Sensing quantum chaos through the non-unitary geometric phase

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.

Many-body localization and the emergence of quantum darwinism

“…Also, we have analyzed the mixing of the redundant records by allowing intra-environment interactions. Despite low disorder is associated to an ergodic dynamics and ergodicity usually yields to a markovian evolution [15], we have found that a highly disordered evolution is less harmful for the appearance of classical objectivity. Hence, a high amount of disorder is not only beneficial for the initial state under consideration but also reduces the mixing of the redundant records in the presence of intra-environment interactions.…”

“…In general, QD has been studied in the simplest scenario, where the fragments of the environment do not interact with each other. However, this may not be the most realistic situation in an experimental setup, where the intrinsic dynamics of the environment can play a significant role in the decoherent dynamics of the open system [14,15]. For this reason, it is essential to understand how different environmental properties influence the emergence of QD and which are the mechanisms that may enhance the proliferation of redundancy.…”