On the fate of travelling waves at the boundary of quantum droplets

TL;DR

This paper studies how traveling matter waves behave at the edges of quantum droplets in a 2D Bose-Einstein condensate, revealing complex phenomena like emission, mode excitation, and vortex splitting.

Contribution

It provides a detailed analysis of wave-boundary interactions in quantum droplets, including numerical simulations and new insights into boundary-induced excitations and dynamics.

Findings

Traveling waves can emit small droplets at the boundary.

Internal modes of the droplet can be excited by traveling waves.

Vortex-antivortex pairs can split into individual vortices near the boundary.

Abstract

We analyze quantum droplets formed in a two-dimensional symmetric mixture of Bose-Einstein condensed atoms. For sufficiently large atom numbers, these droplets exhibit a flat-top density profile with sharp boundaries governed by surface tension. Within the bulk of the droplet, traveling matter waves - localized density dips - can propagate at constant velocity while maintaining their shape. Using numerical simulations and qualitative analysis, we investigate the rich phenomenology that arises when such excitations reach the boundary of a finite droplet. We show that they can emit a small outgoing droplet, excite internal modes of the host soliton, or, in the case of vortex-antivortex pairs, split into individual vortices propagating backward near the edge. Furthermore, we demonstrate that traveling waves can be dynamically generated near the boundary through the collision of distinct droplets, and we discuss their trajectories and interactions.