Echoes in a parametrically perturbed Kerr-nonlinear oscillator

TL;DR

This paper investigates classical and quantum echoes in a Kerr oscillator under pulsed perturbations, revealing how different initial states and dissipation affect echo phenomena, with implications for quantum error correction.

Contribution

It introduces a detailed analysis of classical and quantum echoes in a Kerr oscillator, including the effects of dissipation and initial state superpositions, advancing understanding of quantum state dynamics.

Findings

Long-lived classical echoes from weak parametric drives.

Quantum echoes in cat states depend on initial phase and superposition weights.

Dissipation suppresses revivals but quantum echoes can be recovered with proper tuning.

Abstract

We study classical and quantum echoes in a Kerr oscillator driven by a frequency-controlling pulsed perturbation. We consider dynamical response to the perturbation for a single coherent state and for Schr\"odinger cat states constructed as both balanced and imbalanced superpositions of two coherent states. For individual coherent states, we demonstrate that a weak parametric drive yields a long-lived sequence of classical echoes. Cat states are found to exhibit distinct quantum echoes that are sensitive to the initial relative phase and weights of the coherent states in superposition. We examine the effect of dissipation on quantum echoes and quantum revivals of cat states. We demonstrate that, even when dissipation suppresses quantum revivals, quantum echoes can be recovered by properly tuning the timing and strength of the perturbation. These results may be useful for characterizing and mitigating errors of cat qubits.