Monopole excitations of a harmonically trapped one-dimensional Bose gas from the ideal gas to the Tonks-Girardeau regime

TL;DR

This paper introduces a modified nonlinear Schrödinger equation that accurately models monopole excitation frequencies of a 1D Bose gas across all interaction regimes, from ideal gas to Tonks-Girardeau, matching experimental results.

Contribution

The authors develop and validate a unified numerical approach (m-NLSE) that captures monopole excitations across all interaction regimes in a 1D Bose gas, bridging gaps between existing methods.

Findings

Accurately reproduces experimental monopole frequencies in all regimes

Unified method applicable from ideal gas to Tonks-Girardeau regime

Outperforms standard NLSE and LDA in different regimes

Abstract

Using a time-dependent modified nonlinear Schr\"odinger equation (m-NLSE) -- where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution -- we study frequencies of the collective monopole excitations of a one-dimensional (1D) Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science Vol. 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation (LDA), the situation reverses in the latter case. However, the m-NLSE treats all these regimes within a single numerical method.