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We employ the Loschmidt Echo, i.e. the signal recovered after the reversal ofan evolution, to identify and quantify the processes contributing todecoherence. This procedure, which has been extensively used in single particlephysics, is here employed in a spin ladder. The isolated chains have 1/2 spinswith XY interaction and their excitations would sustain a one-body likepropagation. One of them constitutes the controlled system S whose reversibledynamics is degraded by the weak coupling with the uncontrolled second chain,i.e. the environment E. The perturbative SE coupling is swept through arbitrarycombinations of XY and Ising like interactions, that contain the standardHeisenberg and dipolar ones. Different time regimes are identified for theLoschmidt Echo dynamics in this perturbative configuration. In particular, theexponential decay scales as a Fermi golden rule, where the contributions of thedifferent SE terms are individually evaluated and analyzed. Comparisons withprevious analytical and numerical evaluations of decoherence based on theattenuation of specific interferences, show that the Loschmidt Echo is anadvantageous decoherence quantifier at any time, regardless of the S internaldynamics.

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