Transient dynamics of a superconducting nonlinear oscillator

TL;DR

This paper studies the transient decay behavior of a superconducting nonlinear oscillator based on a SQUID, exploring its dynamics under various conditions and potential applications in flux qubit readout.

Contribution

It provides experimental and simulation insights into the transient ringdown responses of a flux-tunable SQUID-based nonlinear oscillator, including phase jumps and flux-dependent dynamics.

Findings

Good agreement between experiments and simulations.

Identification of crossover between resonance and adiabatic following.

Potential for flux qubit readout based on ringdown signals.

Abstract

We investigate the transient dynamics of a lumped-element oscillator based on a dc superconducting quantum interference device (SQUID). The SQUID is shunted with a capacitor forming a nonlinear oscillator with resonance frequency in the range of several GHz. The resonance frequency is varied by tuning the Josephson inductance of the SQUID with on-chip flux lines. We report measurements of decaying oscillations in the time domain following a brief excitation with a microwave pulse. The nonlinearity of the SQUID oscillator is probed by observing the ringdown response for different excitation amplitudes while the SQUID potential is varied by adjusting the flux bias. Simulations are performed on a model circuit by numerically solving the corresponding Langevin equations incorporating the SQUID potential at the experimental temperature and using parameters obtained from separate measurements characterizing the SQUID oscillator. Simulations are in good agreement with the experimental observations of the ringdowns as a function of applied magnetic flux and pulse amplitude. We observe a crossover between the occurrence of ringdowns close to resonance and adiabatic following at larger detuning from the resonance. We also discuss the occurrence of phase jumps at large amplitude drive. Finally, we briefly outline prospects for a readout scheme for superconducting flux qubits based on the discrimination between ringdown signals for different levels of magnetic flux coupled to the SQUID.