Fragility of superposition states evaluated by the Loschmidt Echo

TL;DR

This paper investigates how quantum superposition states in a harmonic oscillator become fragile due to environmental interactions, using the Loschmidt Echo to quantify decoherence and sensitivity related to energy separation.

Contribution

It introduces a model analyzing the fragility of superposition states under environmental perturbations using the Loschmidt Echo, highlighting exponential sensitivity to energy separation.

Findings

Fragility increases exponentially with energy separation.

Loschmidt Echo effectively quantifies decoherence.

Superposition states are more sensitive than incoherent states.

Abstract

We consider the degradation of the dynamics of a Gaussian wave packet in a harmonic oscillator under the presence of an environment. This last is given by a single non-degenerate two level system. We analyze how the binary degree of freedom perturbs the free evolution of the wave packet producing decoherence, which is quantified by the Loschmidt Echo. This magnitude measures the reversibility of a perturbed quantum evolution. In particular, we use it here to study the relative "fragility" of coherent superpositions (cat states) with respect to incoherent ones. This fragility or sensitivity turns to increase exponentially with the energy separation of the two components of the superposition.