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

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.

Formation and quench of homonuclear and heteronuclear quantum droplets in one dimension

“…Next, we monitor for the first time the nonequilibrium droplet dynamics within an ab-initio approach. Particularly, we exemplify the droplet expansion [44] which deforms in the course of the evolution featuring FT signatures following quenches to stronger intercomponent attractions. In the reverse case, a breathing motion is initiated.…”