Coherent microwave comb generation via the Josephson effect

TL;DR

The paper presents a cavity-free, on-chip microwave frequency comb generated by a time-dependent magnetic drive on a dc SQUID, producing a train of voltage pulses via the ac Josephson effect and yielding a spectrum with evenly spaced lines at $f_n = n f_p$ across 4–8 GHz with $f_{ceo}=0$. It demonstrates coherent single-mode emission with sub-Hz linewidths and seconds-long coherence, and shows phase control where mode phases obey $\theta_n = n\theta_p + \tilde{\theta}_n$, enabling tunable mutual phase relations across the comb. The work reports ultra-low dissipation (≈2×10^-26 J per pulse, ≈10^-18 W at 100 MHz) and a micrometer-scale footprint, highlighting the platform's potential for integration with cryogenic quantum technologies and applications in quantum sensing and computing. By bridging optical-frequency-comb concepts to superconducting circuits, it lays groundwork for scalable, low-power, on-chip frequency comb sources compatible with cryogenic electronics.

Abstract

Frequency combs represent exceptionally precise measurement tools due to the coherence of their spectral lines. While optical frequency comb sources constitute a well-established technology, superconducting circuits provide a relatively unexplored on-chip platform for low-dissipation comb emitters able to span from gigahertz to terahertz frequencies. We demonstrate coherent microwave frequency comb generation by leveraging the ac Josephson effect in a superconducting quantum interference device. A time-dependent magnetic drive periodically generates voltage pulses, which in the frequency domain correspond to a comb with dozens of spectral modes. The micrometer-scale footprint and minimal dissipation inherent to superconducting systems foster the integration of our comb generator with advanced cryogenic electronics. Transferring optical techniques to the solid-state domain may enable new applications in quantum technologies.

Figures (12)

• Figure 1: SQUID-based microwave comb generator.a Scanning electron micrograph of the device with false colors. A time-dependent current with a static bias flows through the coplanar waveguide (in yellow), generating a magnetic flux $\Phi$ threading the dc SQUID (in cyan) loop. The red circles indicate the locations of the two Josephson junctions. The train of voltage pulses produced across the SQUID is transmitted by a 50 $\Omega$ transmission line to the amplification chain. b Phase-flux dependency underlying the device's operating principle for a symmetric SQUID (dashed trace, $r\simeq 0$) and a strongly asymmetric SQUID (solid line, $r=0.1$). Around $\Phi_0/2$, the ac flux with frequency $f_p$ sweeps the phase $\varphi$ across the SQUID, as illustrated in the inset. c Upper panel: Time-domain representation of a train of voltage pulses generated by the SQUID with a repetition rate $1/f_p$. Each pulse has a width of $\tilde{t}$. Lower panel: Sketch of the frequency comb spectrum corresponding to the above voltage signal. The mode spacing is $f_p$, i.e., the inverse of the repetition rate, and the width of the spectral envelope, $1/\tilde{t}$, is on the order of the inverse of the pulse duration.
• Figure 2: Frequency comb spectrum.a Power spectrum from various spectra, each sampled with a 20kHz span. The spikes are evenly spaced and correspond to multiples from $n=4$ to $n=7$ of the pump frequency $f_p=$ 1050MHz and pump power -8. b Same as panel a, with harmonics from 10 to 20 of $f_p=$ 390MHz and pump power 0. c Output power of the 5th harmonic with $f_p=$ 833.34MHz as a function of flux bias $\Phi_{\text{dc}}$ and nominal power of the pump tone $P_p$. Each data point reports the maximum of a spectral trace spanning 500 Hz. The 5th mode (4166.7MHz) lies in the setup bandwidth with highest gain. d Zoom-in of the output power of the 7th harmonic generated by Sample 2. The pump frequency is 597.34MHz, and the resulting signal is at 4181.38MHz. e Output power of the 7th (blue) and 8th (red) harmonics generated by Sample 2 under the same conditions as panel d at fixed pump power. f SPICE simulation of output power for the 7th and 8th harmonics relative to panel e.
• Figure 3: Single-mode linewidth and time stability.a Power spectrum of the 5th harmonic with $f_c=5\times f_p$ ($f_p=833.34$ MHz) measured at $\Phi_0/2$. The full-width at half-maximum of the spectral line profile $\Delta f$ coincides with the instrumental resolution bandwidth (0.3 Hz), establishing a lower bound. b Schematic diagram of the heterodyne setup to acquire the two quadratures in the time domain, $I(t)$ and $Q(t)$, of the comb mode in panel A. c Histogram of the two quadratures over a 10-second acquisition time.
• Figure 4: Phase tunability and mutual phase of comb modes.a Measurement setup for tuning the phase of comb modes by the pump phase $\theta_p$. The phase of the comb modes is addressed by the two-step down-conversion circuit of Fig. \ref{['fig:Fig3']}b. b Histograms of 16 second-long measurements of the 9th harmonic generated by $f_p=597$ MHz with power $P_p=-5$ dBm. The data are clustered into eight point clouds, corresponding to the values of $\theta_p$ stepped by 5 deg every 2 seconds. Each variation of $\theta_p$ by 5 deg leads to a 45 deg tilt in the IQ plane. c Demodulation circuit to acquire both quadratures of five comb modes referenced to the same clock and sampled simultaneously. d Phases of comb modes from $42$ to $46$ as a function of the pump phase acquired with the demodulation circuit of panel c. Each dataset is rescaled by a multiplication factor for clarity and the intercepts of the curves are set to zero to highlight the relative slopes. Inset: linear fit of experimental points obtained by evaluating difference between the phase of mode $43$ ($\theta_{43}$) and the phase of mode $42$ ($\theta_{42}$). The fit yields a slope of $1.00 \pm 0.01$ and an intercept of $-1.56 \pm 0.71$.
• Figure 5: Reflectometry data and fit with model. The evolution of the phase of the S21 parameter shows the flux modulation of the dc SQUID, which allows the calibration of the flux bias. The Vector Network Analyzer is set in continuous wave mode with an applied tone of frequency 4.072 GHz.