Zero-energy modes of two-component Bose-Bose droplets

TL;DR

This paper analytically investigates the zero-energy modes arising from symmetry breaking in two-component Bose-Bose droplets, providing a simplified description of their dynamics and interactions.

Contribution

It introduces explicit expressions for zero-energy modes and Hamiltonians for their evolution, simplifying the complex quantum droplet system to a few global degrees of freedom.

Findings

Derived analytic zero-energy modes for symmetry-broken states

Formulated Hamiltonians for droplet center-of-mass and phase dynamics

Enabled simplified modeling of droplet interactions and collisions

Abstract

Bose-Bose droplets are self-bound objects emerging from a mixture of two interacting Bose-Einstein condensates when their interactions are appropriately tuned. During droplet formation three continuous symmetries of the system's Hamiltonian are broken: translational symmetry and two U1 symmetries, allowing for arbitrary choice of phases of the mean-field wavefunctions describing the two components. Breaking of these symmetries must be accompanied by appearance of zero-energy excitations in the energy spectrum of the system recovering the broken symmetries. Normal modes corresponding to these excitations are the zero-energy modes. Here we find analytic expressions for these modes and introduce Hamitonians generating their time evolution -- dynamics of the droplet's centers of mass as well as dynamics of the phases of the two droplet's wavefunctions. When internal types of excitations (quasiparticles) are neglected then the very complex system of a quantum droplet is described using only few "global" degrees of freedom - the position of the center of mass of the droplet and two phases of two wave-functions, all these being quantum operators. This gives the possibility of describing in a relatively easy way processes of interaction of these quantum droplets, such as collisions.