Oscillating Quantum Droplets from the free expansion of Logarithmic One-Dimensional Bose Gases

TL;DR

This paper investigates the stability and free expansion behavior of one-dimensional logarithmic Bose-Einstein condensates, revealing conditions under which they form oscillating quantum droplets during expansion.

Contribution

It demonstrates that 1D logarithmic condensates can form stable, oscillating quantum droplets, differing from 3D cases, and analyzes their unique expansion dynamics.

Findings

1D logarithmic condensates form quantum droplet configurations.

Oscillations occur during free expansion under certain parameters.

Differences from 3D systems in energy and expansion behavior.

Abstract

We analyze some issues related to the stability and free expansion of a one-dimensional logarithmic Bose-Einstein condensate, particularly its eventual relation to the formation of quantum droplet-type configurations. We prove that the corresponding properties, such as the energy of the associated N-body ground state, differ substantially with respect to its three-dimensional counterpart. Consequently, the free velocity expansion also shows differences with respect to the three-dimensional system when logarithmic interactions are taken into account. The one-dimensional logarithmic condensate tends to form quantum droplet-type configurations when the external trapping potential is turned off, i.e., the self-sustainability or self-confinement appears as in three-dimensions. However, we obtain that for some specific values of the self-interaction parameters and the number of particles under consideration, the cloud oscillates during the free expansion around to a specific equilibrium size. These results show that we can get scenarios in which the one-dimensional cloud reaches stable configurations, i.e., oscillating quantum droplets.