Loschmidt echo in one-dimensional interacting Bose gases

TL;DR

This paper investigates the Loschmidt echo in 1D interacting Bose gases, revealing Gaussian decay in the strongly interacting regime and complex decay patterns with oscillations in the weakly-interacting regime, highlighting how interactions influence quantum reversibility.

Contribution

It provides a comparative analysis of Loschmidt echo dynamics in both strongly and weakly interacting 1D Bose gases, demonstrating different decay behaviors and the impact of interactions.

Findings

Gaussian decay of Loschmidt echo in Tonks-Girardeau regime

Faster decay with increased interactions in mean-field regime

Oscillatory behavior superimposed on decay in mean-field regime

Abstract

We explore Loschmidt echo in two regimes of one-dimensional (1D) interacting Bose gases: the strongly interacting Tonks-Girardeau (TG) regime, and the weakly-interacting mean-field regime. We find that the Loschmidt echo of a TG gas decays as a Gaussian when small perturbations are added to the Hamiltonian (the exponent is proportional to the number of particles and the magnitude of a small perturbation squared). In the mean-field regime the Loschmidt echo decays faster for larger interparticle interactions (nonlinearity), and it shows richer behavior than the TG Loschmidt echo dynamics, with oscillations superimposed on the overall decay.