Spontaneous symmetry breaking, stability and adiabatic changes of 2D quantum droplets in amended Gross–Pitaevskii equation with multi-well potential

Abstract

In this paper, we report the spontaneous symmetry breaking (SSB) of two-dimensional (2D) quantum droplets (QDs) for the amended Gross–Pitaevskii equation with Lee–Huang–Yang corrections and a Gaussian quadruple-well potential. The complete pitchfork symmetry breaking bifurcation diagrams are presented for the possible stationary states with four modes, which involve twelve different real solution branches and one complex solution branch, where the continuous asymmetric QDs branches bifurcate from the fundamental symmetric or antisymmetric one as the strength of nonlinearity exceeds a threshold value. Meanwhile the stability of the 2D QDs is explored by means of linear stability analysis and direct numerical simulations. Especially, for the asymmetric QDs, the SSB effect and the trend for getting the droplet asymmetry are discussed by changing the chemical potential. Finally, the adiabatic changes of stable stationary QDs are explored by modulating the position, depth, and width of the potential well as functions of time, and the strong robustness of QDs is found. Our results provide some theoretical basis for the SSB phenomena and related physical experiments on 2D asymmetric QDs.