Superconductors are characterized by macroscopic phase coherence and have enabled cryogenic electronics and quantum technologies. Recent advances in 3D nanofabrication now offer possibilities for tuning functional properties relevant for on-chip 3D integration of superconductors. However, nonequilibrium phenomena in 3D nanostructures exposed to transport currents remain largeley unexplored. Here, we employ numerical simulations to investigate phase slipsdiscrete 2π jumps in the phase of the superconducting order parameterin a tubular Nb superconductor with a central constriction, which is subjected to both direct current (DC) and alternating current (AC) transport currents. We find that under DC drive, the system stabilizes periodic phase slips, resulting in GHz voltage oscillations. Introducing an additional AC frequency modulation generates microwave frequency combs which depend characteristically on the interaction between moving vortices and phase slips. Our findings open avenues for developing on-chip frequency comb generators in 3D cryoelectronics.
Superconductors are characterized by macroscopic phase coherence and have enabled cryogenic electronics and quantum technologies. Recent advances in 3D nanofabrication now offer possibilities for tuning functional properties relevant for on-chip 3D integration of superconductors. However, nonequilibrium phenomena in 3D nanostructures exposed to transport currents remain largeley unexplored. Here, we employ numerical simulations to investigate phase slipsdiscrete 2π jumps in the phase of the superconducting order parameterin a tubular Nb superconductor with a central constriction, which is subjected to both direct current (DC) and alternating current (AC) transport currents. We find that under DC drive, the system stabilizes periodic phase slips, resulting in GHz voltage oscillations. Introducing an additional AC frequency modulation generates microwave frequency combs which depend characteristically on the interaction between moving vortices and phase slips. Our findings open avenues for developing on-chip frequency comb generators in 3D cryoelectronics.
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 here reported up to mode 46. The emitted power at the device level ranges from -170 dBm to -130 dBm per harmonic, corresponding to 40 dB dynamic range in the 4-8 GHz bandwidth. 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.
A lattice of Abrikosov vortices in type II superconductors is characterized by a periodic modulation of the magnetic induction perpendicular to the applied magnetic field. For a coherent vortex motion under the action of a transport current, the magnetic induction at a given point of the sample varies in time with a washboard frequency fWB = v/d, where v is the vortex velocity and d is the distance between the vortices in the direction of motion. Here, by using a spectrum analyzer connected to a 50 nm-wide Au nanowire meander near the surface of a superconducting Nb film, we detect an ac voltage induced by coherently moving fluxons. The voltage is peaked at the washboard frequency, fWB, and its subharmonics, fTOF = fWB/5, determined by the antenna width. By sweeping the dc current value, we reveal that fWB can be tuned from 100 MHz to 1.5 GHz, thereby demonstrating that patterned normal metal/superconductor nanostructures can be used as dc-tunable generators operating in the radiofrequency range.
Microwave frequency combs constitute promising resources for quantum technologies, cryogenic electronics, and multiplexed sensing architectures. In this work, we propose a frequency-comb generator based on a Josephson field-effect transistor operated in a relaxation-oscillation regime. The device comprises a gate-tunable ballistic superconductor-semiconductor-superconductor junction embedded in a resistively shunted circuit, in which electrostatic control of the carrier density enables in situ tuning of both the critical current and the Josephson inductance. Time-domain circuit simulations indicate that the resulting oscillator produces coherent voltage pulses whose Fourier spectrum forms a microwave frequency comb. In contrast to conventional Josephson-based comb architectures, the proposed platform provides direct electrical control of the comb spacing, emission frequencies, and modal power distribution via a gate electrode. For a representative Al/InAs implementation, we demonstrate continuous frequency coverage in the technologically relevant 1-10 GHz range. Furthermore, the concept is shown to be compatible with higher-Tc superconductors, underscoring its potential as a compact and scalable microwave source for cryogenic quantum information and sensing applications.
A frequency comb, known for its precision as an “optical ruler,” features an evenly spaced spectral pattern. While these combs are vital in integrated photonics, their microwave counterparts are now highly sought in cryogenic quantum technologies, including semiconducting and superconducting qubits as well as quantum electrical metrology. However, microwave combs are still largely underexplored. Existing studies mostly rely on complex, high-power optical systems incompatible with the low-power, cryogenic on-chip architecture. In this manuscript, we present an all-electrical, on-chip, cryogenic microwave frequency comb on strontium titanate (SrTiO3), exploiting its Pockels-like effect in its quantum paraelectric phase. Our device utilizes a superconducting microwave cavity to generate the frequency comb via cavity phase modulation enabled by the field-induced effective χ(2) of SrTiO3. The ability to continuously vary the dielectric constant of SrTiO3 by the application of an electric field, in its quantum paraelectric phase, makes it possible to control the comb's operating frequency span. The exceptionally high dielectric constant of SrTiO3, > 20 000 at low temperatures, enables an ultra-miniature design and on-chip integration with cryogenic quantum technologies.
Superconducting optomechanical circuits enable frequency mixing of optical and mechanical modes, facilitating the generation of microwave frequency combs. However, such optomechanical combs suffer from frequency fluctuations, requiring their stabilization for applications in precision sensing and signal processing. Here, we investigate the sideband injection locking of microwave frequency combs in a niobium-based superconducting optomechanical circuit. By strongly driving the device with a blue-detuned pump to induce parametric instability and introducing an additional tone near individual comb peaks, we study how the locking range varies with the power, the frequency position, and the sweep direction of the injection tone. The locking responses show interesting features such as injection hysteresis, which cannot be explained by existing models. Numerical simulations of the classical optomechanical equations implementing a cubic mechanical nonlinearity show that the nonlinearity contributes to broadening the locking range. We also characterize the Allan deviations and phase noise of the injection-locked combs for different injection frequencies, demonstrating enhanced stability performance. Our results lay the foundation for the utilization of optomechanical combs for applications in nanomechanical sensing and cryogenic microwave pulse generation.
Cavity quantum electrodynamics (QED) with quantum emitters coupled to resonators provides a powerful platform for engineering light-matter interactions and exploring collective phenomena. In particular, superradiance, arising from collective quantum interference among emitters, has been explored as a route to ultrastable continuous radiation. However, engineering superradiance in the time domain to realize periodic pulsed sources or frequency combs remains largely unexplored. Here, we investigate the non-equilibrium many-body dynamics of a driven spin ensemble coupled to an on-chip superconducting resonator and uncover a dynamical phase transition from continuous-wave to periodic pulsed superradiant emission. To quantitatively capture the observed dynamical phases, we introduce a driven-dissipative cavity-QED model that elucidates how the periodic pulsed superradiant phase emerges from collective, periodically repeating spin dynamics stabilized by the interplay of coherence growth, disorder, and dissipation. We also find that rare-earth ion spin systems exhibiting both optical and microwave transitions enable phase-synchronized, dual-rail superradiant frequency combs in both the microwave and optical domains. Our results not only open new avenues for dual-rail frequency-comb applications in quantum metrology and information processing, but also establish a fundamental connection between periodic pulsed superradiance and the emergence of a continuous time crystal as a novel nonequilibrium phase in driven open systems.