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Journal of Radio Electronics

Effective Josephson inductance of RF-SQUID as a function of power of microwave irradiation

Alexander S. Averkin, Lyudmila V. Filippenko

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Radio frequency superconducting quantum interferometers (RF-SQUIDs) are structural elements of nonlinear media used in superconducting metamaterials and superconducting low-noise parametric amplifiers. An expression for the effective Josephson inductance as a function of the external microwave signal power in a two-tone excitation mode is derived. This formula is applied to calculate the effective inductance of a Josephson junction embedded in an RF-SQUID under microwave radiation. The analytically calculated dependences of the resonant frequency and effective Josephson inductance of a non-hysteresis RF-SQUID on microwave power are in good agreement with experimental results.

DOI
10.30898/1684-1719.2026.1.9

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Radio frequency superconducting quantum interferometers (RF-SQUIDs) are structural elements of nonlinear media used in superconducting metamaterials and superconducting low-noise parametric amplifiers. An expression for the effective Josephson inductance as a function of the external microwave signal power in a two-tone excitation mode is derived. This formula is applied to calculate the effective inductance of a Josephson junction embedded in an RF-SQUID under microwave radiation. The analytically calculated dependences of the resonant frequency and effective Josephson inductance of a non-hysteresis RF-SQUID on microwave power are in good agreement with experimental results.
The nonlinear response of a one-dimensional superconducting metamaterial based on 54 non-hysteretic radiofrequency superconducting quantum interference devices (RF-SQUIDs) was experimentally studied. The dependences of the system's resonant frequency on the pump tone power were measured in a two-tone excitation mode both in the absence and with the application of an external constant magnetic field. The metamaterial exhibits bistable behavior over a wide range of pump powers, indicating its potential for use in quantum electronic devices and superconducting parametric amplifiers.
The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency superconducting quantum interference devices (rf-SQUIDs). The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. Using a two time scale analysis technique, we present an analytical theory that successfully explains our experimental observations. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.
Abstract An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.
Abstract We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N × N × 2 overlapping metamaterial array, where we develop an understanding of the many ( 8 N 2 − 8 N + 3 ) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.
Experimental results on some radio-frequency superconducting quantum interference device (rf-SQUID) signal properties are presented. The quantum interferometer was made of ceramic YBa2Cu3O7−x and was due to a low critical current operated in the inductance or nonhysteretic mode. With bias current as reference, amplitude variation, and phase shift of the voltage over the tank circuit coupled to the SQUID were measured simultaneously. It is shown that there is qualitative agreement between calculations based on the resistivity shunted junction model and the data. Moreover, using phase detection, signal instabilities predicted for the rf-SQUID inductance mode were observed. These signal instabilities may be exploited to enhance the transfer coefficient for measured flux-to-output signal.