Observing quantum chaos with noisy measurements and highly mixed states

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 $\hslash$. 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.

3 figures, 5 pages, updated after comments

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Cited by in corpus (2)

• Multi-parameter estimation along quantum trajectories with Sequential Monte Carlo methods
• Exploring the complex dynamics of a Duffing oscillator with ordinal patterns analysis