The stability and collision dynamics of quantum droplets in PT-symmetric optical lattices

Abstract

This paper explores the stability and collision dynamics of two-component quantum droplets within the framework of the two-dimensional Gross-Pitaevskii (GP) equation, incorporating PT-symmetric lattice potentials and Lee-Huang-Yang (LHY) correction terms. Through theoretical analysis and numerical simulations, the behavior of two-component quantum droplets in PT-symmetric lattice potentials is elucidated. The study reveals that bell-shaped zero-vortex quantum droplets can form in PT-symmetric lattices, and their stability adheres to the Vakhitov-Kolokolov (VK) criterion. Numerical simulations demonstrate three distinct post-collision states of droplets: coalescence, separation, and evaporation, with the specific outcome depending on the droplets' particle number, initial momentum, and relative phase. Additionally, the quadrupole oscillation mode of the coalesced droplets is examined, revealing a relationship between the oscillation period and the norm. These findings provide significant insights for understanding quantum droplet phenomena and designing related experiments.