. Dibos, O. G. Poluektov, F. J. Heremans,
S. Guha, and D. D. Awschalom, Optical and spin coherence of er spin qubits in epitaxial cerium dioxide on silicon, npj Quantum
Information 10, 10.1038/s41534-024-00903-z (2024).
[56] E. Miyazono, I. Craiciu, A. Arbabi, T. Zhong, and A. Faraon, Coupling erbium dopants in yttrium orthosilicate to silicon photonic
resonators and waveguides, Optics Express 25, 2863 (2017).
[57] S. Wang, L. Yang, M. Shen, W. Fu, Y. Xu, R. L. Cone, C. W. Thiel, and H. X. Tang, Er:LiNbO3 with High Optical Coherence Enabling
Optical Thickness Control, Physical Review Applied 18, 014069 (2022).
[58] A. Lyasota, J. Bader, S. Q. Lim, B. C. Johnson, J. C. McCallum, Q. Li, S. Rogge, and S. Castelletto, Narrow magneto-optical transitions
of erbium implanted into silicon carbide-on-insulator, Communications Materials 7, 10.1038/s43246-026-01154-5 (2026).
[59] A. Gritsch, L. Weiss, J. Früh, S. Rinner, and A. Reiserer, Narrow Optical Transitions in Erbium-Implanted Silicon Waveguides, Physical
Review X 12, 041009 (2022).
[60] S. Rinner, F. Burger, A. Gritsch, J. Schmitt, and A. Reiserer, Erbium emitters in commercially fabricated nanophotonic silicon waveguides,
Nanophotonics 12, 3455 (2023).
[61] P. Barya, D. Chen, A. Prabhu, L. Heller, E. Chow, H. Kim, J. Akin, V. Niaouris, J. Zhang, A. M. Dibos, P. Wang, and E. A. Goldschmidt,
Telecom quantum memory over one microsecond in nanophotonic lithium niobate (2026).
[62] C. Yang, H. Guo, Y.-Y. An, Q. He, C. Lu, Z. Jiang, Y.-Q. Lu, S. Zhu, and X.-S. Ma, Programmable cavity-enhanced telecom quantum
memory in thin-film lithium niobate (2026).
[63] I. R. Berkman, A. Lyasota, G. G. de Boo, J. G. Bartholomew, S. Q. Lim, B. C. Johnson, J. C. McCallum, B.-B. Xu, S. Xie, N. V.
Abrosimov, H.-J. Pohl, R. L. Ahlefeldt, M. J. Sellars, C. Yin, and S. Rogge, Long optical and electron spin coherence times for erbium
ions in silicon, npj Quantum Information 11, 66 (2025).
[64] M. Guo, Q. Li, Z. Xu, S. Liu, F. Wang, and M. Zhong, Decoherence characterization and quantum memory design in 167 Er3+ :Y2 SiO5 ,
Frontiers of Physics 21, 033201 (2026).
[65] T. Böttger, C. W. Thiel, R. L. Cone, and Y. Sun, Effects of magnetic field orientation on optical decoherence in Er3+ :Y2 SiO5 , Phys. Rev.
B 79, 115104 (2009).
[66] R. Fukumori, Y. Huang, J. Yang, H. Zhang, and T. Zhong, Subkilohertz optical homogeneous linewidth and dephasing mechanisms in
Er3+ :Y2 O3 ceramics, Physical Review B 101, 214202 (2020).
[67] F. Rasekh, N. G. Kamel, M. Bornadel, S. Kumar, E. Saglamyurek, C. Simon, and D. Oblak, Ultra-narrow homogeneous linewidths of
erbium-doped silica glass fibers at millikelvin temperatures: magnetic field and temperature dependence, Optica Quantum 4, 63 (2026).

Page 18 out of 18
</reference>

<statements>
1. In the chemical treatment table, Piranha Clean is used at an operating temperature of 80°C - 120°C (exothermic)
2. In the chemical treatment table, Piranha Clean targets carbonaceous fluoropolymer residues and hardened cross-linked electron-beam resist
3. Immersion in a Piranha solution (\(\text{H}_2\text{SO}_4:\text{H}_2\text{O}_2 = 3:1\)) at \(100^\circ\text{C}\) for \(15\) minutes removes trace organic residues and carbonaceous polymers
</statements>

Begin the assessment now. Output only the JSON list, without any conversational text or explanations.