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arXiv:2605.13571 · Applied Physics Letters

Cryogenic microwave frequency combs based on quantum paraelectric superconducting resonators

Prasad Muragesh, H. Sundaresan, Madhu Thalakulam

Published Aug 17, 2026• 0 citations
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Abstract

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.

DOI
10.1063/5.0349286

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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.
Here, we demonstrate an on-chip cryogenic microwave frequency-comb on a planar superconducting resonator fabricated on Strontium titanate(STO), a quantum paraelectric material. The material's Kerr-type nonlinearity arising from the quantum paraelectric phase, an underexplored state, enables pronounced resonance shifts, Duffing-like bifurcations and comb generation via cascaded foure-wave mixing. Our results establish STO resonators as a low power, cryogenically compatible platforms for nonlinear microwave photonics, with applications in scalable quantum control and on-chip frequency synthesis.
Scaling quantum processors requires cryogenic microwave components to minimize thermal load and wiring complexity. However, conventional microwave components such as mixers and phase shifters perform poorly at millikelvin temperatures. Here, we report an SrTiO 3 (STO)-based microwave frequency mixer and phase shifter operating at sub-Kelvin temperatures. Utilizing the effective χ (2) nonlinearity of STO in the quantum paraelectric state, induced by a static or oscillating field, we achieve efficient microwave frequency mixing. Our device features an aluminum superconducting coplanar waveguide resonator on STO, which resonantly enhances mixing characteristics. The exceptionally high field-tunable dielectric constant of STO—approximately 30,000—allows for highly compact architectures and facilitates voltage-controlled phase shifting. Furthermore, we demonstrate multi-tone frequency mixing via phase modulation, facilitating spectral filtering and shaping. These STO-based devices provide a transformative approach to the generation of intricate microwave waveforms, tailoring control and readout signals in multi-qubit systems and paving the way for co-located quantum-classical integration.
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.
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-TcT_cTc​ superconductors, underscoring its potential as a compact and scalable microwave source for cryogenic quantum information and sensing applications.
Efficient, low-noise, and high-bandwidth transduction between optical and microwave photons is key to long-range quantum communication between distant superconducting quantum processors. Recent demonstrations of microwave-optical transduction using the broadband direct electro-optic (Pockels) effect in optical thin films made of AlN or LiNbO 3 have shown promise. To improve efficiency and added noise, materials with larger Pockels coefficients, such as the soft ferroelectrics BaTiO 3 or SrTiO 3 , are needed. However, these materials require adapted designs and fabrication approaches due to their nonlinear and, in some cases, hysteretic electro-optic response. Here, we engineer an on-chip, triply resonant transducer comprising low-loss BaTiO 3 -on- SiO 2 waveguides monolithically integrated with a superconducting microwave resonator made of Nb. We demonstrate bidirectional microwave-optical transduction and reach total off-chip efficiencies of 1 × 10 − 6 using pulsed pumping. The device design permits poling of the ferroelectric material without introducing excess microwave loss, exploiting superconducting air bridges fabricated using only subtractive patterning steps. In addition, we investigate optically induced heating, revealing fast thermalization and quasiparticle resilience of the microwave resonator. Our transducer concept and fabrication process are applicable to other materials with a large bias-induced Pockels effect like SrTiO 3 and pave the way for efficient, low-power quantum interconnects.
We propose a device architecture capable of direct quantum coherent electro-optical conversion of microwave-to-optical photons. The hybrid system consists of a planar superconducting microwave circuit coupled to an integrated whispering-gallery-mode microresonator made from an electro-optical material. We show that by exploiting the large vacuum electric field of the planar microwave resonator, electro-optical (vacuum) coupling strengths g0{g}_{0}g0​ as large as $\ensuremath{\sim}2\ensuremath{\pi}O(10\ensuremath{-}100)$ kHz are achievable with currently available technology---a more than 3 orders of magnitude improvement over prior designs and realizations. Operating at millikelvin temperatures, such a converter would enable high-efficiency conversion of microwave-to-optical photons. We analyze the added noise and show that maximum quantum coherent conversion efficiency is achieved for a multiphoton cooperativity of unity which can be reached with optical power as low as O(1)O(1)O(1) mW.