title: Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.
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.
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Guanglei
authors.initials: G
authors.lastname: Wang
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.|Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.|Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, UK.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.affiliation: Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, UK.
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi