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Applied Physics Letters

Frequency-tunable superconducting microwave resonators based on quantum paraelectricity

Shu-Kun Ye, Zi-Qing Huang, Ran-Ran Cai, Yong-Qiang Xu, Yuan Kang, Rui Wu, Shi-Hang Ban, Bao-Chuan Wang, Hai-Ou Li, Gang Cao, Guo-Ping Guo

Published Aug 10, 2026• 0 citations
Publisher

Abstract

Frequency tuning enables both high-sensitivity and wide-bandwidth detection in the resonator. Potassium tantalate (KTO) is a quantum paraelectric with tunable permittivity and low microwave loss at cryogenic temperature, making it promising for tunable devices. Here, we demonstrate a superconducting microwave resonator on a KTO substrate. The resonant frequency can be tuned by ∼40 MHz using a 9 V bias at 20 mK, with no observable hysteresis. The absence of hysteresis is a key metric for practical devices, addressing one of the major obstacles in other paraelectric-based tunable resonators. More interestingly, we observed that the quality factor oscillates during voltage tuning, arising from the competition between phonon hardening and charge injection. Therefore, our work provides a practical tunable resonator platform and offers a potential approach to study energy-loss characteristics in quantum paraelectrics.

DOI
10.1063/5.0344969

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Frequency tuning enables both high-sensitivity and wide-bandwidth detection in the resonator. Potassium tantalate (KTO) is a quantum paraelectric with tunable permittivity and low microwave loss at cryogenic temperature, making it promising for tunable devices. Here, we demonstrate a superconducting microwave resonator on a KTO substrate. The resonant frequency can be tuned by ∼40 MHz using a 9 V bias at 20 mK, with no observable hysteresis. The absence of hysteresis is a key metric for practical devices, addressing one of the major obstacles in other paraelectric-based tunable resonators. More interestingly, we observed that the quality factor oscillates during voltage tuning, arising from the competition between phonon hardening and charge injection. Therefore, our work provides a practical tunable resonator platform and offers a potential approach to study energy-loss characteristics in quantum paraelectrics.
Superconducting coplanar waveguide (CPW) resonators are powerful and versatile tools used in areas ranging from radiation detection to circuit quantum electrodynamics. Their potential for low intrinsic losses makes them attractive as sensitive probes of electronic properties of bulk materials and thin films. Here we use superconducting MoRe CPW resonators to investigate the high-frequency (up to 0.3 GHz) and low-temperature (down to 3.5 K) permittivity of SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​, a nonlinear dielectric on the verge of a ferroelectric transition (quantum paraelectricity). We perform a quantitative analysis of its dielectric properties as a function of external dc bias (up to $\ifmmode\pm\else\textpm\fi{}15\phantom{\rule{0.16em}{0ex}}\mathrm{V}$), rf power, and mode number and discuss our results within the framework of the most recent theoretical models. We also discuss the origin of a fatigue effect that reduces the tunability of the dielectric constant of SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​, which we relate to the presence of oxygen vacancies.
Abstract Radiofrequency reflectometry can provide fast and sensitive electrical read-out of charge and spin qubits in quantum dot devices coupled to resonant circuits. In situ frequency tuning and impedance matching of the resonator circuit using voltage-tunable capacitors (varactors) is needed to optimize read-out sensitivity, but the performance of conventional semiconductor- and ferroelectric-based varactors degrades substantially in the millikelvin temperature range relevant for solid-state quantum devices. Here we show that strontium titanate and potassium tantalate, materials which can exhibit quantum paraelectric behaviour with large field-tunable permittivity at low temperatures, can be used to make varactors with perfect impedance matching and resonator frequency tuning at 6 mK. We characterize the varactors at 6 mK in terms of their capacitance tunability, dissipative losses and magnetic field insensitivity. We use the quantum paraelectric varactors to optimize the radiofrequency read-out of carbon nanotube quantum dot devices, achieving a charge sensitivity of 4.8 μe Hz−1/2 and a capacitance sensitivity of 0.04 aF Hz−1/2.
Radio-frequency reflectometry allows for fast and sensitive electrical readout of charge and spin qubits hosted in quantum dot devices coupled to resonant circuits. Optimizing readout, however, requires frequency tuning of the resonators and impedance matching. This is difficult to achieve using conventional semiconductor or ferroelectric-based varactors in the detection circuit as their performance degrades significantly in the mK temperature range relevant for solid-state quantum devices. Here we explore a different type of material, strontium titanate, a quantum paraelectric with exceptionally large field-tunable permittivity at low temperatures. Using strontium titanate varactors we demonstrate perfect impedance matching and resonator frequency tuning at 6 mK and characterize the varactors at this temperature in terms of their capacitance tunability, dissipative losses and magnetic field sensitivity. We show that this allows us to optimize the radio-frequency readout signal-to-noise ratio of carbon nanotube quantum dot devices to achieve a charge sensitivity of 4.8 μμμe/Hz1/2^{1/2}1/2 and capacitance sensitivity of 0.04 aF/Hz1/2^{1/2}1/2.
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.
At cryogenic temperatures and microwave frequencies, the perovskite crystals strontium titanate (STO) and potassium tantalate (KTO) have large, tunable permittivity arising from a quantum paraelectric phase. As such, these materials hold promise as a platform to realize compact, variable capacitance elements for use in quantum devices. From modulating this capacitance, we propose the development of a parametric mixing element: a quantum paraelectric nonlinear dielectric amplifier (PANDA). We calculate that a PANDA made from a nanofabricated parallel plate capacitor and realistic design constraints can demonstrate a three-wave mixing strength of order MHz, in comparison to an effective Kerr strength of sub-Hz. This suggests excellent performance as a three-wave mixing element, with high compression power in analogy to superconducting parametric amplifiers based on kinetic inductance. Beyond parametric amplifiers, we predict that compact, tunable capacitors based on STO, KTO, and related materials can enable a wide class of cryogenic quantum circuits including novel filters, switches, circulators, and qubits.
Hybridizing a microwave mode with a quantum state requires precise frequency matching of a superconducting microwave resonator and the corresponding quantum object. However, fabrication always brings imperfections in geometry and material properties, causing deviations from the desired operating frequencies. An effective and universal strategy for their resonant coupling is to tune the frequency of a resonator, as quantum states like phonons are hardly tunable. Here, we demonstrate gate-tunable, titanium-nitride (TiN)-based superconducting resonators by implementing a nanowire inductor whose kinetic inductance is tuned via the gate-controlled supercurrent (GCS) effect. We investigate their responses for different gate biases and observe 4% (∼150 MHz) frequency tuning with decreasing internal quality factors. We also perform temperature-controlled experiments to support phonon-related mechanisms in the GCS effect and the resonance tuning. The GCS effect-based method proposed in this study provides an effective route for locally tunable resonators that can be employed in various hybrid quantum devices.