Since their discovery, frequency combs have yielded a plethora of applications—spectroscopy,11. A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, Sci. Adv. 4, e1701858 (2018). https://doi.org/10.1126/sciadv.1701858 optical clocks,22. Z. L. Newman, V. Maurice, T. Drake, J. R. Stone, T. C. Briles, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, B. Shen, M.-G. Suh, K. Y. Yang, C. Johnson, D. M. S. Johnson, L. Hollberg, K. J. Vahala, K. Srinivasan, S. A. Diddams, J. Kitching, S. B. Papp, and M. T. Hummon, Optica 6, 680 (2019). https://doi.org/10.1364/optica.6.000680 frequency synthesis,33. D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. H. Lee, D. Y. Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, Nature 557, 81 (2018). https://doi.org/10.1038/s41586-018-0065-7 and distance ranging.44. M.-G. Suh and K. J. Vahala, Science 359, 884 (2018). https://doi.org/10.1126/science.aao1968 Their integration on chip through the use of dissipative Kerr soliton (DKS) states in different platforms5–105. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010). https://doi.org/10.1038/nphoton.2010.1206. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014). https://doi.org/10.1038/nphoton.2013.3437. X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, Nat. Photonics 9, 594 (2015). https://doi.org/10.1038/nphoton.2015.1378. Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, Optica 4, 193 (2017). https://doi.org/10.1364/optica.4.0001939. H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Phys. 13, 94 (2017). https://doi.org/10.1038/nphys389310. G. Moille, L. Chang, W. Xie, A. Rao, X. Lu, M. Davanço, J. E. Bowers, and K. Srinivasan, Laser Photonics Rev. 14, 2000022 (2020). https://doi.org/10.1002/lpor.202000022 has led to a focus on low power1111. B. Stern, X. Ji, Y. Okawachi, A. L. Gaeta, and M. Lipson, Nature 562, 401 (2018). https://doi.org/10.1038/s41586-018-0598-9 and low footprint1212. Z. Ye, F. Lei, K. Twayana, M. Girardi, P. A. Andrekson, and V. Torres‐Company, Laser Photonics Rev. 16, 2100147 (2022). https://doi.org/10.1002/lpor.202100147 devices for deployable metrology outside of the laboratory.1313. S. A. Diddams, K. Vahala, and T. Udem, Science 369, eaay3676 (2020). https://doi.org/10.1126/science.aay3676 The realization of octave-spanning microcombs has been made possible by harnessing unprecedented control of integrated microresonator dispersion,1313. S. A. Diddams, K. Vahala, and T. Udem, Science 369, eaay3676 (2020). https://doi.org/10.1126/science.aay3676 and the additional ability to overlap their spectra with relevant atomic optical transition frequencies1414. S.-P. Yu, T. C. Briles, G. T. Moille, X. Lu, S. A. Diddams, K. Srinivasan, and S. B. Papp, Phys. Rev. Appl. 11, 044017 (2019). https://doi.org/10.1103/physrevapplied.11.044017 has helped spur interest in their use in portable optical atomic clocks.2,152. Z. L. Newman, V. Maurice, T. Drake, J. R. Stone, T. C. Briles, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, B. Shen, M.-G. Suh, K. Y. Yang, C. Johnson, D. M. S. Johnson, L. Hollberg, K. J. Vahala, K. Srinivasan, S. A. Diddams, J. Kitching, S. B. Papp, and M. T. Hummon, Optica 6, 680 (2019). https://doi.org/10.1364/optica.6.00068015. T. E. Drake, T. C. Briles, J. R. Stone, D. T. Spencer, D. R. Carlson, D. D. Hickstein, Q. Li, D. Westly, K. Srinivasan, S. A. Diddams, and S. B. Papp, Phys. Rev. X 9, 031023 (2019). https://doi.org/10.1103/physrevx.9.031023 In such applications, the frequency comb acts as a gear box,1313. S. A. Diddams, K. Vahala, and T. Udem, Science 369, eaay3676 (2020). https://doi.org/10.1126/science.aay3676 translating the optical frequency stability of a comb tooth locked to an atomic transition to a microwave frequency through the DKS repetition rate [Fig. 1(a)]. However, the comb needs to be fully stabilized when realizing such a frequency division scheme. In the clock case, the carrier-envelope offset fceo (i.e., the shift from the zero frequency) [Fig. 1(b)] needs to be locked along with a comb tooth close enough to the optical atomic transition frequency, here called flock [Fig. 1(c)]. Their locking makes the system in Fig. 1(a) stiff, in the sense that only a single set of geometric parameters (ring width and thickness combination) will provide for enough power enhancement at the frequencies of interest [often at the location of dispersive waves (DWs)] while bringing a comb tooth sufficiently close to the atomic transition frequency. Yet, each of these goals is essentially driven by two different parameters: the DW spectral position is defined by the cavity dispersion while flock (the beat-note between a comb tooth and the optical atomic transition) and fceo can be controlled by a simple uniform spectral shift of the comb. Therefore, integrated heaters appear as a suitable solution, leveraging spectral tuning via the thermo-refractive effect1616. A. J. Bosman and E. E. Havinga, Phys. Rev. 129, 1593 (1963). https://doi.org/10.1103/physrev.129.1593 and compatibility with χ(3) microcomb platforms. Frequency tuning ranging up to hundreds of gigahertz has been demonstrated,17–2017. X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, Opt. Express 24, 687 (2016). https://doi.org/10.1364/oe.24.00068718. C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016). https://doi.org/10.1364/ol.41.00256519. Ó. B. Helgason, F. R. Arteaga-Sierra, Z. Ye, K. Twayana, P. A. Andrekson, M. Karlsson, J. Schröder, and V. Torres-Company, Nat. Photonics 15, 305 (2021). https://doi.org/10.1038/s41566-020-00757-920. A. Tikan, J. Riemensberger, K. Komagata, S. Hönl, M. Churaev, C. Skehan, H. Guo, R. N. Wang, J. Liu, P. Seidler, and T. J. Kippenberg, Nat. Phys. 17, 604 (2021). https://doi.org/10.1038/s41567-020-01159-y although mostly in resonators fully embedded in a silica cladding.The use of air-clad devices is, however, often desirable for dispersion engineering. Indeed, as silica presents increasingly normal dispersion as wavelengths become shorter, it is easier to compensate for the normal dispersion of Si3N4 through geometry in the absence of a material cladding. This has been demonstrated in different contexts in microresonator nonlinear optics, including optical parametric oscillators reaching visible wavelengths2222. X. Lu, G. Moille, A. Rao, D. A. Westly, and K. Srinivasan, Optica 7, 1417 (2020). https://doi.org/10.1364/optica.393810 and microcombs whose spectral extent reaches atomic transition frequencies in the short near-infrared and near-visible.2121. G. Moille, D. Westly, G. Simlegor, and K. Srinivasan, in CLEO: Science and Innovations (Optica Publishing Group, 2022), p. SW4H-6. In addition, an air top cladding presents the advantage of allowing post-fabrication processing to tune the geometrical dispersion if needed.2323. G. Moille, D. Westly, N. G. Orji, and K. Srinivasan, Appl. Phys. Lett. 119, 121103 (2021). https://doi.org/10.1063/5.0061238 Direct integration of the heater to the side of the ring results in poor heat build-up at the ring core [Fig. 1(d-i)], caused by the air trenches that act as an insulator but are essential to create the ring during the lithography and etch fabrication steps. The alternative approach we propose in this paper is to bury the integrated heater below the ring resonator [Fig. 1(d-ii)], where a few micrometer gap of silica separates the metal from the optical layer, resulting in no change in the ring losses. Due to the continuous path for heat transfer between the heater and ring layers, the efficiency of such a buried heater is much higher than that of the lateral one, which is confirmed by thermal simulation [Fig. 1(d)]. We demonstrate the fabrication of such unique integrated heaters, which are wire-bonding ready, for integration in optical clock systems. In addition, fully embedding the heater in silica and subsequently planarizing the silica layer make the remainder of the fabrication process compatible with a typical Si photonics process flow.2424. D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, J. Opt. 18, 073003 (2016). https://doi.org/10.1088/2040-8978/18/7/073003 We experimentally show the high tuning efficiency of the system, where a resonator mode shift of 1.5 THz [equal to 1.5× the resonator free spectral range (FSR)] is achieved without degradation of the resonator quality factor and with limited cross-talk. While tuning of air-clad resonators has numerous potential applications, including sensing and coupling to gas-phase quantum emitters, such as neutral alkali atoms, we showcase the utility of these heaters in the context of broadband DKS microcombs. We experimentally demonstrate the tunability of the microcomb with an estimated shift of fceo of 15% of the FSR and an estimated shift of the locked optical clock frequency flock over a range of close to 2 FSR. At the same time, little modification to dispersion—and hence, the DW position—occurs.The fabrication of the system [Fig. 2(a)] starts with a standard commercial silicon substrate with a 3 µm thick thermal oxide. We then define the heater pattern using a direct-write lithography maskless aligner (MLA)2525. Certain commercial products or names are identified to foster understanding. Such identification does not constitute recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the products or names identified are necessarily the best available for the purpose. [Fig. 2(a-i)]. The platinum is then deposited (electron beam evaporation) and lifted off. Another layer of 2.8 µm of SiO2 is deposited above the heater layer using a 180 °C low-temperature high-density plasma chemical vapor deposition (HDPCVD) process [Fig. 2(a-ii)]. We anneal the wafer at 1000 °C for 3 h to allow for the best material and the lowest absorption. Thanks to the low diffusivity of metal into silica,2626. J. D. McBrayer, R. M. Swanson, and T. W. Sigmon, J. Electrochem. Soc. 133, 1242 (1986). https://doi.org/10.1149/1.2108827 the buried heater remains geometrically intact, and the silica layer exhibits low absorption after the annealing. A chemical–mechanical polishing (CMP) step [Fig. 2(a-ii)] is done to create a flat surface before low-pressure chemical vapor deposition (LPCVD) of a 430 nm thick film of silicon nitride2727. G. Moille, D. Westly, G. Simelgor, and K. Srinivasan, Opt. Lett. 46, 5970 (2021). https://doi.org/10.1364/ol.440907 [Fig. 2(a-iii)]. From this point on, the process is the same as our regular nano-patterning and fabrication of air-clad ring resonators.2323. G. Moille, D. Westly, N. G. Orji, and K. Srinivasan, Appl. Phys. Lett. 119, 121103 (2021). https://doi.org/10.1063/5.0061238 The ring resonator patterns are created through electron-beam lithography, with the patterns aligned to the underlying buried heaters using metal alignment marks that are created within the heater layer. The electron-beam resist is used as a mask for a CHF3 reactive ion etch (RIE) of the silicon nitride [Fig. 2(a-iv)]. In order to maintain an air-clad ring resonator for dispersion purposes while allowing for low insertion losses, a lift-off of low-temperature HDPCVD SiO2 using nLOF resist is performed [Figs. 2(a-v) and 2(a-vi)] as described in Ref. 2323. G. Moille, D. Westly, N. G. Orji, and K. Srinivasan, Appl. Phys. Lett. 119, 121103 (2021). https://doi.org/10.1063/5.0061238. The last annealing step is performed to anneal the silicon nitride film, which has been shown to reduce absorption in the C-band through reducing N–H bonds2828. H. J. Stein, P. S. Peercy, and R. J. Sokel, Thin Solid Films 101, 291 (1983). https://doi.org/10.1016/0040-6090(83)90096-2 [Fig. 2(a-vii)]. Finally, an inductively coupled plasma (ICP) etch through the silicon nitride and the substrate silica, combined with a 1 min 6:1 buffered oxide etch dip, reveals the metal layer for electrical contact [Fig. 2(a-viii)]. The chip is then diced and polished for optical testing [Fig. 2(a-ix)].We proceed to characterize the linear performance—spectral tuning, cross talk, and speed—of the buried integrated heater. The experimental setup consists of continuously tunable laser (CTLs) around 970 nm and 1060 nm, each of which can be used to probe a single resonant mode of the cavity. The chip is placed on an aluminum sample holder not thermally connected to the optical table (see supplementary material). Heaters are addressed from the electrical pads with DC probes connected to a current source producing up to 1.5 W of electrical power. We measure the electrical resistance of the integrated heater to be R ≈ 260 Ω, which is of the same order of magnitude as typical integrated heaters.17,1817. X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, Opt. Express 24, 687 (2016). https://doi.org/10.1364/oe.24.00068718. C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016). https://doi.org/10.1364/ol.41.002565 By injecting 1.2 W of electrical power (i.e., a current of 67 mA), we measure a frequency shift of the resonance of more than 1.5 THz, corresponding to an ≈1.5 FSR red-shift [Fig. 3(a)]; among other things, this guarantees the ability to tune one of the microresonator’s modes onto resonance with any fixed pump laser wavelength. From simulations (see supplementary material), this frequency shift is consistent with an increase in temperature at the ring above 900 K. We note that this frequency shift is quite large compared to state-of-the-art integrated heaters in the silicon nitride nonlinear photonics platform that can be obtained through foundry fabrication,2929. A. Rao, G. Moille, X. Lu, D. A. Westly, D. Sacchetto, M. Geiselmann, M. Zervas, S. B. Papp, J. Bowers, and K. Srinivasan, Light: Sci. Appl. 10, 109 (2021). https://doi.org/10.1038/s41377-021-00549-y where a shift of only 1/2 of an FSR was achieved for the same electrical power. The efficiency of the buried heater is η0 = (−1.02 ± 0.012) THz/W, an improvement by a factor of 5 compared to the lateral heater efficiency of ηside = (−220 ± 1) GHz/W. The uncertainty estimation arises from the standard deviation in the confidence interval for the linear fit of the frequency shift with electrical power. In addition, the cross-talk of the integrated heater is limited. The next ring resonator, with its closest point from the neighboring active heater of about 5 µm—which is a relatively tight separation considering the waveguide access needed to address the resonator optically—only shows a thermal shift of η+1 = (−136 ± 0.7) GHz/W. Therefore, the cross-talk of our system can be defined by Ξ = η+1/η0 ≈ 13%. Interestingly, the cross-talk is not highly dependent on the distance from the heater. Indeed, the second neighbor from the active heater shows a spectral shift of η+2 = (−111 ± 0.6) GHz/W, showing that a significant portion of the chip is heating. Therefore, cross-talk could be further improved through an appropriate thermal shunt through the backside of the chip.We proceed to consider the impact of the buried heater on the optical quality factor of the ring resonator [Fig. 3(b)]. We found that the intrinsic quality factor, in addition to being similar to that of our regular fabrication without the metal layer of Q0 ≈ 0.75 × 106 (Ref. 2323. G. Moille, D. Westly, N. G. Orji, and K. Srinivasan, Appl. Phys. Lett. 119, 121103 (2021). https://doi.org/10.1063/5.0061238), remains unchanged for any temperature and electrical power applied to the system. Moreover, we measure that the coupling quality factor Qc ≈ 1 × 106 stays fixed at any temperature, highlighting the small thermal expansion of the system, resulting in a fixed geometry with temperature. Our coupling is based on a straight waveguide, but in the future, using a pulley-like coupling, which is more sensitive to geometrical variations,3030. G. Moille, Q. Li, T. C. Briles, S.-P. Yu, T. Drake, X. Lu, A. Rao, D. Westly, S. B. Papp, and K. Srinivasan, Opt. Lett. 44, 4737 (2019). https://doi.org/10.1364/ol.44.004737 would give a better estimate of the extent to which the thermal expansion is negligible. We also performed dynamical measurements in the small signal regime using a vector network analyzer to measure the recovery time of the buried heater and the frequency up to which the system can function [Fig. 3(c)]. It exhibits a 3 dB cut-off at about 26 kHz, which corresponds to a recovery time of the system of ≈38 µs. It is worth noting that this value is similar to that of integrated heaters on top of silica-clad rings1717. X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, Opt. Express 24, 687 (2016). https://doi.org/10.1364/oe.24.000687 and is essentially limited by the thermal lifetimes of silicon nitride and silica.88. Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, Optica 4, 193 (2017). https://doi.org/10.1364/optica.4.000193 We note that the SiO2 gap between the microring and the heater has not been optimized and remains large (2.8 µm). Further engineering of this distance could help increase the thermal recovery speed and even increase the heater efficiency for static frequency tuning. In addition, reduction of thermal cross-talk and improved heater efficiency may also be realized through trench isolation of the heaters, for example, during or after step viii of the fabrication process.The integrated buried heater presented here shows a high efficiency with a large thermo-refractive mediated spectral shift of the resonant mode. It remains to characterize how the thermal tuning of a ring resonator impacts the metrics associated with the optical atomic clock frequency comb, namely frep, fceo, and flock. In previous work, it has been demonstrated that thermal tuning of the ring resonator allows for small tuning of frep.1717. X. Xue, Y. Xuan, C. Wang, P.-H. Wang, Y. Liu, B. Niu, D. E. Leaird, M. Qi, and A. M. Weiner, Opt. Express 24, 687 (2016). https://doi.org/10.1364/oe.24.000687 Here, we also proceed to characterize other metrics to assess the impact of the thermal tuning on the cavity dispersion, fceo, and flock, representing two other important quantities for effective microcomb application in optical atomic clocks. To do so, we create dissipative Kerr soliton microcombs at different electrical powers [Fig. 4(a)]. Interestingly, the overall shape of the frequency comb remains mostly the same, with only a slight shift of the DW position, despite introducing another dispersion contribution. Indeed, the variation of the effective refractive index with temperature is wavelength-dependent, given the discrepancy in the thermo-refractive coefficient between Si3N4 (∂n/∂T = 2.5 × 10−5 K−1),31,3231. A. W. Elshaari, I. E. Zadeh, K. D. Jons, and V. Zwiller, IEEE Photonics J. 8, 2701009 (2016). https://doi.org/10.1109/jphot.2016.256162232. G. Moille, X. Lu, A. Rao, Q. Li, D. A. Westly, L. Ranzani, S. B. Papp, M. Soltani, and K. Srinivasan, Phys. Rev. Appl. 12, 034057 (2019). https://doi.org/10.1103/physrevapplied.12.034057 SiO2 (∂n/∂T = 1 × 10−5 K−1),3131. A. W. Elshaari, I. E. Zadeh, K. D. Jons, and V. Zwiller, IEEE Photonics J. 8, 2701009 (2016). https://doi.org/10.1109/jphot.2016.2561622 and air (∂n/∂T ≡ 0 K−1) and the variation of the effective mode area, which decreases with higher frequency (or mode number) [Fig. 4(b)]. The integrated dispersion, as obtained from finite element method simulations considering Joule heating, temperature distribution, and thermo-refractive coefficient (see supplementary material), shows only a slight modification across the thermal tuning range. Therefore, the dispersive waves—essential for achieving octave spans and self-referencing of a microcomb—would remain mostly unchanged despite variation of the above parameters. As reported in Fig. 4(c), the experimental DW shift is only two modes, from μ = −77 to μ = −79, and shows a slight discrepancy from finite element method simulations (μ = −74 to μ = −78). Although the overall shape of the DKS microcomb remains unchanged, its fundamental characteristics of relevance for clock applications—repetition rate and carrier-envelope offset frequency—are tuned with the electrical power injected. As seen previously, the resonances are red-shifted with the electrical power; ergo, the pump frequency is also red-shifted [Fig. 4(d)]. As the refractive index of the material increases with the temperature, the group index should also increase, resulting in a lower repetition rate of the DKS circulating in the resonator, as measured experimentally [Fig. 4(e)]. Given the repetition rate shift and the shift of the pump resonance, it is expected that fceo will also vary. We extract it from the measurements of fpmp and frep as fceo = fpmp − Nfrep, where N is the integer that brings fceo within the range [−frep/2, +frep/2], and find that fceo tuning of more than 100 GHz (i.e., about 10% of frep) is achievable [Fig. 4(f)]. This tuning can be crucial to allow for fceo to be shifted into a detection bandwidth of a photodetector. Finally, we demonstrate the possibility of tuning flock to a stabilized optical reference [Fig. 4(g)]. Here, we have assumed that a comb tooth is present near the 87Sr transition at 698 nm. In practice, our demonstrated combs in this work do not extend to this wavelength due to poor comb extraction, resulting from the straight waveguide coupling scheme employed;3030. G. Moille, Q. Li, T. C. Briles, S.-P. Yu, T. Drake, X. Lu, A. Rao, D. Westly, S. B. Papp, and K. Srinivasan, Opt. Lett. 44, 4737 (2019). https://doi.org/10.1364/ol.44.004737 however, we have demonstrated similar combs (without heaters) extending to 698 nm using optimized pulley couplers.2121. G. Moille, D. Westly, G. Simlegor, and K. Srinivasan, in CLEO: Science and Innovations (Optica Publishing Group, 2022), p. SW4H-6. Finally, we note that because the flock comb tooth mode order is large, it provides a large multiplicative factor on the temperature-induced shift in frep. Thus, with only 1 W of electrical power, flock shifts across three different comb teeth, constituting a span >2.5frep.In summary, we have demonstrated a new technique to integrate an efficient micro-heater on-chip with an air-cladding resonator, by burying the heater below the optical device layer. Once the buried heater is patterned, encased in SiO2, and planarized, the subsequent process flow is the same as for standard Si3N4 photonic devices. We show that such a buried heater is 5× more efficient than lateral heaters and exhibits low cross-talk, which could be even further improved by a proper thermal shunt of the chip. We then demonstrate the use of the heaters with broadband microcombs and measure/extract tuning of critical comb parameters for use in optical atomic clocks. While the microcomb measurements are indicative of the use of the buried heater technology for nonlinear integrated photonics applications, we envision many other uses in scenario for which air cladding is required. This, in particular, would include microresonator-based sensors3333. D. Yu, M. Humar, K. Meserve, R. C. Bailey, S. N. Chormaic, and F. Vollmer, Nat. Rev. Methods Primers 1, 83 (2021). https://doi.org/10.1038/s43586-021-00079-2 and cavity QED experiments with gas-phase atoms,34,3534. J. L. O’Brien, A. Furusawa, and J. Vučković, Nat. Photonics 3, 687 (2009). https://doi.org/10.1038/nphoton.2009.22935. T.-H. Chang, X. Zhou, M. Zhu, B. M. Fields, and C.-L. Hung, Appl. Phys. Lett. 117, 174001 (2020). https://doi.org/10.1063/5.0023464 where both the wide tuning range and negligible impact on resonator quality factor are important factors.In the supplementary material, we discuss the thermal mitigation of the experimental setup for stability in order to create DKS with different power of the buried heaters. We also discuss the simulation multi-physics coupling between Joule heating and thermo-refractive frequency shift to accurately account and model the metric presented in Fig. 4.

The authors thank Nikolai Klimov and Feng Zhou for their valuable inputs. The authors acknowledge partial funding support from the DARPA APHI, DARPA SAVaNT, and NIST-on-a-chip programs.

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Grégory Moille: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (equal); Methodology (equal); Software (equal); Validation (lead); Visualization (lead); Writing – original draft (lead). Daron Westly: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – original draft (supporting). Edgar F. Perez: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Writing – original draft (supporting). Meredith Metzler: Conceptualization (supporting); Investigation (supporting); Methodology (equal); Writing – original draft (supporting). Gregory Simelgor: Conceptualization (supporting); Investigation (supporting); Methodology (supporting). Kartik Srinivasan: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Supervision (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

REFERENCES

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