Squeezed field path integral description of second sound in Bose-Einstein condensates

TL;DR

This paper introduces a squeezed field path integral framework for Bose-Einstein condensates, revealing second sound as a squeezing oscillation of the order parameter, and generalizing the Gross-Pitaevskii equation.

Contribution

It develops a novel squeezed coherent state path integral approach for BECs, capturing second sound as a squeezing mode, and extends the Gross-Pitaevskii equation to include squeezing effects.

Findings

Second sound in BECs is described as a squeezing oscillation.

The approach generalizes the Gross-Pitaevskii equation.

Numerical comparison supports the squeezing interpretation.

Abstract

We propose a generalization of the Feynman path integral using squeezed coherent states. We apply this approach to the dynamics of Bose-Einstein condensates, which gives an effective low energy description that contains both a coherent field and a squeezing field. We derive the classical trajectory of this action, which constitutes a generalization of the Gross Pitaevskii equation, at linear order. We derive the low energy excitations, which provides a description of second sound in weakly interacting condensates as a squeezing oscillation of the order parameter. This interpretation is also supported by a comparison to a numerical c-field method.