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

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.