Phases and dynamics of quantum droplets in the crossover to two-dimensions

TL;DR

This paper investigates the properties and dynamics of quantum droplets transitioning from three to two dimensions, revealing how their size, energy, and behavior change with interaction sign and confinement, with implications for experiments.

Contribution

It provides a detailed analysis of droplet phases and dynamics in the 2D crossover, including validity regimes and the effects of interaction quenches, using numerical and variational methods.

Findings

Droplets become more extended with positive mean-field interactions.

Binding energies decrease inversely with the square of droplet size.

Large quenches induce continuous expansion and density ring formation.

Abstract

We explore the ground states and dynamics of ultracold atomic droplets in the crossover region from three to two dimensions by solving the two-dimensional and the quasi two-dimensional extended Gross-Pitaevskii equations numerically and with a variational approach. By systematically comparing the droplet properties, we determine the validity regions of the pure two-dimensional description, and therefore the dominance of the logarithmic nonlinear coupling, as a function of the sign of the averaged mean-field interactions and the size of the transverse confinement. One of our main findings is that droplets become substantially extended upon transitioning from negative-to-positive averaged mean-field interactions. This is accompanied by a significant reduction of their binding energies which are approximately inversely proportional to the square of their size. To explore fundamental dynamical properties in the crossover region, we study interaction quenches and show that the droplets perform a periodic breathing motion for modest quench strengths, while larger quench amplitudes lead to continuous expansion exhibiting density ring structures. We also showcase that it is possible to form complex bulk and surface density patterns in anisotropic geometries following the quench. Since we are working with realistic parameters, our results can directly facilitate future experimental realizations.