Abstract
Frequency combs, specialized laser sources emitting multiple equidistant frequency lines, have revolutionized science and technology with unprecedented precision and versatility. Recently, integrated frequency combs are emerging as scalable solutions for on-chip photonics. Here, we demonstrate a fully integrated superconducting microcomb that is easy to manufacture, simple to operate, and consumes ultra-low power. Our turnkey apparatus comprises a basic nonlinear superconducting device, a Josephson junction, directly coupled to a superconducting microstrip resonator. We showcase coherent comb generation through self-started mode-locking. Therefore, comb emission is initiated solely by activating a DC bias source, with power consumption as low as tens of picowatts. The resulting comb spectrum resides in the microwave domain and spans multiple octaves. The linewidths of all comb lines can be narrowed down to 1 Hz through a unique coherent injection-locking technique. Our work represents a critical step towards fully integrated microwave photonics and offers the potential for integrated quantum processors.
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Introduction
Frequency combs serve as high-precision rulers for frequency and time measurement, playing a pivotal role in a wide variety of modern science and technologies1,2,3,4,5, including optical clocks, LIDAR, spectroscopy, arbitrary waveform generation, and optical neural networks. Over the past two decades, integrated combs have garnered significant research interests5,6,7,8,9,10,11,12,13,14,15,16,17,18, leading to miniaturized and chip-based photonic systems7. However, most on-chip frequency combs, such as integrated semiconductor mode-locked lasers and microresonator-based Kerr combs, mainly operate in the optical frequency domain. A fully integrated frequency comb functioning in the microwave domain remains elusive, impeding the advancement of chip-based microwave spectroscopy and integrated quantum circuits, which typically require precise microwave control. Here, we address these challenges by introducing an all-superconductor-based microcomb, featuring an elegantly simple structure, effortless operation, and ultra-low power consumption.
Our superconducting frequency comb is fully integrated, comprising two fundamental superconductor devices: a Josephson junction directly coupled to a superconducting coplanar waveguide (CPW) resonator, as illustrated in Fig. 1a (see Supplementary Fig. 1 for a photo of our device). Device fabrication is achieved through straightforward procedures utilizing standard photolithography and electron beam evaporation techniques (See Methods). The Josephson junction consists of two superconductors connected by a weak link or a thin insulating barrier. It acts as an ideal voltage-to-frequency converter, emitting photons at the Josephson frequency \({f}_{J}=2e{V}_{{{{{{{\mathrm{dc}}}}}}}}/h\), where \(2e\) is the charge of a Cooper pair, \({V}_{{{{{{{\mathrm{dc}}}}}}}}\) is the DC voltage bias across the junction, and \(h\) is Planck’s constant. Meanwhile, the superconducting CPW resonator is another crucial superconductor device widely used in high-sensitive detectors and circuits for qubit control and read-out19. We demonstrate that the combination of these two fundamental superconducting elements can generate a coherent frequency comb (Fig. 1b, c). Its on-chip generation of pulse waves and inherent compatibility with production, operation, and integration into circuit quantum electrodynamics20,21,22 offers the potential for miniaturized, low-cost, and energy-efficient quantum processors.
The Josephson junction-coupled superconducting resonator has drawn significant research interest due to its capability not only to operate as ultrasensitive sensors, such as for single photon detection23 and/or thermometry24, but also to function as a coherent photon source25,26,27,28,29,30,31,32,33,34. Particularly, in the strong coupling regime, the device generates stable microwave lasing25 and demonstrates remarkably low noise26. However, in previous investigations, the coupled devices were all operated in single mode, resulting in continuous-wave emissions. Their properties under a multimode operation have not been explored.
Results
Coherent comb generation
We demonstrate that a Josephson junction coupled to a superconducting resonator can generate a self-phase-locked coherent frequency comb under multimode operation. The coupling between a Josephson junction and a resonator is proportional to the Josephson energy \({{{{{{\boldsymbol{E}}}}}}}_{{{{{{\boldsymbol{J}}}}}}}{{{{{\boldsymbol{\equiv }}}}}}{{{{{\boldsymbol{h}}}}}}{{{{{{\boldsymbol{I}}}}}}}_{{{{{{\boldsymbol{c}}}}}}}{{{{{\boldsymbol{/}}}}}}{{{{{\boldsymbol{2}}}}}}{{{{{\boldsymbol{e}}}}}}\), where \({{{{{{\boldsymbol{I}}}}}}}_{{{{{{\boldsymbol{c}}}}}}}\) is superconducting critical current25,28. To directly ensure strong coupling, we employ a Josephson junction with a large \({{{{{{\boldsymbol{I}}}}}}}_{{{{{{\boldsymbol{c}}}}}}}\). This is achieved by fabricating a sizable Josephson junction (approximately 4 µm2), resulting in a relatively large supercurrent of ID ≈ 2 µA in the lasing state (Fig. 1b), which surpasses by more than two orders of magnitude compared to that in the continuous-wave Josephson laser25. To achieve multimode operation within the frequency range of interest (typically 1–10 GHz), we fabricate a superconducting resonator with a low free spectrum range of 0.75 GHz. The strong coupling allows stable microwave lasing when a dc voltage bias Vdc \({{{{{\boldsymbol{\ge }}}}}}{{{{{\boldsymbol{20}}}}}}\) µV is applied to the Josephson junction (Fig. 1b).
Figure 1c shows the comb spectrum measured at Vdc = 43 μV. First, we will prove that the observed spectrum in Fig. 1c indeed represents a coherent frequency comb. The raised background between 3–10 GHz in Fig. 1c is a consequence of the limited bandwidth of amplifiers. Therefore, our subsequent investigations will focus on the frequency range in the detection bandwidth. The frequencies of a comb are given by the formula: \({f}_{m}={f}_{0}+m{f}_{r}\), where \({f}_{0}\) denotes the carrier offset frequency, \({f}_{r}\) represents the repetition frequency, and m stands for the mode number1,2,3,4,5. The extracted mode frequencies are shown in Fig. 1d, align perfectly with fitting to the comb formula. The result indicates a negligible offset frequency (\({f}_{0}\approx 0\) GHz). Consequently, our superconducting microcomb can be expressed by a simplified comb formula:
Additionally, Fig. 1c, d demonstrate that the repetition frequency \({f}_{r}\) nicely aligns with the free spectrum range (0.75 GHz) of the half-wave resonator.
The evenly spaced spectral lines alone are not sufficient for correlations among the comb teeth. To examine the coherence state of the emitted signal, we first proved that each individual mode has a stable phase using the heterodyne detection technique (Supplementary Fig. 2). One direct consequence of phase-coherent comb is the generation of pulses in the time domain1,2,3,4,5. Figure 2a displays a comb spectrum, and its corresponding time-dependent waveform is shown in Fig. 2b, c. The waveform reveals a sequence of microwave pulses, indicating that all spectrum modes are phase-locked and maintain a stable phase relationship. Moreover, every pulse displays identical features, as seen in Fig. 2d by the perfect overlap of two pulse waves. This indicates that all pulses are in-phase, and also suggests a carrier offset frequency of 0 Hz, thus confirming that all the spectral lines share a uniform phase. The coherence of the comb modes can be further validated through a unique coherent injection-locking effect, as demonstrated below.
The emission power of each individual comb line, ranging up to subpicowatt (see Supplementary Fig. 3), is consistent with that of the continuous-wave (or single-mode) source25. The microcomb’s performance could be further enhanced by refining the structures and parameters of the Josephson junction-coupled resonators26. The stability of the frequency comb is determined by the linewidth of the spectral lines (see Supplementary Fig. 4). In general, the overall linewidth is influenced by the quality factor of the resonator, the stability of the DC bias voltage, and environmental electromagnetic and thermal noise. Moreover, our experiments demonstrate that the linewidth of our comb increases quadratically with the mode number (or frequency), as illustrated in Supplementary Fig. 5. This finding is consistent with the observations in quantum-limited optical combs35,36.
Coherent injection-locking effect
Injection-locking is a widely used technique for effectively narrowing the linewidth of a laser source25,26,37,38. In optical frequency combs, it has been demonstrated only in a few cases in quantum cascade lasers by injecting a radio-frequency (RF) modulation at the cavity roundtrip frequency39,40,41,42. In our superconducting microcomb, we showcase a distinct coherent injection-locking effect that can be achieved by injecting an external microwave at any arbitrary comb mode. For instance, we select an arbitrary mode, such as minj = 7, as the injection tone (Fig. 3a). Then, an injection signal finj is applied and swept around f7 = 5.26 GHz. We measure the spectra at frequencies fsen around various sensing modes msen (Fig. 3a). The resulting spectra maps are illustrated in Fig. 3b–d (additional results in Supplementary Fig. 6). We find that all modes are simultaneously locked within the same injection frequency range Δfinj = 8.08 MHz (see Fig. 3b, d for definition and Fig. 3k for extracted values). This reaffirms that all spectral lines are coherently phase-locked.
This unique coherent injection-locking effect results in an ultra-high-resolution comb, with the linewidth of all comb teeth significantly narrowed down to ≤1 Hz, as shown in Fig. 3e–g and their insets. It’s worth noting that the observed linewidth of 1 Hz is constrained by the resolution bandwidth of the spectrum analyzer used in the experiments26, implying the potential for even narrower linewidths.
The injection-locking range Δfinj of our microcomb widens with the injection power Pinj (Supplementary Fig. 7). Specifically, when msen=minj (Fig. 3c, f, i), the injection-locking phenomena replicate those observed in the continuous-wave source25,26, and can therefore be explained by the Adler’s theory43. However, the results for the comb modes with msen ≠ minj cannot be described by Adler’s equation (see Supplementary Fig. 8a,b). We find that the locked sensing frequency range Δfsen (see Fig. 3b–d for definition) is proportional to m (Fig. 3l). This implies that the radiation frequencies of the injection-locked comb satisfy the comb formula \((1)\) over the entire locked frequency range. Consequently, this introduces an in-situ tunable superconducting microcomb, allowing for adjustable \({f}_{r}\) within the range of \(\Delta {f}_{{{{{{{\mathrm{inj}}}}}}}}/{m}_{{{{{{{\mathrm{inj}}}}}}}}\).
The coherent injection-locking leads to a unique frequency-pulling effect, particularly noticeable when msen ≠ minj. Figure 3h–j illustrate these effects when finj is fixed at an off-resonance tone (the corresponding on-resonance injection results are shown in Supplementary Fig. 9), shifted from the free-running emission tone by Δfoff = 8 MHz. When msen = minj, the emission line is gradually pulled toward finj with increasing injection power Pinj, ultimately locking at finj (Fig. 3i). This behavior mirrors that observed in a continuous-wave source25,26. However, the remarkable outcome arises when msen ≠ minj. In this case, although no injection tone is applied around each sensing mode, notable emission lines are induced at the corresponding tones, termed “induced-injection tone” and labeled as fid in Fig. 3b, d, h, 3j. The linewidth of the fid lines is considerably narrower than those of the free-running emissions and the side-band harmonics (see Supplementary Fig. 10). Furthermore, neither fid emission nor Kerr comb generation are observed with RF injection under zero DC bias voltage (Supplementary Fig. 11). These indicate that the fid emissions originate from the mutual interactions among Josephson photons, injection photons, and the resonator’s multi-modes, setting the fid signals apart from the Kerr combs generated directly from RF pumping44.
When msen ≠ minj, as depicted in Fig. 3h, j, while the emissions of all the modes are pulled toward fid tones with increasing Pinj, the fid tones themselves also shift with Pinj. Consequently, this results in the locked frequency range Δflock≠Δfoff (see Fig. 3h, j). Figure 3m demonstrates that Δflock is also proportional to m with \(\Delta {f}_{{{{{{{\mathrm{lock}}}}}}}}=\frac{m}{{m}_{{{{{{{\mathrm{inj}}}}}}}}}\Delta {f}_{{{{{{{\mathrm{off}}}}}}}}\), perfectly aligned with the requirements of the comb formula \((1)\) for the emissions within the locking range.
There is no existing theory that can describe our observed coherent injection-locking effect. We have derived an extended Adler’s equation to quantitatively describe these unique phenomena. As analyzed above, in the locking range Δfinj, all comb emissions are described by the comb formula \((1)\). In the unlocking range outside Δfinj, the emission signals are given by (please refer to Method for detailed derivation):
Here, fh denotes the repetition frequency of the harmonic emissions induced by off-resonance injection, and \(n{f}_{h}\) represents the nth harmonic shift. The fh is given by:
where \(\Delta {f}_{{{{{{{\mathrm{inj}}}}}}}}=\alpha \sqrt{{P}_{{{{{{{\mathrm{inj}}}}}}}}}\) (with \(\alpha\) as a constant related to cavity losses), and \({f}_{{m}_{{inj}}}\) is the mode frequency at \({m}_{{inj}}\). Notably, when m=minj, the extended Alder’s Eq. (2) reduces to the standard Alder’s equation. The perfect fittings in Fig. 3b–d, 3h–j indicate that our extended Alder’s Eq. (2) accurately describes all the coherent injection-locking effects in our superconducting microcomb.
In previous studies of continuous-wave superconducting lasers, the downconversion of higher-order Josephson frequencies to the resonator’s fundamental mode has been demonstrated25. However, the upconversion of Josephson photons to higher mode has not been reported. In Fig. 4a, we present a comb spectrum (red) within our typical experimental bandwidth of 3–10 GHz. The applied DC bias voltage across the Josephson junction is Vdc = 36.387 µV, corresponding to a Josephson frequency fJ = 17.60 GHz. As illustrated in Fig. 4a, all the comb modes with fm < fJ are generated through downconversion, and any modes with fm > fJ (if existing) would result from upconversion. However, emissions with fm > 17.60 GHz lie beyond the bandwidth of our spectrum measurements, preventing their direct observation.
The coherent injection-locking effect provides an advanced methodology for sensing comb emissions beyond the detection bandwidth. To demonstrate this, we perform injection-locking measurements using various injection tones with minj = 1, 6, 54, as illustrated in Fig. 4a, while selecting a fixed sensing tone within the detection bandwidth, such as msen = 7. Figures 4b–d display the coherent injection-locking effects. The injection-locking phenomenon arises from the nonlinear interaction between emission tone and external injection signal43. Since no injection signal is applied at m = 7, the coherence injection-locking effect displayed in Fig. 4d suggests the presence of a comb emission tone at f54 = 39.28 GHz, which is significantly higher than the Josephson frequency fJ = 17.6 GHz. This observation provides evidence for the upconversion process of Josephson photons to higher modes. The presence of comb emissions at m = 1 (Fig. 4b) and 54 (Fig. 4d) indicates that our Josephson microcomb spans a frequency range exceeding five octaves, a span typically challenging to achieve in semiconductor-based frequency combs. It is essential to note that this octave value is limited by the upper-frequency limit of the microwave generator used in our experiments. Hence, it is highly likely that even higher modes could exist beyond this range.
Discussion
We have demonstrated a fully integrable superconducting microcomb. Unlike previously reported superconductor-based frequency combs44,45,46,47,48,49,50,51,52, which all operated under microwave pumping using externally supplied, expensive, and energy-consuming microwave sources, our superconducting microcomb is driven solely by a DC bias voltage. This makes it highly desirable for scalable and on-chip integration. The initiation of our microcomb requires simply tuning on a low-power DC bias source, with a minimal input power as low as 40 pW (Fig. 1b)—approximately nine orders of magnitude lower than the semiconductor-based frequency combs. This presents significant advancement for ultrasensitive and energy-efficient applications.
The exceptional coherence of our comb enables a unique coherent injection-locking effect previously inaccessible in frequency combs, leading to an ultra-high-resolution and tunable comb. This innovation introduces unique functionalities, such as the generation of coherent subcombs through four-wave mixing, as showcased in Supplementary Fig. 12. The simultaneous up- and down-conversion of Josephson photons significantly expands the comb’s frequency range over multiple octaves. These capabilities offer added flexibility and tunability for applications of superconducting microcomb technology.
This DC-biased superconducting microcomb with ultra-low power consumption (down to a few tens of picowatts) can work at ultra-low temperatures, aligning seamlessly with the operating conditions of superconducting quantum circuits. For a typical dilution refrigerator, which has a cooling power of hundreds of microwatts at 20 mK, in principle, it is feasible to integrate up to millions of the combs at the base temperature based on their energy efficiency. Our comb can serve as a multifrequency microwave source for multiplexed quantum measurement53. An important potential application of our superconducting microcomb is the development of a low-cost, on-chip arbitrary waveform generator. This could be achieved by controlling the intensities of the comb teeth54, which is possible by integrating our superconducting comb with a series of frequency-tunable superconducting resonators serving as adjustable filters55. This advancement promises substantial benefits for future quantum technologies. Moreover, implementing superconducting frequency combs in the terahertz domain could be feasible by using intrinsic Josephson junctions in high-temperature superconductors56. This approach could also extend the technology’s working temperature range.
Methods
Device fabrication
We fabricated four superconducting microcombs (#1-#4), and detailed parameters are listed in Supplementary Tables 1. The superconducting resonators are fabricated using a superconducting Nb film for device #1 and a Ta (\({{{{{\rm{\alpha }}}}}}\)-phase) film57 for devices #2, #3, and #4. The film was sputtered on a 10 \({{{{{\rm{mm}}}}}}\) by 10 \({{{{{\rm{mm}}}}}}\) sapphire substrate (C-plane, thickness 650 \(\,{{{{{\rm{\mu }}}}}}{{{{{\rm{m}}}}}}\)). Standard photolithography followed by reactive ion etching in a CF4 was then used to define the resonators. The Al/AlOx/Al (Al thicknesses 40 nm/80 nm) Josephson junction was fabricated using standard double-angle evaporation and lift-off techniques. To ensure good electrical contact between the Josephson junction and the resonator layers, the sample was ion-beam milled to remove residual oxides and resist residue from the surface of the resonator before the double-angle evaporation.
Experiments
The devices are mounted in a dilution refrigerator with a base temperature of 20 mK. A complete circuit is shown in Supplementary Fig. 13. We adopt a similar approach to refs. 25,30,31 for the low noise biasing scheme to measure the tunneling current and provide a stable voltage bias to the device. The bias voltage is supplied by an on-chip voltage divider circuit consisting of a 10 Ω shunt resistor and a 10 Ω reference resistor. The current through the device is then measured via the voltage drop Vr across the 10 Ω reference resistor. The current \({I}_{D}\) and voltage \({V}_{{{{{{{\mathrm{dc}}}}}}}}\) of the device is given by \({I}_{D}=\,{V}_{r}/10\) and \({V}_{{{{{{{\mathrm{dc}}}}}}}}=10{I}_{{{{{{{\mathrm{bias}}}}}}}}-20{I}_{D}\). Here,\(\,{V}_{r}\) is obtained from a nano voltmeter (Keithley 2182 A) and \({I}_{{{{{{{\mathrm{bias}}}}}}}}\) is the output from a current source (Keithley 6221). Additional filtering for the circuit is provided by two 100 \({{{{{\rm{\mu }}}}}}{{{{{\rm{F}}}}}}\) chip capacitors. Additionally, all low-frequency lines are heavily filtered outside the PCB with multi-pole RC and PI low-pass filters located in the mixing chamber of the dilution refrigerator.
The device’s output signal is amplified by an amplifier chain consisting of a cryogenic amplifier (+42 dB) and two room-temperature amplifiers (+32 dB). The spectra are acquired by an Agilent N9010A spectrum analyzer (S/A), and the waveforms are recorded using a Keysight MSOV334A digital oscilloscope (D/O). The injection signal to the resonator is generated by an Agilent N5183A analog signal generator (S/G) and is attenuated by a low-temperature attenuation chain to assure that the thermal contribution of photons to the cavity is negligible.
Extended Adler’s equation
In the unlocking range outside Δfinj, the emission signals for msen = minj, which can be described by Adler’s theory43, are given by:
where fh is the repetition frequency of the harmonic emissions. The first term, finj + fh, accounts for the comb’s emission at minj, while \(n{f}_{h}\) represents the nth harmonic shift. The fh is given by:
where \(\Delta {f}_{{{{{{{\mathrm{inj}}}}}}}}=\alpha \sqrt{{P}_{{{{{{{\mathrm{inj}}}}}}}}}\) (with \(\alpha\) as a constant related to cavity losses). The comb’s emission at minj corresponds to n = 0, therefore we obtain \({f}_{{m}_{{{{{{{\mathrm{inj}}}}}}}},0}={f}_{{{{{{{\mathrm{inj}}}}}}}}+{f}_{h}\) from Eq. (3). Utilizing the superconducting microcomb formula (1) (see the main text), we can express the comb’s emissions for any arbitrary m as \({f}_{m,0}=\frac{m}{{m}_{{{{{{{\mathrm{inj}}}}}}}}}{f}_{{m}_{{{{{{{\mathrm{inj}}}}}}}},0}={\frac{m}{{m}_{{{{{{{\mathrm{inj}}}}}}}}}}({f}_{{{{{{{\mathrm{inj}}}}}}}}+{f}_{h})\). By adding the nth harmonic shift nfh, we derive an extended Adler’s Eq. (2), as shown in the main text, for the coherent injection-locking in our superconducting combs.
Data availability
All the data that support the findings of this study are available on the public repository https://doi.org/10.6084/m9.figshare.25480621
References
Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555 (2011).
Picqué, N. & Hänsch, T. W. Frequency comb spectroscopy. Nat. Photon 13, 146–157 (2019).
Fortier, T. & Baumann, E. 20 years of developments in optical frequency comb technology and applications. Commun. Phys. 2, 153 (2019).
Diddams, S. A., Vahala, K. & Udem, T. Optical frequency combs: coherently uniting the electromagnetic spectrum. Science 369, 267 (2020).
Chang, L., Liu, S. & Bowers, J. E. Integrated optical frequency comb technologies. Nat. Photon 16, 95–108 (2022).
Guo, Q. et al. Ultrafast mode-locked laser in nanophotoniclithium niobate. Science 382, 708–713 (2023).
Shu, H. et al. Microcomb-driven silicon photonic systems. Nature 605, 457–463 (2022).
Xiang, C. et al. Laser soliton microcombs heterogeneouslyintegrated on silicon. Science 373, 99–103 (2021).
Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, 567 (2018).
Xu, X. et al. 11 TOPS photonic convolutional accelerator for optical neural networks. Nature 589, 44–51 (2021).
Feldmann, J. et al. Parallel convolutional processing using an integrated photonic tensor core. Nature 589, 52–58 (2021).
Yang, Q.- et al. Vernier spectrometer using counterpropagating soliton microcombs. Science 363, 965–968 (2019).
Riemensberger, J. et al. Massively parallel coherent laser ranging using a soliton microcomb. Nature 581, 164–170 (2020).
Stern, B., Ji, X., Okawachi, Y., Gaeta, A. L. & Lipson, M. Battery-operated integrated frequency comb generator. Nature 562, 401–405 (2018).
Bai, B. et al. Microcomb-based integrated photonic processing unit. Nat. Commun. 14, 66 (2023).
Shen, B. et al. Integrated turnkey soliton microcombs. Nature 582, 365–369 (2020).
Jin, W. et al. Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high-Q microresonators. Nat. Photon 15, 346–353 (2021).
Marpaung, D., Yao, J. & Capmany, J. Integrated microwave photonics. Nat. Photon 13, 80–90 (2019).
Krantz, P. et al. A quantum engineer’s guide to superconducting qubits. Appl. Phys. Rev. 6, 021318 (2019).
Blais, A., Girvin, S. M. & Oliver, W. D. Quantum information processing and quantum optics with circuit quantum electrodynamics. Nat. Phys 16, 247 (2020).
Clerk, A. A., Lehnert, K. W., Bertet, P., Petta, J. R. & Nakamura, Y. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys 16, 257 (2020).
Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).
Golubev, D. S., Il’ichev, E. V. & Kuzmin, L. S. Single-photon detection with a Josephson junction coupled to a resonator. Phys. Rev. Appl. 16, 014025 (2021).
Saira, O.-P., Zgirski, M., Viisanen, K. L., Golubev, D. S. & Pekola, J. P. Dispersive thermometry with a Josephson junction coupled to a resonator. Phys. Rev. Appl. 6, 024005 (2016).
Cassidy, M. C. et al. Demonstration of an ac Josephson junction laser. Science 355, 939–942 (2017).
Yan, C. et al. A low-noise on-chip coherent microwave source. Nat. Electron 4, 885 (2021).
Astafiev, O. et al. Single artificial-atom lasing. Nature 449, 588–590 (2007).
Meister, S. et al. Resonators coupled to voltage-biased Josephson junctions: from linear response to strongly driven nonlinear oscillations. Phys. Rev. B 92, 174532 (2015).
Rolland, C. et al. Antibunched photons emitted by a dc-biased Josephson junction. Phys. Rev. Lett. 122, 186804 (2019).
Chen, F. et al. Realization of a single-Cooper-pair Josephson laser. Phys. Rev. B 90, 020506(R) (2014).
Hofheinz, M. et al. Bright side of the Coulomb blockade. Phys. Rev. Lett. 106, 217005 (2011).
Grimm, A. et al. Bright on-demand source of antibunched microwave photons based on inelastic Cooper pair tunneling. Phys. Rev. X 9, 021016 (2019).
Simon, S. H. & Cooper, N. R. Theory of the Josephson junction laser. Phys. Rev. Lett. 121, 027004 (2018).
Danner, L., Padurariu, C., Ankerhold, J. & Kubala, B. Injection locking and synchronization in Josephson photonics devices. Phys. Rev. B 104, 054517 (2021).
Newbury, N. R. & Swann, W. C. Low-noise fiber-laser frequency combs. J. Opt. Soc. Am. B 24, 1756–1770 (2007).
Liehl, A. et al. Deterministic nonlinear transformations of phase noise in quantum-limited frequency combs. Phys. Rev. Lett. 122, 203902 (2019).
Liu, Y.-Y., Stehlik, J., Gullans, M. J., Taylor, J. M. & Petta, J. R. Injection locking of a semiconductor double-quantum-dot micromaser. Phys. Rev. A 92, 053802 (2015).
Liu, Y.-Y., Hartke, T. R., Stehlik, J. & Petta, J. R. Phase locking of a semiconductor double-quantum-dot single-atom maser. Phys. Rev. A 96, 053816 (2017).
Hillbrand, J., Andrews, A. M., Detz, H., Strasser, G. & Schwarz, B. Coherent injection locking of quantum cascade laser frequency combs. Nat. Photon 13, 101–104 (2018).
Gellie, P. et al. Injection-locking of terahertz quantum cascade lasers up to 35 GHz using RF amplitude modulation. Opt. Express 18, 20799–20816 (2010).
Barbieri, S. et al. Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis. Nat. Photon 5, 306–313 (2011).
St-Jean, M. R. et al. Injection locking of mid-infrared quantum cascade laser at 14 GHz, by direct microwave modulation. Laser Photon. Rev. 8, 443–449 (2014).
Adler, R. A study of locking phenomena in oscillators. Proc. IRE 34, 351–357 (1946).
Erickson, R. P., Vissers, M. R., Sandberg, M., Jefferts, S. R. & Pappas, D. P. Frequency comb generation in superconducting resonators. Phys. Rev. Lett. 113, 187002 (2014).
Wang, S.-P., Chen, Z. & Li, T. Controllable microwave frequency comb generation in a tunable superconducting coplanar-waveguide resonator. Chin. Phys. B 30, 048501 (2021).
Lu, P. et al. Nearly quantum-limited Josephson-junction frequency-comb synthesizer. Phys. Rev. Appl. 15, 044031 (2021).
Shin, J. et al. On-chip microwave frequency combs in a superconducting nanoelectromechanical device. Nano Lett. 22, 5459–5465 (2022).
Wu, S. et al. Hybridized frequency combs in multimode cavity electromechanical system. Phys. Rev. Lett. 128, 153901 (2022).
Han, X. et al. Superconducting cavity electromechanics: the realization of an acoustic frequency comb at microwave frequencies. Phys. Rev. Lett. 129, 107701 (2022).
Khan, S. & Türeci, H. E. Frequency combs in a lumped-element Josephson-junction circuit. Phys. Rev. Lett. 120, 153601 (2018).
Solinas, P., Gasparinetti, S., Golubev, D. & Giazotto, F. A Josephson radiation comb. Sci. Rep. 4, 12260 (2015).
Ilin, D., Poshakinskiy, A. V., Poddubny, A. N. & Iorsh, I. Frequency combs with parity-protected cross-correlations and entanglement from dynamically modulated qubit arrays. Phys. Rev. Lett. 130, 023601 (2023).
Essig, A. et al. Multiplexed photon number measurement. Phys. Rev. X 11, 0311045 (2021).
Cundiff, S. T. & Weiner, A. M. Optical arbitrary waveform generation. Nat. Photon 4, 760–766 (2010).
Strickland, W. M. et al. Superconducting resonators with voltage-controlled frequency and nonlinearity. Phys. Rev. Appl. 19, 034021 (2023).
Ozyuzer, L. et al. Emission of coherent THz radiation from superconductors. Science 318, 1291–1293 (2007).
Shi, L. et al. Tantalum microwave resonators with ultra-high intrinsic quality factors. Appl. Phys. Lett. 121, 242601 (2022).
Acknowledgements
This work is supported by the National Key R&D Program of China (2021YFA0718802 (Y.-Y.L., Y.-L.W., and H.W.), 2018YFA0209002 (Y.-L.W.), and 2023YFF0718400 (Y.D.)), the National Natural Science Foundation of China (62274086 (Y.L.W.), 62288101 (H.W.), 12204434(Y.D.), and 62271245 (X.T.)), Postdoctoral Fellowship Program of CPSF (W.-C.Y. and Y.-Y.L.), Jiangsu Outstanding Postdoctoral Program (W.-C.Y. and Y.-Y.L.), Shenzhen Science and Technology Program (KQTD20200820113010023 (X.D.)), and Jiangsu Key Laboratory of Advanced Techniques for Manipulating Electromagnetic Waves.
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Y.L.W., H.W., and P.W. conceived and supervised the project. C.-G.W. designed and fabricated the devices, as well as conducted the experiments. L.S., J.J., T.G., C.C., X.J., and J.C. provided support for the fabrication of resonators. T.L., Y.-Y.L., and G.S. assisted in the fabrication of Josephson junctions. W.X., C.L., W.-C.Y., X.T., and L.K. provided support for optical lithography. W.X., S.D., P.Z., Y.-Y.L., J.P., and L.Z. assisted in microwave spectrum and waveform measurements. C.G.W. and Y.L.W. performed the analysis and interpretation of the experimental data. C.-G.W., X.D., Y.D., and Y.-L.W. conducted the theoretical analysis. C.-G.W. and Y.-L.W. wrote the manuscript. Y.-L.W. and H.W. edited the manuscript.
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Wang, CG., Xu, W., Li, C. et al. Integrated and DC-powered superconducting microcomb. Nat Commun 15, 4009 (2024). https://doi.org/10.1038/s41467-024-48224-1
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DOI: https://doi.org/10.1038/s41467-024-48224-1
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