Fidelity decay in trapped Bose-Einstein condensates

TL;DR

This paper investigates how quantum fidelity in trapped Bose-Einstein condensates decays over time under small perturbations, revealing a critical time after which fidelity drops abruptly, with potential experimental observability.

Contribution

It introduces a numerical analysis of fidelity decay in BECs in anharmonic traps, highlighting a logarithmic dependence of critical time on atom number and perturbation strength.

Findings

Fidelity remains constant until a critical time

Fidelity drops abruptly over one trap oscillation period

Critical time depends logarithmically on atom number and perturbation amplitude

Abstract

The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.