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Applied Physics Letters

In situ frequency tuning of superconducting resonators via nonlinear kinetic inductance

Michael R. Vissers, J. D. Wheeler, Paul Szypryt, Andrea Giachero, Jason E. Austermann, Johannes Hubmayr, G. C. O’Neil, Joel N. Ullom, Jiansong Gao

Published Mar 21, 2026• 2 citations
Publisher

Abstract

Superconducting microresonators have diverse applications, including microwave kinetic inductance detectors, microwave superconducting quantum interference device multiplexers, and superconducting qubits. Arrays of such devices are typically addressed using microwave frequency combs with probe tones matched to individual device resonances. However, resonator frequency collisions caused by wafer non-uniformity and fabrication variations significantly limit usable device yields. In this Letter, we present a technique that mitigates these frequency collisions without the need for ex post facto processing. By leveraging nonlinear kinetic inductance and persistent current in a superconducting loop, we achieve in situ tuning of individual resonator frequencies within an array during device cooldown, effectively resolving frequency collisions in a way that is both highly flexible and reversible. We successfully demonstrate this technique by tuning a small array of four resonators to both identical frequencies and a uniformly spaced frequency comb. This in situ resonator tuning approach provides a universal solution for improving yield and multiplexing density in large resonator arrays, addressing a critical need for scaling up superconducting detector and qubit systems.

DOI
10.1063/5.0316371

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Superconducting microresonators have diverse applications, including microwave kinetic inductance detectors, microwave superconducting quantum interference device multiplexers, and superconducting qubits. Arrays of such devices are typically addressed using microwave frequency combs with probe tones matched to individual device resonances. However, resonator frequency collisions caused by wafer non-uniformity and fabrication variations significantly limit usable device yields. In this Letter, we present a technique that mitigates these frequency collisions without the need for ex post facto processing. By leveraging nonlinear kinetic inductance and persistent current in a superconducting loop, we achieve in situ tuning of individual resonator frequencies within an array during device cooldown, effectively resolving frequency collisions in a way that is both highly flexible and reversible. We successfully demonstrate this technique by tuning a small array of four resonators to both identical frequencies and a uniformly spaced frequency comb. This in situ resonator tuning approach provides a universal solution for improving yield and multiplexing density in large resonator arrays, addressing a critical need for scaling up superconducting detector and qubit systems.
Microwave Kinetic Inductance Detector (MKID) arrays are currently being developed and deployed for astronomical applications in the visible and near infrared and for sub-millimetre astronomy. One of the main challenges of MKIDs is that large arrays would exhibit a pixel yield, defined as the percentage of individually distinguishable pixels to the total number of pixels, of 75 80 %.1 Imperfections arising during the fabrication can induce an uncontrolled shift in the resonance frequency of individual resonators which end up resonating at the same frequency of a different resonator. This makes a number of pixels indistinguishable and therefore unusable for imaging. This paper proposes an approach to individually re-tune the colliding resonators in order to remove the degeneracy and increase the number of MKIDs with unique resonant frequencies. The frequency re-tuning is achieved through a DC bias of the resonator since the kinetic inductance of a superconducting thin film is current dependent and its dependence is non linear. Even though this approach has been already proposed,2 our innovative pixel design may solve two issues previously described in literature such as non-negligible electromagnetic losses to the DC bias line, and the multiplexibility of multiple resonators on a single feed-line.
We present a method of spatially mapping microwave kinetic inductance detector (MKID) arrays, in a dark setup. MKIDs are superconducting natively multiplexed resonators which enable kilopixel arrays, such as for the proposed Probe far-Infrared Mission for Astrophysics (PRIMA). In such telescope applications one must map the spatial location of each MKID with their individual resonance frequencies. Traditional LED arrays or beam-mapping methods become increasingly difficult as pixel spacing decreases, e.g., 900μ\muμm separated MKIDs in the spectrometer module of PRIMA. Our new mapping technique uses a cryogenic interferometer in reflection mode. As on-resonance signals reflect from an MKID, they accrue a phase proportional to the path-length, exactly corresponding to their physical distance on the feedline. Specifically, we use a superconducting transmission line that has nonlinear kinetic inductance. The slow-wave structure of this nonlinear device is designed to have a signal speed of 0.64% the speed of light, enabling a compact system. Current biasing this line allows for varying the wave speed and ensuring that the phase measured is periodic within a nulling interferometric mode. Using this setup, we measure a length ordering that reflects the bimodal MKID distribution of a 44 pixel array of MKIDs designed for PRIMA which contains the same spacing as the final kilopixel array design.
We describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain. A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.
Superconducting microwave resonators have the potential to revolutionize submillimeter and far-infrared astronomy, and with it our understanding of the universe. The field of low-temperature detector technology has reached a point where extremely sensitive devices like transition-edge sensors are now capable of detecting radiation limited by the background noise of the universe. However, the size of these detector arrays are limited to only a few thousand pixels. This is because of the cost and complexity of fabricating large-scale arrays of these detectors that can reach up to 10 lithographic levels on chip, and the complicated SQUID-based multiplexing circuitry and wiring for readout of each detector. In order to make substantial progress, next- generation ground-based telescopes such as CCAT or future space telescopes require focal planes with large-scale detector arrays of 104–106 pixels. Arrays using microwave kinetic inductance detectors (MKID) are a potential solution. These arrays can be easily made with a single layer of superconducting metal film deposited on a silicon substrate and pattered using conventional optical lithography. Furthermore, MKIDs are inherently multiplexable in the frequency domain, allowing ∼ 103 detectors to be read out using a single coaxial transmission line and cryogenic amplifier, drastically reducing cost and complexity. An MKID uses the change in the microwave surface impedance of a superconducting thin-film microresonator to detect photons. Absorption of photons in the superconductor breaks Cooper pairs into quasiparticles, changing the complex surface impedance, which results in a perturbation of resonator frequency and quality factor. For excitation and readout, the resonator is weakly coupled to a transmission line. The complex amplitude of a microwave probe signal tuned on-resonance and transmitted on the feedline past the resonator is perturbed as photons are absorbed in the superconductor. The perturbation can be detected using a cryogenic amplifier and subsequent homodyne mixing at room temperature. In an array of MKIDs, all the resonators are coupled to a shared feedline and are tuned to slightly different frequencies. They can be read out simultaneously using a comb of frequencies generated and measured using digital techniques. This thesis documents an effort to demonstrate the basic operation of ∼ 256 pixel arrays of lumped-element MKIDs made from superconducting TiNx on silicon. The resonators are designed and simulated for optimum operation. Various properties of the resonators and arrays are measured and compared to theoretical expectations. A particularly exciting observation is the extremely high quality factors (∼ 3 × 107) of our TiNx resonators which is essential for ultra-high sensitivity. The arrays are tightly packed both in space and in frequency which is desirable for larger full-size arrays. However, this can cause a serious problem in terms of microwave crosstalk between neighboring pixels. We show that by properly designing the resonator geometry, crosstalk can be eliminated; this is supported by our measurement results. We also tackle the problem of excess frequency noise in MKIDs. Intrinsic noise in the form of an excess resonance frequency jitter exists in planar superconducting resonators that are made on dielectric substrates. We conclusively show that this noise is due to fluctuations of the resonator capacitance. In turn, the capacitance fluctuations are thought to be driven by two-level system (TLS) fluctuators in a thin layer on the surface of the device. With a modified resonator design we demonstrate with measurements that this noise can be substantially reduced. An optimized version of this resonator was designed for the multiwavelength submillimeter kinetic inductance camera (MUSIC) instrument for the Caltech Submillimeter Observatory.
Coplanar waveguide resonators are central to the thriving field of circuit quantum electrodynamics. Recently, we have demonstrated the generation of a broadband microwave-frequency comb spectrum using a superconducting quantum interference device (SQUID) driven by a time-dependent magnetic field. Here, the frequency comb is used to spectroscopically probe a bank of coplanar microwave resonators, inductively coupled to a common transmission line, a standard circuit with a variety of applications. We compare the resonator line shape obtained from signals synthesized at room temperature using conventional electronics with the radiation produced in the cryogenic environment by our source, showing substantial equivalence in the estimation of the resonator quality factors. To measure non-uniformly spaced resonant frequencies, we drive the generator with a bi-chromatic tone to generate intermodulation products. Such a dense frequency comb spectrum enables simultaneous addressing of a few resonators via frequency multiplexing. Finally, we discuss the criteria for achieving effective spectroscopic coverage of a given frequency bandwidth.
We present a design and implementation of a frequency-tunable superconducting resonator. The resonance frequency tunability is achieved by flux-coupling a superconducting LC loop to a current-biased feedline; the resulting screening current leads to a change of the kinetic inductance and shift in the resonance frequency. The thin-film aluminum resonator consists of an interdigitated capacitor and thin line inductors forming a closed superconducting loop. The magnetic flux from the nearby niobium current feedline induces Meissner shielding currents in the resonator loop leading to a change in the kinetic part of the total inductance of the resonator. We demonstrate continuous frequency tuning within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1) frequency up-conversion is achieved when a kilohertz ac modulation signal is superimposed onto the dc bias resulting in sidebands to the resonator tone; (2) three-wave mixing is attained by parametrically pumping the nonlinear kinetic inductance using a strong rf pump signal in the feedline. The simple architecture is amenable to large-array multiplexing and on-chip integration with other circuit components. The concept could be applied in flux magnetometers, up-converters, and parametric amplifiers operating above 4 K when alternative high-critical-temperature material with high kinetic inductance is used.