The Casimir-like effect in a one-dimensional Bose gas

TL;DR

This paper investigates the Casimir-like interaction between impurities in a one-dimensional Bose gas, revealing a crossover from exponential decay at short distances to power-law decay at larger separations, incorporating quantum fluctuations.

Contribution

The authors develop an analytic theory based on the Gross-Pitaevskii equation that captures the crossover behavior of impurity interactions in a 1D Bose gas, including quantum effects.

Findings

Interaction decays exponentially at short distances

Interaction follows a power law at large distances

Analytic expression interpolates between the two regimes

Abstract

The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross-Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is a classical result that can be understood using the mean-field Gross-Pitaevskii equation. We find that at larger distances, the induced interaction crosses over into a power law dependence due to the quantum fluctuations. We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization.