Recovery of classical chaotic-like behaviour in a quantum three-body problem

Abstract

Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and dissipative systems. The relevance and impact of chaoticlike phenomena to quantum systems has been highlighted in recent studies which have shown that quantum chaos is significant in some aspects of quantum computation and information processing. In this paper we study a three-body system comprising of identical particles arranged so that the system's classical trajectories exhibit Hamiltonian chaos. Here we show that it is possible to recover very nearly classical-like, conservative, chaotic trajectories from such a system through an unravelling of the master equation. First, this is done through continuous measurement of the position of each system. Second, and perhaps somewhat surprisingly, we demonstrate that we still obtain a very good match between the classical and quantum dynamics by weakly measuring the position of only one of the oscillators.

6 pages, 6 figures

References in corpus (5)

• Continuous Quantum Measurement and the Quantum to Classical Transition
• Conservative chaotic map as a model of quantum many-body environment
• The transition to classical chaos in a coupled quantum system through continuous measurement
• Persistent Entanglement in the Classical Limit
• Quantum chaos in the spectrum of operators used in Shor's algorithm

Cited by in corpus (3)

• The quantum-classical crossover of a field mode
• On the correspondence principle: implications from a study of the chaotic dynamics of a macroscopic quantum device
• Non-linear dynamics, entanglement and the quantum-classical crossover of two coupled SQUID rings