Sensing quantum chaos through the non-unitary geometric phase

TL;DR

This paper introduces a decoherence-based method to detect quantum chaos by analyzing the geometric phase of a probe coupled to a many-body system, providing a universal tool for identifying the transition from integrability to chaos.

Contribution

It proposes a novel sensing mechanism using the correction to the geometric phase under decoherence to detect quantum chaos transitions.

Findings

The geometric phase correction signals the integrable to chaotic transition.

The method is effective across systems with different symmetries and interactions.

It demonstrates universality in sensing quantum chaos.

Abstract

Quantum chaos is usually characterized through its statistical implications on the energy spectrum of a given system. In this work we propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it under a dephasing interaction. By introducing the notion of an effective averaged decoherence factor, we show that the correction to the geometric phase acquired by the probe with respect to its unitary evolution can be exploited as a robust tool for sensing the integrable to chaos transition of the many-body quantum system to which it is coupled. This sensing mechanism is verified for several systems with different types of symmetries, disorder and even in the presence of long-range interactions, evidencing its universality.