Lyapunov exponents of quantum trajectories beyond continuous measurements

TL;DR

This paper introduces a new way to quantify quantum chaos using quantum jump trajectories, extending the concept of Lyapunov exponents beyond continuous measurements, and demonstrates this approach on a quantum dimer system.

Contribution

It proposes an alternative generalization of quantum Lyapunov exponents based on quantum jump trajectories, applicable beyond continuous measurement frameworks.

Findings

Uncovered transition to quantum chaos in a modulated quantum dimer.

Matched quantum chaos transition with classical period-doubling route.

Extended the toolbox for quantifying dissipative quantum chaos.

Abstract

Quantum systems interacting with their environments can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. Yet, despite many attempts, the toolbox for quantifying dissipative quantum chaos remains very limited. In particular, quantum generalizations of Lyapunov exponent, the main quantifier of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization which is based on the unraveling of a quantum master equation into an ensemble of so-called 'quantum jump' trajectories. These trajectories are not only a theoretical tool but a part of the experimental reality in the case of quantum optics. We illustrate the idea by using a periodically modulated open quantum dimer and uncover the transition to quantum chaos matched by the period-doubling route in the classical limit.