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.
Highlights
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
For a specific physical process in a quantum system, if a large number of energy levels are involved, the evolution of the expected values of the observables will be governed by the classical Newtonian dynamics
We report our discovery of transient chaos as a natural paradigm to explain the recently discovered phenomenon of the breakdown of quantum-classical correspondence in optomechanics
Summary
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. For a specific physical process in a quantum system, if a large number of energy levels are involved (e.g., in the high energy regime), the evolution of the expected values of the observables will be governed by the classical Newtonian dynamics In a recent work[25], it was demonstrated that, in the classical regime the system exhibits chaos, but in the corresponding quantum regime the motion becomes regular and no signatures of chaos appear to exist. This is the so-called quantum-classical correspondence breakdown in optomechanics. Rather than focusing on the average properties of the system, we study the individual quantum trajectories of the system as related to the continuous weak measurement to probe into the quantum-classical correspondence breakdown
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