Observing quantum chaos with noisy measurements and highly mixed states

TL;DR

This paper demonstrates that quantum chaos, indicated by positive Lyapunov exponents, can be observed directly in noisy, mixed quantum states of a Duffing oscillator, even with low measurement efficiency.

Contribution

It shows the first direct observation of quantum trajectories with positive Lyapunov exponents under realistic noisy measurement conditions.

Findings

Positive Lyapunov exponents observed with 20% measurement efficiency

Quantum chaos signatures are robust to highly mixed states

Transition to chaos persists despite parameter variations

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.