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

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• Chaos in circuit QED: decoherence, localization, and nonclassicality
• Detecting measurement-induced relative-position localisation
• Orbits of hybrid systems as qualitative indicators of quantum dynamics
• Non-linear dynamics, entanglement and the quantum-classical crossover of two coupled SQUID rings