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arXiv:2312.12755 · Physical Review Applied

Flux-coupled tunable superconducting resonator

Juliang Li, Peter S. Barry, Tom Cecil, M. Lisovenko, Volodymyr G. Yefremenko, Gensheng Wang, Serhii Kruhlov, Goran Tripun Karapetrov, C. L. Chang

Published Jul 30, 2024• 9 citations
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Abstract

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.

DOI
10.1103/physrevapplied.22.014080

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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.
Frequency-tunable microwave resonators are in great demand especially in hybrid systems where precise frequency alignment of resonances is required. Here, we present frequency-tunable high-Q superconducting resonators fabricated from thin niobium nitride and niobium titanium nitride films. The resonant frequency is tuned by applying a magnetic field perpendicular to the hole structures in the resonator's inductor wire, whose kinetic inductance is modified by wirelessly induced DC supercurrents. A continuous in situ frequency tuning of over 300 MHz is achieved for a 10 GHz resonator with a moderate magnetic field of 1.2 mT. The planar resonator design and the noncontact tuning scheme greatly ease the fabrication complexity and can be widely applied in many hybrid systems for coupling microwave modes with other forms of excitations such as optical photons, phonons, magnons, and spins.
We have designed, fabricated, and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor Qi > 180 000. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurement. It also provides a useful tool to study the nonlinear response of a superconductor. In addition, it may be developed into techniques for measurement of the complex impedance of a superconductor at its transition temperature and for readout of transition-edge sensors.
We present a tunable coupler scheme that allows us to tune the coupling strength between a feedline and a superconducting resonator in situ over a wide range. In this scheme, we shunt the feedline with a 50-Ω lumped-element nonlinear transmission line made from a 20 nm NbTiN film. By injecting a DC current, the nonlinear kinetic inductance changes and the effective impedance shunting the resonator periodically varies from a short to an open, which tunes the coupling strength and coupling quality factor Qc. We have demonstrated Qc tuning over a factor of 40, between Qc∼5.5×104 and Qc∼2.3×106, for a 4.5 GHz resonator by applying a DC current less than 3.3 mA. Our tunable coupler scheme is easy to implement and may find broad applications in superconducting detector and quantum computing/information experiments.
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.
Nonlinear resonators of superconducting thin-film kinetic inductance have attracted considerable research interest in the fields of detectors, qubits, parametric amplifiers, and more. By tuning the deposition parameters, niobium titanium nitride (NbTiN) films (∼12 nm in thickness) present high resistivity(∼2000 μΩ cm) and large sheet kinetic inductance (∼0.7 nH/□). We designed resonators with NbTiN micronwire as the inductor and aluminum as the capacitor, which result in a high internal quality factor and a Kerr nonlinearity of a few hertz. The radio frequency response of the resonators demonstrates nonlinear behavior similar to that of the cubic Duffing oscillator, including frequency shift and hysteresis region. The kinetic inductance resonator is a promising candidate for high saturation power parametric amplifiers.
Predictable frequency trimming of superconducting resonators at liquid-helium temperatures requires a tuning element whose usable range remains well defined despite screening currents and hysteresis. Here, we realize flux-controlled λ/4 coplanar-waveguide resonators terminated by two-junction DC superconducting quantum interference devices (SQUIDs) fabricated in a standard Nb/Al-AlOx/Nb multilayer process. Integrated on-chip flux-bias lines allow the resonant frequency to be controlled at 4.2 K. RF measurements show periodic frequency modulation with applied flux, with a maximum shift of δfr=8.63 MHz and a single-valued tuning interval of δfr0=2.85 MHz. Near half-integer flux quanta, the response exhibits hysteretic jumps caused by the finite SQUID loop inductance, so that the usable single-valued tuning interval is smaller than the full modulation range. We develop a semi-analytical model of the frequency–flux response, supported by numerical simulations and 3D electromagnetic extraction of the device parameters, which reproduces the measured hysteretic branches and identifies the SQUID loop inductance and junction critical current as the main parameters limiting the usable tuning range. These results provide a quantitative design framework for MHz-scale frequency trimming of Nb superconducting resonators in 4 K cryogenic readout circuits.