Hybrid phase-space--Fock-space approach to evolution of a driven nonlinear resonator

TL;DR

This paper introduces a hybrid phase-space and Fock-space method to efficiently analyze the quantum evolution of a driven nonlinear resonator, capturing transient and steady-state squeezing effects with simplified equations.

Contribution

It develops a Gaussian approximation-based hybrid approach that simplifies the analysis of nonlinear resonator dynamics, surpassing traditional full density matrix simulations in efficiency.

Findings

Steady-state squeezing limited to 3 dB

Transient squeezing can exceed 3 dB

Method provides accurate transient and steady-state analysis

Abstract

We analyze the quantum evolution of a weakly nonlinear resonator due to a classical near-resonant drive and damping. The resonator nonlinearity leads to squeezing and heating of the resonator state. Using a hybrid phase-space--Fock-space representation for the resonator state within the Gaussian approximation, we derive evolution equations for the four parameters characterizing the Gaussian state. Numerical solution of these four ordinary differential equations is much simpler and faster than simulation of the full density matrix evolution, while providing good accuracy for the system analysis during transients and in the steady state. We show that steady-state squeezing of the resonator state is limited by 3 dB; however, this limit can be exceeded during transients.