The Loschmidt Echo as a robust decoherence quantifier for many-body systems

TL;DR

This paper demonstrates that the Loschmidt Echo is an effective and robust measure for quantifying decoherence in many-body quantum systems, specifically in a spin ladder with controlled system-environment interactions.

Contribution

It extends the use of Loschmidt Echo to many-body systems and analyzes its effectiveness across different interaction regimes and time scales.

Findings

Loschmidt Echo decay follows a Fermi golden rule scaling.

Different SE interaction terms contribute distinctly to decoherence.

Loschmidt Echo outperforms other measures in quantifying decoherence over time.

Abstract

We employ the Loschmidt Echo, i.e. the signal recovered after the reversal of an evolution, to identify and quantify the processes contributing to decoherence. This procedure, which has been extensively used in single particle physics, is here employed in a spin ladder. The isolated chains have 1/2 spins with XY interaction and their excitations would sustain a one-body like propagation. One of them constitutes the controlled system S whose reversible dynamics is degraded by the weak coupling with the uncontrolled second chain, i.e. the environment E. The perturbative SE coupling is swept through arbitrary combinations of XY and Ising like interactions, that contain the standard Heisenberg and dipolar ones. Different time regimes are identified for the Loschmidt Echo dynamics in this perturbative configuration. In particular, the exponential decay scales as a Fermi golden rule, where the contributions of the different SE terms are individually evaluated and analyzed. Comparisons with previous analytical and numerical evaluations of decoherence based on the attenuation of specific interferences, show that the Loschmidt Echo is an advantageous decoherence quantifier at any time, regardless of the S internal dynamics.