Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

TL;DR

This paper demonstrates that transient chaos explains the quantum-classical correspondence breakdown in optomechanics, showing that quantum trajectories exhibit temporary chaos aligning with classical chaos before settling into regular behavior.

Contribution

It introduces the concept of transient chaos in quantum trajectories as a resolution to the quantum-classical paradox in optomechanics, and develops a theory for the scaling law of transient lifetime.

Findings

Transient chaos appears in quantum trajectories under continuous measurement.

The transient lifetime increases faster than Ehrenfest time as the system approaches the classical limit.

A physical theory explains the scaling law of transient chaos duration.

Abstract

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.