Classical phase-space approach for coherent matter waves

TL;DR

This paper explores a classical phase-space method using the Truncated Wigner Equation to analyze matter-wave propagation, successfully capturing key dynamics of Bose-Einstein condensates and identifying quantum signatures beyond classical approximation.

Contribution

It demonstrates the applicability of the TWE for modeling ideal and interacting matter waves, providing a bridge between classical phase-space methods and quantum condensate dynamics.

Findings

TWE accurately predicts low-energy spectra of condensates.

TWE reproduces breathing mode frequencies for specific interactions.

Quantum signatures require dynamics beyond classical phase-space description.

Abstract

We investigate a classical phase-space approach of matter-wave propagation based on the Truncated Wigner Equation (TWE). We show that such description is suitable for ideal matter waves in quadratic time-dependent confinement as well as for harmonically trapped Bose Einstein condensates in the Thomas-Fermi regime. In arbitrary interacting regimes, the TWE combined with the moment method yields the low-energy spectrum of a condensate as predicted by independent variational methods. TWE also gives the right breathing mode frequency for long-ranged interactions decaying as $1/r^2$ in 3D and for a contact potential in 2D. Quantum signatures, beyond the TWE, may only be found in the condensate dynamics beyond the regimes of classical phase-space propagation identified here.