Observing quantum chaos with noisy measurements and highly mixed states

Ralph, Jason F ORCID: 0000-0002-4946-9948, Jacobs, Kurt and Everitt, Mark J (2017) Observing quantum chaos with noisy measurements and highly mixed states. PHYSICAL REVIEW A, 95 (1). 012135-.

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Abstract

A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to $\hbar$. While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low purity states and to variations in the parameters of the system.

Item Type:	Article
Additional Information:	3 figures, 5 pages, updated after comments
Uncontrolled Keywords:	quant-ph, quant-ph
Depositing User:	Symplectic Admin
Date Deposited:	10 Jan 2017 11:13
Last Modified:	19 Jan 2023 07:20
DOI:	10.1103/PhysRevA.95.012135
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005114