Parametric resonance in tunable superconducting cavities

TL;DR

This paper presents a comprehensive theory of parametric resonance in tunable superconducting cavities, analyzing nonlinear dynamics, amplification properties, and quantum noise characteristics relevant for quantum information applications.

Contribution

It introduces a detailed theoretical framework accounting for nonlinearity and damping, and explores classical and quantum behaviors of the cavity near parametric resonance.

Findings

Identification of multistability regimes

Analysis of phase-sensitive and detuned signal amplification

Evaluation of quantum noise, squeezing, and entanglement

Abstract

We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the SQUID attached to the cavity, and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate the amplifier performance to that of linear parametric amplifiers. We also discuss applications of the device for dispersive qubit readout. Beyond the classical response of the cavity, we investigate small quantum fluctuations around the amplified classical signals. We evaluate the noise power spectrum both for the internal field in the cavity and the output field. Other quantum statistical properties of the noise are addressed such as squeezing spectra, second order coherence, and two-mode entanglement.