Ultra high-Q tunable microring resonators enabled by slow light

Domain: physics
Published: 2025-11-25
Editorial outcome: major_revision

Abstract
High-Q nanophotonic resonators are crucial for many applications in classical and quantum optical processing, communication, and sensing. We achieve ultra-high quality factors via a method previously limited to bulk systems, preparing a highly transparent and strongly dispersive medium within the resonator that causes a reduction in the group velocity and a corresponding increase in the quality factor. We implement this via spectral hole burning in erbium-doped thin-film lithium niobate microring resonators, and show Q-factors enhanced by nearly three orders of magnitude to exceed 10^8. Additionally, we show dynamic control of the resonances via electro-optic tuning. Finally, we present a theoretical model for our experimentally observed resonator linewidths, which are not well-described by the standard Bloch equations. Our results show a dramatic reduction in the erbium dephasing rate under a strong optical drive, leading to much narrower linewidths than would otherwise be expected given the large circulating intensity in the resonator.

Introduction
High-Q optical resonators are essential components in nanophotonics, enabling narrowband filtering, enhanced nonlinearity, cavity quantum electrodynamics, sensing, precision spectroscopy, laser stabilization, and more. Quality factors in these resonators are fundamentally limited by optical losses from material absorption and surface scattering, and can be as high as 10^7 for microring resonators in the thin-film lithium niobate platform studied here. Higher quality factors would have a direct impact for enabling functionality on a chip that is currently only possible in macroscopic systems, which is vital for making scalable, robust, and deployable devices. For instance, the most stringent sensing and spectroscopic applications require Q-factors that are far out of reach for nanophotonics and only possible in macroscopic cavities (Q ≳ 10^11) and atomic systems (Q ≳ 10^15). Higher Q factors would also enable new functionalities for building scalable quantum networks such as integrating ultra-narrowband photon generation and efficient quantum memory on-chip. Continued materials and fabrication improvements will likely lead to continued incremental improvements in Q, but here we pursue a pathway that gets around the materials and fabrication limits by engineering a slow group velocity for light propagating in the cavity. This approach uses the fact that optical losses are propagation losses, and therefore depend on the propagation length, while Q depends on the rate of optical loss in time. Thus, a reduction in the group velocity of light leads directly to an increase in the Q by the same factor. High optical depth atomic ensembles enable group velocity reduction of many orders of magnitude via electromagnetically induced transparency and other schemes, however, incorporating such ensembles with nanophotonics is challenging. Previous work on resonance narrowing via slow light has primarily focused on two regimes: very slow group velocities in macroscopic cavities and modest group velocity reduction via band engineering in nanophotonic cavities. We use a unique platform, erbium-doped thin-film lithium niobate (Er:TFLN), in which a high optical depth ensemble of coherent Er emitters is directly coupled to low-loss nanophotonic structures fabricated in TFLN. We employ spectral hole-burning (SHB), a powerful technique for absorption and dispersion engineering in rare-earth ensembles and other media. A narrowband laser selectively depopulates or shelves a spectrally narrow subset of emitters from a large inhomogeneously broadened ensemble, thereby creating a narrow transparency window (and a corresponding sharp slope in the index of refraction) that can persist for ms or longer depending on the medium. The group velocity of light propagating through this spectral hole v_g = c/(n(ω) + ω∂n/∂ω) ≈ Δ_hole/α where Δ_hole/(2π) is the width of the spectral hole and α is the absorption coefficient outside the spectral hole. This can be dramatically reduced from c for typical rare-earth spectral holes with Δ_hole/(2π) ≳ MHz and α ≳ cm^-1. In this work, we show a nearly three order of magnitude decrease in the group velocity, and a corresponding Q-factor greater than 10^8, beyond the limits of current TFLN technology. Such narrow features are useful for on-chip Q-factor enhancement, which is also a key requirement for optical storage, laser stabilization, and more. We also work out a theoretical model for the unique regime we are able to study in the Er:TFLN platform. We show that the narrowing can be understood as an interference of resonances, which lead to tunable Fano line shapes, which we demonstrate by electro-optic (EO) tuning of our narrowed Fano feature. We further model the spectral hole width and show that the large circulating intensity in the resonator during the hole-burning phase decouples the Er emitters from the surrounding spin bath and dramatically reduces the excess dephasing. This results in much narrower features than expected based on a naive Bloch equation treatment. We showcase the necessary modification to the Bloch equations and show good agreement with our data, a vital step for accurately modeling and understanding spectral hole-burned features in rare-earth emitters coupled to resonators.

Results
The maximum achievable Q-factor (Q = ω/κ) of resonators is primarily constrained by intrinsic loss mechanisms (κ_i > κ_ext), which includes both the material absorption rate and imperfect mode confinement, resulting in coupling to undesired radiation modes. We overcome this limitation by adding a highly dispersive medium within the resonator, which leads to a significant reduction in the group velocity of light (v_g). When introduced into a microcavity, this reduction increases the round-trip time of circulating light, effectively extending the cavity lifetime and enhancing the Q-factor. One might initially guess that such a slowdown would actually increase the coupling to lossy modes, as photons would interact with the absorptive medium and radiative decay channels for a longer time. However, Soljačić et al. demonstrated that dispersion not only reduces the group velocity but also slows down the coupling rates to lossy modes, thereby increasing the Q. In our system, we first investigate the bare cavity resonance of the microring resonators away from the Er absorption band (≈ 1534.5 nm). Two bus waveguides are used to evanescently couple light in and out of the ring cavity with a rate of κ_ext = 2π × 324 MHz each (Supplementary Note 2E), while the intrinsic loss rate was extracted to be κ_i = 2π × 471 MHz, resulting in the total κ = 2π × 1.12 GHz or a Q-factor of 1.8 × 10^5. We further measured similar κ for identically fabricated devices with no Er, validating that the loss rates are mainly limited by the sidewall roughness of waveguides (Supplementary Note 2E). The 300 μm diameter of our resonators means we are guaranteed at least 2 resonances within the ~158 GHz wide Er absorption band on the I_15/2 - I_13/2 transition centered at 1531.6 nm. The large inhomogeneous linewidth is due to charge compensation and disorder created when Er substitutes for lithium, as well as the intrinsic disorder in congruent lithium niobate. We use devices with heavy erbium doping (0.5%) to achieve high optical depth. The resulting Er absorption introduces an additional loss rate of κ_Er = 2π × 16 GHz (Supplementary Note 2E), which dominates both intrinsic and coupling losses, leading to significantly broadened and undercoupled resonances within the erbium absorption bandwidth. We next perform SHB at the center of the cavity resonance by optically pumping a spectrally narrow subset Er ions (see Supplementary Fig. 1 for experimental setup details).

This results in a narrow transparent window, or spectral hole, in the absorption profile at the frequency of the burn pulse. The width of the spectral hole is fundamentally limited to be larger than twice the measured homogeneous linewidth, Δ_hole/2π ≥ 490 kHz (Supplementary Note 2C). However, due to power broadening the holes are much broader, estimated to be between 30 and 100 MHz for the range of optical powers used here (Supplementary Note 2F), which is still much narrower than the resonator κ even away from the Er absorption. The narrow transparency window is accompanied by strong dispersion, resulting in a dramatically reduced group velocity and a longer time for the photons to finish each round trip, described by the expression nv_g/c = Δ_hole/κ_Er. Consequently, this results in a narrowed resonance mode at the frequency of the spectral hole. Since the decay rate of the spectral hole is slow compared to all other frequency scales (< 10 kHz), we can ignore any hole dynamics beyond the approximately flat spontaneous emission background we observe during our measurements. We note that moving to lower temperatures and/or higher magnetic fields would extend the lifetime of our spectral holes beyond the Er optical lifetime and enable operation without this spontaneous emission background. We measure the transmission as a function of detuning by sending a weak probe pulse 4 μs after the burn pulse and detecting at the through port of the device. We observe a sharp Lorentzian dip at the burn frequency with a width of 1.9 MHz, corresponding to a Q-factor of 1.1 × 10^8. Furthermore, we measured the output at the drop port and observed a corresponding peak, consistent with the microring resonator model.

To verify that the Q-factor extends the cavity lifetime, we perform time-domain measurements to measure the ringdown time. Specifically, we send an optical square pulse and measure the decaying tail at the falling edge at the drop port (“Methods”). Our measurements reveal that the narrowed cavity mode exhibits a lifetime of 82 ns, whereas the bare cavity (in the absence of absorption) has an expected lifetime of 0.14 ns, below the resolution of our detection scheme. This significant increase further validates the formation of a high-Q resonance mode and confirms the extended cavity lifetime.

To further investigate the slow light effect, we measure the resonant group delay experienced by a Gaussian pulse. We send a narrowband, 1.5 μs Gaussian pulse through the resonance and observe a 200 ns delay compared to the bare cavity mode case. This corresponds to a group velocity reduced to nearly 2 × 10^5 m/s in the ring waveguide, ~700× slower than the speed of light in the LN waveguide. This result aligns closely with our theoretical estimates (Eq. S41) as well as the scaling of the Q-factor compared to the bare cavity Q. The delay could be further extended by employing a coupled resonator optical waveguide architecture, which can provide a linear scaling of pulse delay with the number of coupled rings. The current delays represent some of the longest optical pulse delays achievable on an integrated chip, offering promising opportunities for scalable quantum memory and quantum information applications.

We can think of our slow-light resonances as arising from the interference of a spectrally narrow resonant mode (the spectral hole) and a broader continuum (the damped resonator mode). Such a system is described by a Fano profile, which is apparent from the rigorous theoretical description of our system in the Supplementary Note 1C. A Fano profile will shift and become asymmetric as the detuning increases between the narrow and broad resonances. In our case, we can identify the Fano asymmetry parameter as a function of the detuning between the burn laser frequency (ω_l) and the bare cavity mode (ω_c): q = (ω_l - ω_c) / (κ_c + κ_Er/2). In Fig. 3a we see a clear shift of the experimentally measured resonance as we detune the burn laser from the center of the bare cavity mode. The center of the slow light mode matches our theory predictions, though the shape deviates due to the uncertainties in the extracted parameters and the effects of residual absorption in the bus waveguide. We see clear Fano shapes when the optical depth is lower and this residual absorption is smaller (see Supplementary Note 2H). In addition to tuning the burn laser frequency, we can alternatively manipulate the bare cavity mode itself to shift the resonance. The high χ^(2) nonlinearity of lithium niobate (LN) provides an effective mechanism for this control. By applying a DC voltage across the resonator, we electro-optically shift the bare cavity resonance frequency by a rate of 0.12 GHz V^-1 (Supplementary Note 2G), thereby tuning the slow-light mode. As shown in Fig. 3b, we observe a voltage-induced tuning range of ≈ 15 MHz, limited by our electro-optic setup. We also note that the system exhibits a broader spectral response at higher applied voltages, a characteristic feature of the Fano line shape under increased detuning.

We next examine the dependence of resonance linewidth on input pump power (P_in). To providedeeper insight, our model diverges from heuristic group velocity approach used earlier and instead considers a more fundamental approach of analyzing a cavity coupled to an atomic ensemble (Supplementary Note 1). One might expect the standard optical Bloch equations, incorporating the experimentally extracted system parameters including the spontaneous decay rate (γ_s), decoherence rate (γ), cavity loss rates (κ_i, κ_ext, κ_Er), and the single-photon coupling rate (g) to explain the resonance width. In this model the slow light induced narrowed resonance loss rate (κ_SL) would be expected to follow the form: κ_SL = (Δ_hole / κ_Er) * κ. Since, the group velocity can be expressed as nv_g/c = Δ_hole/κ_Er, the theory naturally reveals the scaling of the cavity linewidth (κ) with the group velocity. The simple Bloch model exhibits a striking discrepancy with the experimentally observed linewidths, which are up to two orders of magnitude narrower than the theoretical prediction. This deviation cannot be attributed solely to experimental uncertainties in parameter extraction (see Supplementary Note 2A) and, furthermore, the observed linewidths do not follow the square root dependence on optical power predicted by the Bloch model. The failure of the conventional Bloch equations stems from the underlying assumption that the Lindbladian describing the dephasing and decoherence is independent of the optical field strength. However, prior investigations of rare-earth-doped solids such as Pr^3+:LaF_3 have demonstrated that the dephasing induced by a dynamic bath is effectively suppressed when the Rabi oscillation frequency at high intensity exceeds the correlation time τ_c of the bath. In our system, the erbium ions couple to a dense nuclear spin bath composed of lithium and niobium nuclear spins as well electron spins of other erbium ions, a phonon bath, and an electronic bath consisting of charge traps and charged two level systems. Irrespective of the microscopic details of the bath, it can modeled as stochastic process with a correlation time τ_c. The bath and, consequently, the corresponding stochastic process, can be assumed to be Markovian when the condition γ_cτ_c < 1 is satisfied. At an intuitive level, fast Rabi flopping results in time averaging of the dephasing, similar to continuous dynamical decoupling. Reaching the requisite Rabi frequencies to observe this effect in bulk rare-earth-doped materials is difficult, as the optical intensity required is typically out of reach. However, in a nanophotonic waveguide with sub-micron mode area (A_mode = 0.78 μm^2), the local intensity is greatly enhanced. Additionally, in a ring resonator configuration, the circulating optical power is further amplified. For instance, an input power P_in = 21 μW in the bus waveguide leads to a Rabi Frequency Ω = 2π × 10^6 MHz in the ring resonator. To account for this phenomenon, we introduce a dephasing rate described by the modified Bloch equation formalism (γ_m), given by: γ_m = γ_s/2 + γ / (1 + (Ωτ_c)^2). At sufficiently high optical power (Ω ≫ 1/τ_c) the dephasing rate asymptotically approaches the spontaneous emission limit (γ_m → γ_s/2), thereby eliminating spin-bath-induced broadening. By incorporating γ_m and fitting the experimental data, we extract a correlation time of τ_c ≈ 1 μs. This value lies well within the range of typical correlation times previously observed in Er:LN systems and satisfies the Markovianity condition γ_cτ_c < 1. With this correction, the theoretical prediction aligns closely with the experimental data, effectively resolving the discrepancy encountered with the conventional model. It is also important to note that the experimental data also align qualitatively with the trend predicted by the modified theory, deviating from the standard saturable absorber power broadening κ_SL ∝ √P_in dependence expected from the Bloch model. The modification accounts for the significant decoherence narrowing at higher input power, suppressing the linewidth increase from the power-broadening term. This finding is consistent with prior studies demonstrating that optical linewidths in impurity-ion solids can exhibit a field-dependent narrowing due to suppression of local environmental fluctuations, but goes beyond past demonstrations that could not reach such high Rabi rates. This modified model is vital for understanding the limits on (and possibilities for) atomic frequency comb storage in nanophotonic devices, as it dramatically changes the optical power required to prepare a high-resolution comb in the presence of a dephasing spin bath.

Methods
Device design and fabrication
We use grating couplers to couple light from angle-cut optical fiber into our waveguides. The grating couplers are designed such that they couple in and out only the transverse electric (TE) mode. The bus waveguide width is 800 nm, which allows us to effectively couple light into the 1200 nm width and 300 μm diameter ring resonator. The through and drop waveguides are positioned symmetrically on opposite sides of the ring resonator, each separated by a 800 nm gap from the ring. Electrodes were placed 5 μm away from the in-plane ring waveguides.
We use a wafer with 600 nm of 0.5% erbium-doped lithium niobate on insulator. We fabricate the devices using a two step electron-beam (e-beam) lithography process. First, we pattern the waveguides, rings, and grating couplers using ZEP e-beam resist. We then etch 300 nm using Argon-based inductively coupled plasma reactive ion etching. The device is next cleaned of the remaining resist and redeposition of LN with a standard RCA clean. We anneal the sample in an O_2 environment at 500°C for 2 h. To fabricate the electrodes, we perform the second e-beam step using PMGI SF6 resist. We use electron beam deposition to deposit 15 nm of Cr and 285 nm of Au. We then clean and lift-off the deposited metals using a PG remover bath in a sonicated bath at 70°C.

Experimental setup
The devices were characterized in a 1.7 K closed cycle cryostat (Montana Instruments). The laser utilized is a Velocity 1628 tunable telecom laser whose polarization was controlled using a fiber polarization controller. A single acousto-optical modulator (AOM) (Aerodiode) is used to pulse the light and tune the frequency for probe scans. By switching between two RF drives for the AOM, we were able to interchange between the pump and probe fields. We used angle-cut fiber array v-grooves (OZ Optics) to couple light in and out of the grating couplers from the through port and the drop port (see Supplementary Fig. 1). The sample is mounted on a 3-axis nanopositioner (AttoCube) to allow precise alignment of the fiber array with the grating couplers. A Samarium-cobalt magnet was used to provide a static magnetic field of 0.1–0.2 T. The light collected from the device passes through another AOM, polarizer, and attenuator before being detected by a superconducting nanowire single photon detector (SNSPD) (PhotonSpot). The second AOM is used to shutter the SNSPD while high-intensity input pulses are used in burning or photoluminescence.

Linewidth narrowing using spectral hole burning
Spectral hole burning was performed by applying a 50 μs burn pulse at a fixed frequency, followed by measuring the transmission of a probe pulse at the drop or through port. The probe pulse, with a duration of 5 μs and a weaker power of P_probe = 40 nW, was introduced 4 μs after the burn pulse. This process was repeated while maintaining a fixed burn laser frequency and sweeping the probe detuning from -20 MHz to 20 MHz. By recording the probe transmission at various detunings relative to the pump, we extracted the transmission of the narrowed resonance. The input power into the device was varied by changing the rf power supplied to the input AOM. It is important to note that the linewidth data used for analyzing power dependence and Fano resonance characteristics were acquired using a 5 ms burn pulse. This extended burn time ensured that the system reached a steady state, a critical assumption in our theoretical framework for deriving analytical solutions. In contrast, the 50 μs burn pulse resulted in an even narrower resonance feature, which was challenging to model due to the transient nature of the atomic population dynamics.

Ring-down time and slow light measurement
The ring-down measurement was done by sending a square wave optical pulse of 1 μs at a frequency where the narrowed resonance was burned. The pulse width was chosen to allow the the square pulse to fit spectrally within the narrowed resonance bandwidth. The trailing edge was fit with an exponential function Ae^-τt where τ is the ring-down time. The slow light measurement was done similarly by sending a Gaussian optical pulse of 1.5 μs at the burn frequency. The pulse was fit with a Gaussian and the center was compared with center of a reference pulse to give us τ_g. In both these experiments, the reference was measured at a frequency of the bare cavity mode, which is a resonance away from the Er absorption.

Electro-optic tuning of Fano shape
The electro-optic tuning was done by depositing gold electrodes around the ring resonator as described earlier. The two electrodes were wire-bonded to two ports of a printed circuit board (see Supplementary Fig. 6). The details of device architecture used in Fig. 3b are given in the Supplementary Note 2G. A DC voltage was applied to produce a strong DC electric field across the waveguide, which changed the effective refractive index (n_eff) of the LN via its χ^(2) nonlinearity. Consequently, the resonance wavelength of the bare cavity shifts, as does the Fano q parameter.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is a very interesting work, where the authors presented sound experimental results to support the idea of using slow light to obtain high-Q resonance, and coupled with a theoretical model. The paper reported significantly improved high quality factors (>10⁸) in lithium niobate microring resonators by employing a spectral hole burning (SHB) using erbium as dopants. The interaction between a spectrally narrowed resonance and a broader bare resonance produces a Fano lineshape, which is electro-optically tunable. The authors also developed a theoretical model to explain the observed linewidths, showing that strong optical driving significantly reduces the erbium dephasing rate, resulting in narrower linewidths than expected from standard models. The findings presented in the work points out a new direction in achieving high-Q microresonators. I’d recommend acceptance after the authors address the following points in a revisions.\n1. If this is the first work to observe such phenomena (Modified Bloch Equation model) and enhance Q-factor with almost 3 orders? If so, can this novelty be emphasized in the abstract. If there were prior work, could you provide a brief overview on how researchers used similar strategy to enhance Q-factor of resonators, or other applications?\n2. The authors hint that Q-factors exceeding 10¹⁰ are feasible if the bare cavity Q can be improved to 2×10⁷. Does the observed Q-factor enhancement factor (~700×) independent of the bare cavity Q? Are there fundamental or practical upper limits to the Q-factor achievable with this method? What are the requirements for materials to achieve such feats? e.g. can this approach be applied to other material platforms or dopants beyond erbium?\n3. Please clarify the expected relationship between linewidth and input power for each theoretical model shown in Figure 4. Specifically, why does the linewidth increase with increasing input power for both models?\n4. I wonder if the achieved high Q can be related to the reduced loss in the SHB regime, and the microring is operating at under-coupling condition, which could also result in increased Q.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The manuscript reports on the experimental demonstration of spectral hole burning in erbium-doped lithium niobate, with a focus on potential applications in laser stabilization. The work is interesting, and the results are of interest to the photonics community. However, the novelty and significance of the findings do not, in my view, meet the high bar required for publication in Nature Communications and more rigorous analysis is needed. The manuscript would be more appropriately suited for a specialized optics journal such as Optics Express or Optics Letters.\nMajor Concerns:\n1)The work has limited Impact for laser stabilization. The observed spectral hole linewidth (~2 MHz) is too broad for effective laser frequency stabilization. Given that erbium has an excited-state lifetime on the order of milliseconds and hyperfine levels with coherence times up to seconds, the performance falls short of what has been demonstrated using other rare-earth ions such as praseodymium and europium, which exhibit much narrower linewidths and significantly longer coherence times (up to days) as cited in references [49, 50]. Also, spectral hole burning for laser stabilization has been previously demonstrated using rare-earth-doped crystals with much narrower hole linewidths. For example, see the IEEE conference paper “Spectral Hole Burning for Ultrastable Lasers” (2021), which demonstrates far superior stabilization performance.\n2)Several other groups, including those of Andrei Faraon, Hong Tang, and Edo Waks, have already reported narrow-linewidth on-chip rare-earth photonic systems. See, for instance Ref.1 [ npj Nanophotonics 1, 22 (2024)]. The current manuscript does not sufficiently distinguish itself from these prior efforts nor it offers a new understanding. If the narrow hole is used to stabilize a laser it can be well differentiated from Ref1.\n3)Fig. 1d shows the off-atomic-resonance cavity linewidth. It’s not clear what frequency detuning is used. I think at this Q factors, event 100s of GHz is not large enough to avoid atomic absorption, given inhom broadening of Er in LN.\n4)The authors state that the assumptions made when deriving the theoretical models for the linewidth narrowing do not accurately describe the experiments of Section A. Additional context is required as to how the models deviate from experimental conditions and how such deviation impacts the accuracy of these explanations.\n5)The claimed observation of Fano resonances is not well supported by the experimental data. The line shape asymmetry is weak and does not convincingly match theoretical expectations. A more rigorous comparison between theory and experiment is needed.\n6)Additionally, the claim of observing a hole linewidth beyond the predictions of standard Bloch theory is not convincingly supported by the experimental data or theoretical analysis. The theoretical model shows comparable deviation from the experimental data even at low optical powers, undermining the argument that power broadening alone is responsible. Moreover, the definition and application of the Rabi frequency in the context of an inhomogeneously broadened ensemble are not clearly established, making the comparison between theory and experiment less rigorous. Further detail and justification are necessary to substantiate this claim.\nMinor Issues:\n7)The symbols used for variables such as coherence times are inconsistent between the main text and the Supplementary Material.\n8)The magnetic field strength, which is referenced in the analysis, is not specified in the main body of the manuscript and should be included.\n9)The Mims decoherence formula (Eq. S43) in the Supplementary Material is missing an appropriate citation.\n10)The predicted maximum quality factor of 10101010 exceeds the theoretical limit for lithium niobate (1.63×1081.63×10). This discrepancy should be acknowledged and explained.\nI recommend rejection from Nature Communications in its current form. However, the work may be suitable for publication in a specialized optics journal following revision and clarification of the points above", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_5": "The authors report on an experiment where they realized slow-light effects in a Erbium doped thin film lithium niobate (TFLN) resonator through spectral hole burning. Slow light is used to increase the roundtrip time of a weak coherent probe inside the hole band, demonstrating an improvement of nearly three orders of magnitude in the quality factor compared to the bare cavity mode. The authors also provided a comprehensive theoretical model of the Erbium ions dynamics within the cavity, including the effects of decoherence caused by the external environment and the bath-decoupling induced by the strong optical circulating intensities within the cavity. In general, there is a good match between the theory and the experiment, especially by considering the large number of free parameters in the model, which have been experimentally extracted by conducting independent experiments. The authors also proposed to exploit the ultra-high Q that would be reached in state-of-art TFLN for optical filtering, laser stabilization and narrow-band photon pair generation.\nOverall the manuscript is well written and present convincing results that might be of interest for the broad audience working in the field of quantum optics, spectroscopy, laser stabilization and sensing. I have some concerns that should be addressed before considering it ready for publication in Nature Communications:\n1) The intrinsic Q of the resonator is around 500000 (471 MHz bandwidth), which is below state of art for TFLN. Is this due to the Er doping? Do the authors have any data on the intrinsic Q of cavities without Er doping? I believe this is an important point of discussion if ultra-high Q exceeding 10^10 are targeted.\n2) Slow-light effects are limited to a narrow-bandwidth of 158 GHz, corresponding to the Er absorption band. This introduces limitations in the bandwidth of operation of the device. Could the authors comment on the possible strategies to extend this range, or even to make it tunable?\n3) In the Discussion section the authors claim that there is no Purcell enhancement coming from slow-light. To my understanding, this implies that photon pairs are generated over the broader spectrum of the bare resonance, and not only in the narrow spectral region of SHB. Am I missing something? Is it possible to exploit slow-light effects to generate ultra-narrow band photon pairs naturally matched to atomic memories?\n4) The statement “We note that moving to lower temperatures and/or higher magnetic fields would extend the lifetime of our spectral holes beyond the Er optical lifetime and enable operation without this spontaneous emission background” is a little bit confusing to me. Isn’t the lifetime of the hole upper bounded by the Er optical lifetime? Moreover, can the authors comment about the observed background intensity at the investigated temperature and magnetic fields? What are the count/rates at the output waveguide?\n5) I suggest to incorporate Fig.S1 into Fig.1 of the main manuscript to better understand the experimental setup."}, "author_response": "Response to Reviewers\nReviewer #1 (Remarks to the Author):\nThis is a very interesting work, where the authors presented sound experimental results to sup-\nport the idea of using slow light to obtain high-Q resonance, and coupled with a theoretical model.\nThe paper reported significantly improved high quality factors (>108) in lithium niobate microring\nresonators by employing a spectral hole burning (SHB) using erbium as dopants. The interaction\nbetween a spectrally narrowed resonance and a broader bare resonance produces a Fano lineshape,\nwhich is electro-optically tunable. The authors also developed a theoretical model to explain the\nobserved linewidths, showing that strong optical driving significantly reduces the erbium dephasing\nrate, resulting in narrower linewidths than expected from standard models. The findings presented\nin the work points out a new direction in achieving high-Q microresonators. I’d recommend accep-\ntance after the authors address the following points in a revisions.\nWe thank the reviewer for their interest and valuable feedback on this work.\n1. If this is the first work to observe such phenomena (Modified Bloch Equation model) and\nenhance Q-factor with almost 3 orders? If so, can this novelty be emphasized in the abstract. If\nthere were prior work, could you provide a brief overview on how researchers used similar strategy\nto enhance Q-factor of resonators, or other applications?\nWe thank the reviewer for the feedback. The modified Bloch theory approach has been previously\nobservedinbulkrare-earthcrystals[1]wheretherelevantregimeisonlyjustbarelyachievablegiven\npractical optical powers. It becomes an important effect here due both to the large circulating\nintensity in our nanophotonic resonators and due to the large initial gap between the lifetime and\ncoherence time in the lithium niobate host. We emphasize the importance of this effect for other\nsimilarsystemsinourdiscussion,butsincewearenotthefirsttorecognizeit,wedonotclaimnovelty.\nThe slow light narrowing of the resonance has also been observed in bulk cavities and microres-\nonators, but implementing it in a nanophotonic device is new. We note that Zhao et al. [2] saw a\nsimilar effect (away from the telecom band and without elecro-optic tuning), but their description\ndiffers substantially. We have added a line to the abstract to emphasize the novelty.\n2. TheauthorshintthatQ-factorsexceeding108 arefeasibleifthebarecavityQcanbeimproved\nto 2×107. Does the observed Q-factor enhancement factor ( 700×) independent of the bare cavity\nQ? Are there fundamental or practical upper limits to the Q-factor achievable with this method?\nWhat are the requirements for materials to achieve such feats? e.g. can this approach be applied to\nother material platforms or dopants beyond erbium?\nYes, indeed, the Q-factor enhancement achievable is fundamentally independent of the bare cav-\nity Q, since according to Equation (2), the scaling factor ∆ /κ can be decoupled from the bare\nhole Er\n1\ncavity κ. Thus, in theory, the narrowed Q will increase by the same factor we can increase the bare\nQ by improving our fabrication.\nBecause we use the same input/output port for both burning and probing, the hole width (∆ )\nhole\nin practice has some dependence on the bare cavity κ due to power buildup in the resonator, re-\nsulting in wider holes for a given input power P . However, hole burning could be performed by\nin\nilluminating the chip from the top using an objective or lens, which would make ∆ completely\nhole\nindependent of κ.\nFundamentally, the hole width is limited to 2γ, implying that our current configuration could, in\nprinciple,enableuptoa∼33,000×increaseintheQ-factor. Thatsaid,achievingradiativelylimited\nhole widths requires extremely weak optical powers, which cannot be implemented by propagating\nalong the large optical depth where the power drops over the propagation length. Furthermore, the\nrelativelyshortholelifetimeinoursystemmeansitishardtoburnforlongenoughtogetadeephole\nwithlowpowerbeforetheholerefills. Thesechallengescanbeovercomebytopilluminationtoavoid\nthe optical depth challenges and by increasing the hole lifetime by moving to lower temperatures,\nhigher magnetic fields, and/or isotopically purified dopants.\nThecurrentschemecanbegeneralizabletootherrare-earthdopedmaterials,suchasPr,Eu,Tm,and\nYb,whoseabsorptionbandsareinthevisibleandNIR.Forinstance,Saboonietal. [3]demonstrated\nasimilarQ-factorenhancementinabulkcavityusingPr:YSO.Theprimarycriterionwhenselecting\na dopant is whether narrow holes (or equivalently, transparency windows) can be created, which is\nultimately governed by the decoherence rate γ. Using a host material like YSO enables particularly\nlargenarrowingfactorsduetothelongopticalcoherencetimeandnarrowinhomogeneouslinewidth.\n3. Pleaseclarifytheexpectedrelationshipbetweenlinewidthandinputpowerforeachtheoretical\nmodel shown in Figure 4. Specifically, why does the linewidth increase with increasing input power\nfor both models?\nWe thank the reviewer for the feedback and want to clarify that the power here is the power used\nto create the spectral hole, not the power of the field used in the measurement of the feature.\nThe (cid:16) (cid:17)\nloss rate of our resonance is generally given by the expression κ SL = ∆ κ h E o r le κ, as described in the\nsection on Modified Bloch theory. The dependence on input burn power arises through the hole\nq √ q\nwidth ∆ hole = 2Ω γ γ s , where the Rabi frequency √ is given by Ω = 2g κ/ κ 2 ext h¯ P ω in c . This leads to\na naive expectation of linewidth scaling as κ ∝ P due to power broadening in the saturable\nSL in\nabsorber medium.\nWhileconventionalBlochtheorypredictsthatthedecoherencetime—andhencetheholewidth—does\nnot depend on the input power, our data shows clear deviations. This is captured by a modified\ndecoherence rate γ = γ + γs, which introduces additional power dependence in the hole\nmod 1+(Ωτc)2 2 √\nwidth and thus the resonance linewidth. This results in a slower-than- P scaling at intermediate\nin\npowers. However, at higher powers, γ asymptotically approaches the radiative limit γ /2, caus-\nmod √ s\ning the linewidth to once again scale approximately as P . Therefore, in both theoretical models\nin\nshown in Fig. 4, the linewidth increases with increasing input burn power: initially slower due to\ndecoherence narrowing, then faster as the system approaches the power-broadened limit. We have\nadded a figure and more discussion in the Supplementary Section 2F showing the large qualitative\ndeviation from the conventional scaling with Rabi frequency.\nWe have edited the following sentences for further clarity in the main text\n2\n“It is also important to note that the experimental data also aligns qualitatively with\nthe trend predicted by the modified theory, deviating from the standard saturable ab-\n√\nsorber power broadening κ ∝ P dependence expected from the Bloch model. The\nSL in\nmodification accounts for the significant decoherence narrowing at higher input power,\nsuppressing the linewidth increase from the power-broadening term”\n4. I wonder if the achieved high Q can be related to the reduced loss in the SHB regime,\nand the microring is operating at under-coupling condition, which could also result in increased\nQ.\nWethankthereviewerforthegreatquestion. Yes,thisquestionpuzzledustoointhebeginning.\nHowever, we figured out this is not the case. First, the loss in the SHB regime is the same as the\nlosswhenwetunethelaserfarfromtheerbiumabsorption(whatwecallthebarecavitymode). By\nhole burning we recover the near critical coupling we see in that regime. Furthermore, we directly\ndetermined that the width of our resonances are much narrower than the width of the low-loss\nspectral hole by performing spectral hole burning in a waveguide structure where we can directly\nmeasure the resulting hole width and observe that for a given optical burn power the hole width is\nmuchbroaderthanthecorrespondingresonanceinthering. Thisimpliesthattheresonancefeature\ncannot be explained by reduced absorption alone, and we see that by using the inferred hole width\ntocalculatethegroupvelocitywecanaccuratelypredicttheslow-lightinducednarrowing. Wehave\nprovided some details on this in the Supplemental section 2F as -\n“As a representative example (Fig. S5a) of spectral hole burning in a waveguide, we\nused a pump power of 120 nW, corresponding to a Rabi frequency of 2π ×780 kHz.\nThis is lower than the Rabi frequency observed in the ring resonator (∼ 2π×10 MHz)\nat the same power. Nonetheless, we observed broader hole with ∆ = 2π×39 MHz\nhole\n(Fig. S5a), significantly wider than those in the resonator, with a linewidth of κ ≈\nSL\n2π×3MHz. Thisobservationconfirmsthatthenarrowfeaturesobservedintheresonator\nare not solely due to reduced absorption. If they were, we would expect the resonator\nlinewidth to be comparable to the spectral hole width, i.e., κ ∼ ∆ . Instead, we\nSL hole\nmeasure κ < ∆ , indicating that the resonator features are primarily governed\nSL hole\nby dispersion effects rather than reduced absorption alone. Additionally, the similar\ndepth of transmission observed in Fig. 1 indicates that the coupling condition is nearly\nmaintained. Thisfurthervalidatesthatthedeviceisnotbecomingseverelyundercoupled\ndue to reduced absorption, but rather that the slow-light effect is the main source of the\nobserved narrowing. ”\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nThe manuscript reports on the experimental demonstration of spectral hole burning in erbium-\ndoped lithium niobate, with a focus on potential applications in laser stabilization. The work is\ninteresting, and the results are of interest to the photonics community. However, the novelty and\nsignificance of the findings do not, in my view, meet the high bar required for publication in Nature\nCommunications and more rigorous analysis is needed. The manuscript would be more appropri-\nately suited for a specialized optics journal such as Optics Express or Optics Letters.\nWe thank the referee for their careful reading of our manuscript. We agree with the other ref-\nerees that our findings are of broad interest and demonstrate the novelty and significance required\nforpublicationinNatureCommunications. Inparticular,wedidnotintendtofocusonapplications\nin laser stabilization, as we believe there are many exciting applications for our devices throughout\nquantum and classical photonics (tunable narrowband filtering, efficient on-chip delays and photon\nstorage, high resolution dispersion engineering, and more). We have highlighted these throughout\nthe text, and we address the referee’s concerns below.\nMajor Concerns:\n1)The work has limited Impact for laser stabilization. The observed spectral hole linewidth (∼\nstate lifetime on the order of milliseconds and hyperfine levels with coherence times up to seconds,\nthe performance falls short of what has been demonstrated using other rare-earth ions such as\npraseodymium and europium, which exhibit much narrower linewidths and significantly longer co-\nherence times (up to days) as cited in references [49, 50]. Also, spectral hole burning for laser\nstabilization has been previously demonstrated using rare-earth-doped crystals with much narrower\nholelinewidths. Forexample,seetheIEEEconferencepaper“SpectralHoleBurningforUltrastable\nLasers” (2021), which demonstrates far superior stabilization performance.\nWe mentioned on-chip laser stabilization as a potential application of this device, and we can\nclarify that we do not claim any laser stabilization or mean to imply that is the only potential\napplication here. However, we would point out to the reviewer that there are virtually no other\nways to obtain a < 2 MHz linewidth feature suitable for laser stabilization in a nanophotonic\nplatform. For making compact and scalable atom and ion traps, integrating the laser and the laser\nstabilizationonchipwouldbeanimportantstep. Furthermore,wepointoutinthemanuscriptthat\nachieving well sub-MHz features should be straightforward with modest improvement of our device\nfabricationtoreachthecurrentstateoftheartforthebareQfactor. Wehaveclarifiedourmeaning\nin the text and added references for laser stabilization to slow light narrowed cavities:\n“Another challenge, particularly for quantum information, is integrating highly stable\nlasers with chip-based atom and ion traps. This requires a sub-MHz reference for laser\nstabilizationthatiscurrentlyoutofreachinanintegratedplatform,butshouldbeeasily\nattainable with our system [4].”\n2)Several other groups, including those of Andrei Faraon, Hong Tang, and Edo Waks, have al-\nready reported narrow-linewidth on-chip rare-earth photonic systems. See, for instance Ref.1 [ npj\nNanophotonics 1, 22 (2024)]. The current manuscript does not sufficiently distinguish itself from\nthese prior efforts nor it offers a new understanding. If the narrow hole is used to stabilize a laser it\ncan be well differentiated from Ref1.\nWe agree with the referee that these other groups are investigating similar systems and that\nthe work from Edo Waks’s group in particular is related to ours. However, our work has a few\nclear advances over that paper. First, our system has two key features, telecom-band operation\nand electro-optic tunability, that dramatically broaden the potential applications over the system\nin Zhao et al. [2], particularly for tunable narrowband filtering. Second, and no less important, we\nprovide a much more complete and robust theoretical description of the phenomenon. Unlike the\nattribution in that work of the narrow feature to the reduction in absorption, we show conclusively\nthat the narrowing is due to the slow light effect (see our response to referee 1 for more details).\nFurthermore, we provide a comprehensive theoretical description for the spectral hole width in the\npresence of a dephasing spin bath. We have added a figure that shows conclusively that the hole\nwidth does not scale linearly with the Rabi frequency (as is suggested in that reference) and can\nonlybeaccuratelypredictedbyaccountingforthestrongdependenceofthedephasingonthepump\npower.\nWe agree that Mi Lei. et al. [5] from Andrei Faraon’s report narrow transparency window in\nan on-chip platform. However, the physical origins of their transparency window are fundamentally\ndifferent. This is most evident from the fact that their transparency window width decreases as\nthey raise their input power. In the theoretical model detailed in the supplementary material, we\nhave deliberately adopted the same notation used by Mi Lei. et al. so that interested readers can\ncompare the differing origins of the observed narrow features.\n3)Fig. 1d shows the off-atomic-resonance cavity linewidth. It’s not clear what frequency detun-\ning is used. I think at this Q factors, event 100s of GHz is not large enough to avoid atomic\nabsorption, given inhom broadening of Er in LN.\nWe thank the reviewer for pointing out the missing information. The resonator position off res-\nonance was at 1534.5 nm, which is roughly ≈ 450 GHz away from the center of the ≈ 160 GHz\ninhomogeneous line. Fig. S4a of the supplemental information shows directly that the Er absorp-\ntion near 1534.5 nm is minimal. Furthermore, we added additional data by fabricating identical\ndevices with no Er in LN. We get a Q-factor 2.3×105 which is very close to the Q-factor we get\nEr:LN off the absorption. Therefore, we believe it would be safe to conclude the intrinsic Q-factor\noff the atomic frequency is mainly limited by scattering losses of LN. We have made appropriate\nedits in the main text and the additional data supplementary information Section 2E.\n4)The authors state that the assumptions made when deriving the theoretical models for the\nlinewidth narrowing do not accurately describe the experiments of Section A. Additional context is\nrequiredastohowthemodelsdeviatefromexperimentalconditionsandhowsuchdeviationimpacts\nthe accuracy of these explanations.\nIn the first section labeled Slow light-induced linewidth narrowing, the hole burning period is\n50 µs. This is not long enough to reach steady state, which is assumed in our modified Bloch\nmodel, and as a result the observed holes are narrower by a factor of up to 2 than predicted by\nour model. Our model does accurately capture the hole widths for longer burn times where steady\nstate is reached, while the conventional Bloch model predicts holes more than 10× broader than\nseen in either regime and does not capture the qualitative shape of the hole width vs burn power.\nWe emphasize that our model is not capable of perfectly capturing our experimental results due to\n6\ntheeffectofabsorptioninthebuswaveguidesandotherexperimentalartifacts,butitcapturesboth\nthe qualitative and quantitative behavior that is missed by orders of magnitude with a conventional\ntreatment. We have added a figure to the supplemental information (Fig. S5) to show the dramatic\ndeviation from the simple linear dependence on Rabi frequency that one would expect without the\neffect of power dependent decoupling from the spin bath.\n5)The claimed observation of Fano resonances is not well supported by the experimental data.\nThe line shape asymmetry is weak and does not convincingly match theoretical expectations. A\nmore rigorous comparison between theory and experiment is needed.\nWe thank the reviewer for the thoughtful feedback. We would like to clarify that the main\nnovelty emphasized in this manuscript is the electro-optic tuning of the observed lineshape, not\nthe asymmetric, Fano-like character. We have modified the manuscript to refocus this emphasis.\nThisuniquetuningcapabilityrepresentsanimportantsteptowardadaptableopticalfilterresponses\nand fast switching applications. Our theoretical model predicts an asymmetric Fano-like resonance\narising from the interference between a narrow resonant mode and a broader continuum. The\nassociated shift is accurately predicted by our model in figure 3 (which we note is not a fit, but\ntheory based on independently measured parameters). The discrepancy in the shape at higher\ndetuningsismostlikelyduetouncertaintiesintheextractedparametersandtheeffectofabsorption\nin the bus waveguide. At lower optical depth (near the edge of the Er absorption band at 1530.3\nnm) we see clearly asymmetric Fano shapes, and we have included the figure and analysis in the\nSupplementary Section 2H showing this. We added the following sentence in the main text to\nemphasis this discussion -\n“In Fig. 3a we see a clear shift of the experimentally measured resonance as we detune\ntheburnlaserfromthecenterofthebarecavitymode. Thecenteroftheslowlightmode\nmatches our theory predictions, though the shape deviates due to the uncertainties in\nthe extracted parameters and the effects of residual absorption in the bus waveguide.\nWe see clear Fano shapes when the optical depth is lower and this residual absorption is\nsmaller (see Supplementary Section 2H). ”\n7\n6)Additionally, theclaimofobservingaholelinewidthbeyondthepredictionsofstandardBloch\ntheory is not convincingly supported by the experimental data or theoretical analysis. The theo-\nretical model shows comparable deviation from the experimental data even at low optical powers,\nunderminingtheargumentthatpowerbroadeningaloneisresponsible. Moreover,thedefinitionand\napplicationoftheRabifrequencyinthecontextofaninhomogeneouslybroadenedensemblearenot\nclearly established, making the comparison between theory and experiment less rigorous. Further\ndetail and justification are necessary to substantiate this claim.\nWethanktherefereeforcarefulreadingofthemanuscriptinidentifyingthisimportantsubtlety. We\ngive a detailed response to this issue here, but the top line is that any theory that assumes a linear\ndependence on the Rabi frequency has massive qualitative and quantitative disagreement with our\ndata. We recognize that this is not fully evident from our figure 4, so we include additional data in\nthe supplemental where we are able to use lower burn powers in a short waveguide rather than in\na resonator. This plot we have added to the supplement is reproduced below here for convenience.\nWesee that theshapeof the holedependenceon Rabi frequency is farfrom linear. We also seethat\nour theory (which is not fully valid for the waveguide data, further explained in the Supplementary\nSection 2F) captures the qualitative trend as well as predicting the right approximate hole width.\nThe standard approach predicts a linear dependence with values orders of magnitude larger.\nThe reviewer points out that the theoretical model shows deviation from the experimental data\neven at low powers. We would like to highlight that even at low optical powers, the electric field\n(andconsequentlytheRabifrequency)isfarhigherinoursystemascomparedtoatypicalfreespace\nsystem involving collimated beams with comparable optical power. The reason for this is twofold-\noneistheconfinementofthefieldinthewaveguideandtheotheristhecirculatingpowerinthering\nresonatoronresonanceishigherduetoconstructiveinterferencebetweenmultiplepasses. Thepower\nvalues in the plot are input power values. In our case, the circulating power is nearly 12 times the\ninput power. As a result, even at the lowest reported input power, the electric field assumes values\nthat are high enough that one would expect departure from the standard Bloch theory predictions\n8\n(see [6]). We could not attempt lower pump power in the ring, since the pump powers were not\nenough to get an effective hole across the entire ring.\nTothisend, wecollectedadditionaldataofspectralholewidthsinashortwaveguideandcompared\nit with the modified bloch theory estimates from Equation (3). The theoretical model showcases a\n√\nqualitative agreement with the waveguide data, clearly showing a deviation from ∝ Ω or ∝ P .\nin\nWe note, however, that the ring-based estimates relied on several extracted parameters determined\nfrom independent measurements, and uncertainties in these parameters may contribute to the ob-\nserved deviations. Furthermore, at lower Rabi frequencies, additional refinements to the theoretical\nframework would be required to achieve a more quantitative match. We plan to investigate these\ncorrections in future work and have added this information in the supplementary section 2F.\nThereviewerstatesthattheRabifrequencyisnotclearlyestablishedforaninhomogeneouslybroad-\nenedensemble. Bythis, weassumethatthereviewerishighlightingthefactthattheionswhichare\ndetuned from the pump laser, experience a detuning dependent generalized Rabi frequency. This\nspecific question has been addressed in [7]. According to the conclusions obtained in the reference,\nthe generalized Rabi frequency can be replaced with the resonant Rabi frequency without a signif-\nicant change in the predicted linewidths. The main difference in the two cases lies in the extent of\nnon-Lorentzian character of the predicted spectral holes.\n7)The symbols used for variables such as coherence times are inconsistent between the main text\nand the Supplementary Material.\nThank you for pointing out this error. We have changed the notation of γ to γ to make it\nmod m\nconsistent between the main and supplementary text.\n8)The magnetic field strength, which is referenced in the analysis, is not specified in the main\nbody of the manuscript and should be included.\nWe have included the magnetic field value in the Figure 1b caption.\n9)TheMimsdecoherenceformula(Eq. S43)intheSupplementaryMaterialismissinganappropriate\ncitation.\nWe have added the following references B¨ottger et al. ([8]) and Wang et al. ([9]) in the Supplemen-\ntary text.\n10)The predicted maximum quality factor of 1010 exceeds the theoretical limit for lithium nio-\nbate (1.63×108). This discrepancy should be acknowledged and explained.\nWe thank the reviewer for this observation. The value of 1.63×108 represents the material-limited\n10\nquality factor of lithium niobate under the assumption of negligible scattering losses and in the\nabsence of dispersion or slow-light effects. In contrast, our predicted maximum Q of 1010 arises\nfrom slow-light resonances, where the reduced group velocity effectively enhances the photon life-\ntime beyond the conventional material limit. We clarify the point by stating the following in the\nmain -\n“The commonly cited upper bound of 108 in LN arises from material limits under the\nassumptionofnegligiblescatteringandnoslow-lighteffects. Withstate-of-the-artTFLN\nfabrication (Q=2×107 [10]), slow-light resonances could surpass this bound, reaching\neffective Q factors approaching 1010”\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nThe authors report on an experiment where they realized slow-light effects in a Erbium doped\nthin film lithium niobate (TFLN) resonator through spectral hole burning. Slow light is used to\nincrease the roundtrip time of a weak coherent probe inside the hole band, demonstrating an im-\nprovement of nearly three orders of magnitude in the quality factor compared to the bare cavity\nmode. The authors also provided a comprehensive theoretical model of the Erbium ions dynamics\nwithin the cavity, including the effects of decoherence caused by the external environment and the\nbath-decoupling induced by the strong optical circulating intensities within the cavity. In general,\nthere is a good match between the theory and the experiment, especially by considering the large\nnumber of free parameters in the model, which have been experimentally extracted by conducting\nindependent experiments. The authors also proposed to exploit the ultra-high Q that would be\nreached in state-of-art TFLN for optical filtering, laser stabilization and narrow-band photon pair\ngeneration. Overall the manuscript is well written and present convincing results that might be of\ninterest for the broad audience working in the field of quantum optics, spectroscopy, laser stabiliza-\ntion and sensing. I have some concerns that should be addressed before considering it ready for\npublication in Nature Communications:\nWe thank the reviewer for their interest and constructive feedback on this study.\n1)TheintrinsicQoftheresonatorisaround500000(471MHzbandwidth), whichisbelowstate\nof art for TFLN. Is this due to the Er doping? Do the authors have any data on the intrinsic Q\nof cavities without Er doping? I believe this is an important point of discussion if ultra-high Q\nexceeding 1010 are targeted.\nWe thank the reviewers for their feedback. We characterized an identically fabricated undoped\nLN device, which showcased an intrinsic Q of nearly 4.94×105. This is quite close to the intrinsic\nQ we obtained in the Er:LN. The small variation may arise from the difference in the growth\nprocess of the LN wafer or variation in fabrication, for instance, the thickness variation across\nthe chip. Therefore, we don’t attribute the Er absorption to be a significant source of loss off the\ninhomogeneousbroadening. Wehaveincludedthisdiscussioninthemaintextandthesupplemental\nsection 2E.\n“We further measured similar κ for identically fabricated devices with no Er, validating\ni\nthat the loss rates are mainly limited by the sidewall roughness of waveguides (Supple-\nmentary Section 2E)”\nOur Q-factor is lower than the state-of-the,-art art can mainly be attributed to the difference in\nfabrication adopted. We use ZEP as our resist, which may be inferior to HSQ resist due to the\nresolution and stability of the mask under intense etching conditions. We may need to also further\nimprove our post cleaning procedures to reduce the effects of redeposition. We believe by utilizing\nfoundry level fabrication technique we can improve the current result and allow even narrower\nlinewidths.\n13\n2) Slow-light effects are limited to a narrow-bandwidth of 158 GHz, corresponding to the Er\nabsorption band. This introduces limitations in the bandwidth of operation of the device. Could\nthe authors comment on the possible strategies to extend this range, or even to make it tunable?\nWethankthereviewerfortheirinsightfulquestion. Weacknowledgethattheschemeproposedin\nthe manuscript is inherently limited by the absorption properties of the rare-earth ion. Since these\nare fixed-frequency transitions, and the inhomogeneous broadening can only be modestly tuned via\nstrainorotherperturbations,itisindeedchallengingtodynamicallytunetheoperationalbandwidth\nwithout changing the material system.\nEr:LN is particularly attractive because it offers one of the largest inhomogeneous broadenings\namong rare-earth-doped materials, enabling a relatively broader bandwidth of operation. One po-\ntential strategy to extend the usable spectral range would be to co-dope the material with other\nrare-earth ions such as Pr, Yb, or Tm. While this approach would still constrain operation to dis-\ncrete absorption lines, it would enable access to a broader range of wavelengths corresponding to\nthe inhomogeneous profiles of the co-doped ions.\nAlternatively, rare-earth-doped glasses such as Er-doped silica offer even larger inhomogeneous\nbroadening, up to 1.3 THz (10 nm), as demonstrated by Saglamyurek et al. [11]. Adapting our\nscheme to such materials may allow for broader bandwidths, though it would require re-engineering\nof the photonic platform. We have added a sentence in the discussion to point out this issue -\n14\n“The proposed scheme is fundamentally limited by the fixed absorption frequencies and\ninhomogeneous broadening of rare-earth ions, with potential extension to other dis-\ncrete wavelengths through co-doping oralternative materialswith largerinhomogeneous\nbroadening, such as Er-doped silica [11].”\n3)IntheDiscussionsectiontheauthorsclaimthatthereisnoPurcellenhancementcomingfrom\nslow-light. To my understanding, this implies that photon pairs are generated over the broader\nspectrum of the bare resonance, and not only in the narrow spectral region of SHB. Am I missing\nsomething? Is it possible to exploit slow-light effects to generate ultra-narrow band photon pairs\nnaturally matched to atomic memories?\nWe would like to clarify that the slow-light narrowing, in itself, does not lead to an increase in the\nPurcellfactorrelativetothebarecavity. Rather,thespectrallynarrowedcavitymoderesultingfrom\nslowlightservesasaneffectivenarrowbandspectralfilterforphotonsgeneratedviaprocessessuchas\nspontaneous parametric down-conversion (SPDC). Consequently, while the slow-light configuration\nenablesthegenerationofentangledphotonpairswithinanultra-narrowspectralwindow,itdoesnot\nenhancetheoverallpairgenerationrate. Nonetheless,astherefereecorrectlynotes,suchnarrowband\nphoton pairs are highly desirable for interfacing with atomic quantum memories. Moreover, lithium\nniobate is a particularly promising platform for this purpose due to its intrinsic support for efficient\nSPDC via periodic poling. We have added a sentence in the discussion about this point -\n“Such a device is vital for quantum applications to collect photons from spin qubits or\nother highly coherent sources. Combined with the ability to generate entangled photon\npairsinlithiumniobate,ournarrowbandfeaturescouldbeusedtogeneratephotonswith\nsufficiently narrow linewidths to interface with narrowband spin qubits. This is a major\nchallenge in quantum information and can currently only be achieved with free-space\ncavities [12].”\n4) The statement “We note that moving to lower temperatures and/or higher magnetic fields\nwould extend the lifetime of our spectral holes beyond the Er optical lifetime and enable operation\nwithout this spontaneous emission background” is a little bit confusing to me. Isn’t the lifetime of\nthe hole upper bounded by the Er optical lifetime? Moreover, can the authors comment about the\nobserved background intensity at the investigated temperature and magnetic fields? What are the\ncount/rates at the output waveguide?\nWe thank the reviewer for the insightful question. Yes, in our current experiment, we utilize the\n4I excitedstatetoburnaspectralhole,whichresultsinatransientspectralhole. Analternative\n13/2\napproach involves persistent spectral hole burning, which transfers the population to a lower-lying\nmetastable state.\nHowever, our present experimental conditions, specifically a high doping concentration (0.5%), rel-\natively low magnetic field (<0.2 T), and an operating temperature around 2 K, pose a challenge for\nachieving persistent holes. Under these conditions, the spin lifetime is short due to a higher spin\nflip rate, which limits the hole’s persistence.\nTo enable persistent spectral holes, one would typically need to lower the temperature further or\nincrease the applied magnetic field. This suppresses neighboring nuclear spin flips and extends the\nspin lifetime, allowing persistent holes to last for several minutes, as demonstrated in Thiel et al.\n[13]. Currently, due to the limitation of our instrument, we are unable to showcase persistent holes\nbut this should be possible in a dilution refrigerator with an appropriate vector magnet.\nThenoisecounts/secduetothephotoluminescenceofErisshownbelowatthethroughport. Itcan\nbe clearly seen the noise exhibits >107 counts/sec at measurement times below 1 ms. The noise is\nsignificantly reduced if we measure well beyond the optical lifetime. We have added this plot (Fig.\nS7c) and the analysis in supplemental information Section 2I.\n15\n5) I suggest to incorporate Fig.S1 into Fig.1 of the main manuscript to better understand the\nexperimental setup.\nWe thank the reviewer for this suggestion. We feel that including the setup figure in the main\ntext would not provide additional insights into the experiment, but rather add technical details on\nhow the setup is constructed. We also acknowledge that Fig. S1 and Fig. 1 (a) and (b) were\nnot explicitly referenced in the main text, and we have now incorporated the relevant references.\nFurthermore, we have expanded the description of the experimental setup in the Methods section\nto provide additional clarity. We believe that including Fig. S1 directly in Fig. 1 would make the\nillustration cluttered and reduce readability.\n[1] DeVoe, R. G. & Brewer, R. G. Experimental test of the optical bloch equations for solids.\nPhysical Review Letters 50, 1269 (1983).\n[2] Zhao, Y. et al. Cavity-enhanced narrowband spectral filters using rare-earth ions doped in\nthin-film lithium niobate. npj Nanophotonics 1, 22 (2024).\n[3] Sabooni, M., Li, Q., Rippe, L., Mohan, R. K. & Kr¨oll, S. Spectral engineering of slow light,\ncavity line narrowing, and pulse compression. Physical review letters 111, 183602 (2013).\n[4] Gustavsson, D. et al. Using slow light to enable laser frequency stabilization to a short, high-q\ncavity. Optics Express 33, 2866–2877 (2025).\n[5] Lei,M.etal. Many-bodycavityquantumelectrodynamicswithdriveninhomogeneousemitters.\nNature 617, 271–276 (2023).\n[6] Berman, P. & Brewer, e. R. Modified optical bloch equations for solids. Physical Review A 32,\n2784 (1985).\n[7] Yamanoi, M. & Eberly, J. Hole-burning line shape at high intensity. Physical Review A 34,\n1609 (1986).\n[8] B¨ottger, T., Thiel, C., Sun, Y. & Cone, R. Optical decoherence and spectral diffusion at 1.5 µ\nm in er 3+: Y 2 sio 5 versus magnetic field, temperature, and er 3+ concentration. Physical\nReview B—Condensed Matter and Materials Physics 73, 075101 (2006).\n[9] Wang, S. et al. Er: Li nb o 3 with high optical coherence enabling optical thickness control.\nPhysical Review Applied 18, 014069 (2022).\n[10] Zhu, X. et al. Twenty-nine million intrinsic q-factor monolithic microresonators on thin-film\nlithium niobate. Photonics Research 12, A63–A68 (2024).\n[11] Saglamyurek, E. et al. Broadband waveguide quantum memory for entangled photons. Nature\n469, 512–515 (2011).\n[12] Rakonjac, J. V. et al. Entanglement between a telecom photon and an on-demand multimode\nsolid-state quantum memory. Physical review letters 127, 210502 (2021).\n[13] Thiel, C. et al. Optical decoherence and persistent spectral hole burning in er3+: Linbo3.\nJournal of Luminescence 130, 1603–1609 (2010).\n17"}, {"round": 2, "reviewer_comments": {"reviewer_1": "We are satisfied with the authors response and revision.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "Authors provided more details and additional data in the supporting document. This is an interesting work and added data to the supplementary materials is helpful, but I still have reservation about the suitability of the current work for publication in Nature Communications. The impact and rigor of the current results are limited.\nAlso, authors indicate that tunability of a narrow-line resonance is a key result of the paper. Figure 3 shows that tuning the volage leads to shift of the resonance but also broadening of the line. This should be explained. Authors should also discuss what limits the tuning range.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_5": "The authors properly addressed most of my concerns and I think the paper is now almost suited for publication.\nThere is still however a point which is not clear to me, specifically the answer to point 3. I understand that the circulating field in the resonator is not enhanced within the spectral hole region. However, due to this fact, I am expecting the field enhancement to be essentially the same of the bare cavity mode, i.e. having a Lorentzian profile with a FWHM equal to that of the bare cavity mode. Since the spectral width of the generated signal-idler photon pairs depends on the product of their field enhancements, their joint-spectra should have a FWHM of the order of the bare cavity mode.\nTherefore, I am not expecting the system to directly generate pairs with ultra-narrow spectra. The ultra high-Q resonator could be used as a narrow spectral filter for broadband photon pairs generated from a different resonator, but in this case it would act as a passive filter.\nIs that something which I am missing? I think this is an important point to be clarified, since one of the major statements in the conclusions is that \"Combined with the ability to generate entangled\nphoton pairs in lithium niobate, our narrowband features could be used to generate photons with sufficiently narrow\nlinewidths to interface with narrowband spin qubits. This is a major challenge in quantum information and can currently only be achieved with free-space cavities\"."}, "author_response": "Response to Reviewers\nReviewer #1 (Remarks to the Author):\nWe are satisfied with the authors response and revision.\nWe thank the reviewer for their previous comments and their positive review.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank the reviewer for their input.\nReviewer #3 (Remarks to the Author):\nAuthors provided more details and additional data in the supporting document. This is an in-\nterestingworkandaddeddatatothesupplementarymaterialsishelpful, butIstillhavereservation\nabout the suitability of the current work for publication in Nature Communications. The impact\nand rigor of the current results are limited.\nWe believe the significant enhancement enabled by the slow-light effect in atomic systems remains\nwidely unexplored within the nanophotonics community. This work could enable important appli-\ncations such as ultrafast narrowband filtering, optical switching, quantum memory, and more. We\nalso present foundational advances through our modified Bloch theory framework. Taken together,\nthese results not only deepen the theoretical understanding of slow-light phenomena in cavities but\nalso provide readers with versatile platform to explore new directions. We expect that this paper\nwill inspire numerous possibilities, making it well suited for the broad readership of Nature Com-\nmunications.\nAlso, authors indicate that tunability of a narrow-line resonance is a key result of the paper. Figure\n3 shows that tuning the volage leads to shift of the resonance but also broadening of the line.\nThis should be explained. Authors should also discuss what limits the tuning range.\nWe thank the reviewer for their comments. We show a tunability range of ≈ 15 MHz (corre-\nsponding to > 5 linewidths) over ≈ ±30 V of applied voltage (limited by our electro-optic setup).\nThe applied voltage tunes the cavity resonance (at ≈0.12 GHz/V) and the interference of the spec-\ntrally narrow resonant mode and the broad damped cavity resonance produces a Fano resonance,\n1\nwhose minimum shifts with the detuning of the damped resonance and the burn laser frequency.\nThe resonance also exhibits the characteristic broadening and asymmetry associated with such a\nFano lineshape. The electro-optic tuning range depends on a number of parameters, including the\nprepared hole width and the Er optical density, though in our case we are limited by our voltage\nsupply. We note that this is the dynamic tuning range that is possible with electro-optics. We can\nplacethenarrowfeatureanywherewithinthe≈160GHzabsorptionbandwidthoftheErbytuning\nour hole burning field.\nWe have added the following sentences in the manuscript:\n“As shown in Fig. 3b, we observe a voltage-induced tuning range of ≈ 15 MHz, limited\nby our electro-optic setup. We also note that the system exhibits a broader spectral\nresponse at higher applied voltages, a characteristic feature of the Fano lineshape under\nincreased detuning.”\nReviewer #4 (Remarks to the Author)\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nWe thank the reviewer for their input.\nReviewer #5 (Remarks to the Author)\nThe authors properly addressed most of my concerns and I think the paper is now almost suited\nfor publication. There is still however a point which is not clear to me, specifically the answer to\npoint 3. I understand that the circulating field in the resonator is not enhanced within the spec-\ntral hole region. However, due to this fact, I am expecting the field enhancement to be essentially\nthe same of the bare cavity mode, i.e. having a Lorentzian profile with a FWHM equal to that\nof the bare cavity mode. Since the spectral width of the generated signal-idler photon pairs de-\npends on the product of their field enhancements, their joint-spectra should have a FWHM of the\norder of the bare cavity mode. Therefore, I am not expecting the system to directly generate pairs\nwith ultra-narrow spectra. The ultra high-Q resonator could be used as a narrow spectral filter\nfor broadband photon pairs generated from a different resonator, but in this case it would act as\na passive filter. Is that something which I am missing? I think this is an important point to be\nclarified, since one of the major statements in the conclusions is that ”Combined with the ability to\ngenerateentangledphotonpairsinlithiumniobate,ournarrowbandfeaturescouldbeusedtogener-\nate photons with sufficiently narrow linewidths to interface with narrowband spin qubits. This is a\nmajorchallengeinquantuminformationandcancurrentlyonlybeachievedwithfree-spacecavities”.\nWe thank the reviewer for their careful reading of our manuscript. These questions have led us\nto think more deeply about making photon pairs in our system and it turns out that we think this\nis a theoretical problem that requires substantial analysis that is beyond the scope of this paper\n(and may turn into a theory paper in its own right). The referee is correct that the electric field\nenhancement is the same as the bare cavity mode, but we don’t think this corresponds to pair pro-\nduction with the same bandwidth as the bare cavity mode because the spectral hole is acting as an\nintra-cavity filter,notasafilterafterpairproduction. Wearelookingintothisfurther,butwethink\n2\nthat what will happen (assuming signal and idler both resonant with slow-light narrowed modes)\nis that the pair rate per bandwidth will be the same as it is in the bare cavity, but limited to the\nnarrow bandwidth of the slow light mode. If we used the slow-light narrowed mode as a filter after\npair production in a bare cavity then we would reduce the heralding efficiency due to the random\nlosses in both signal and idler.\nWe have rewritten the statement in the paper to illustrate our residual uncertainty.\n“Combined with the ability to generate entangled photon pairs in lithium niobate, our\nnarrowband features likely could be used to generate photons with sufficiently narrow\nlinewidthstointerfacewithnarrowbandspinqubitsinawaythatisotherwisenotpossible\non-chip. The details of such a scheme would have to be worked out, as this represents a\nsubstantially different configuration than other cavity-enhanced photon pair schemes.”\n3"}]

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