Phenomenological Theory of Mode Collapse-revival in Confined Bose Gas

TL;DR

This paper develops a phenomenological theory describing the collapse and revival of modes in a weakly nonlinear confined Bose gas, accounting for quantum fluctuations and providing estimates relevant for experiments.

Contribution

It introduces a new phenomenological framework for mode collapse-revival in Bose gases, incorporating fluctuations and calculating the nonlinear correction coefficient for specific modes.

Findings

Collapse time estimated to be around 250 ms under typical conditions.

Derived the nonlinear correction coefficient for the breathing mode.

Provided a theoretical basis for understanding mode dynamics in confined Bose gases.

Abstract

A phenomenological theory of mode collapse-revival for a system with a weak nonlinearity is presented. The theory takes into account fluctuations of the number n of quanta of oscillations. The collapse time $\tau _c ^{-1}$ for a mode of frequency $\omega _0$ turns out to be $\omega _0(\sqrt{n/2}\hbar \omega _0 \mid \nu \mid)$, where \nu is a coefficient in a nonlinear correction to the mode frequency with respect to the oscillation energy E. For a Bose gas in a harmonic trap $\tau _c$ is order of $\omega _0^{-1}\sqrt{\mu N/E\hbar \omega _0}$. This value is order of 250 ms. for typical experimental conditions. The coefficient \nu is calculated for the breathing mode in an isotropic trap.