Dynamical transition from a quasi-one dimensional Bose-Einstein condensate to a Tonks-Girardeau gas

TL;DR

This paper investigates the dynamical transition of a one-dimensional Bose gas from a Bose-Einstein condensate to a Tonks-Girardeau gas during expansion, revealing a non-self-similar density evolution that asymptotically approaches a fermionized profile.

Contribution

It demonstrates the transition dynamics using a nonlinear Schrödinger equation with variable nonlinearity and compares it with an exact Bose-Fermi mapping, providing new insights into 1D quantum gas expansion.

Findings

Density approaches Tonks-Girardeau profile during expansion

Expansion is not self-similar for general cases

Exact self-similar expansion for initial Tonks-Girardeau gas

Abstract

We analyze in detail the expansion of a 1D Bose gas after removing the axial confinement. We show that during its one-dimensional expansion the density of the Bose gas does not follow a self-similar solution, but on the contrary, it asymptotically approaches a Tonks-Girardeau profile. Our analysis is based on a nonlinear Schr\"odinger equation with variable nonlinearity whose validity is discussed for the expansion problem, by comparing with an exact Bose-Fermi mapping for the case of an initial Tonks-Girardeau gas. For this case, the gas is shown to expand self-similarly, with a different similarity law compared to the one-dimensional Thomas-Fermi condensate.