Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas

TL;DR

This paper analytically and numerically investigates the breathing mode frequency in a one-dimensional Bose gas, revealing reentrant behavior influenced by particle number, interactions, and trap strength, and confirms results with experimental data.

Contribution

It provides a new analytical and numerical approach to understanding the breathing mode frequency in 1D Bose gases, linking it to energy differences and experimental observations.

Findings

Reentrant behavior of the breathing mode frequency identified.

Excellent agreement with experimental data from Innsbruck.

Frequency depends on particle number, interactions, and trap strength.

Abstract

We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $\omega_z$. We predict Exciting temporal oscillations of the density distribution is a high-precision method for probing ultracold trapped atomic gases. Interaction effects in their many-body dynamics are particularly puzzling and counter-intuitive in one spatial dimension (1D) due to enhanced quantum correlations. We consider 1D quantum Bose gas in a parabolic trap at zero temperature and explain, analytically and numerically, how oscillation frequency depends on the number of particles, their repulsion and the trap strength. We identify the frequency with the energy difference between the ground state and a particular excited state. This way we avoided resolving the dynamical evolution of the system, simplifying the problem immensely. We find an excellent quantitative agreement of our results with the data from the Innsbruck experiment [Science 325, 1224 (2009)].