Stability and collisions of quantum droplets in [formula omitted]-symmetric dual-core couplers

Abstract

We study the effect of the interplay between parity-time (PT) symmetry and optical lattice (OL) potential on dynamics of quantum droplets (QDs) forming in a binary bosonic condensate trapped in a dual-core system. It is found that the stability of symmetric QDs in such non-Hermitian system depends critically on the competition of gain and loss γ, inter-core coupling κ, and OL potential. In the absence of OL potential, the PT-symmetric QDs are unstable against symmetry-breaking perturbations with the increase of the total condensate norm N, and they retrieve the stability at larger N, in the weakly-coupled regime. As expected, the stable region of the PT-symmetric QDs shrinks when γ increases, i.e., the PT symmetry is prone to break the stability of QDs. There is a critical value of κ beyond which the PT-symmetric QDs are entirely stable in the unbroken PT-symmetric phase. In the presence of OL potential, the PT-symmetric on-site QDs are still stable for relatively small and large values of N. Nevertheless, it is demonstrated that the OL potential can assist stabilization of PT-symmetric on-site QDs for some moderate values of N. On the other hand, it is worth noting that the relatively small PT-symmetric off-site QDs are unstable, and only the relatively large ones are stable. Furthermore, collisions between stable PT-symmetric QDs are considered too. It is revealed that the slowly moving PT-symmetric QDs tend to merge into breathers, while the fast-moving ones display quasi-elastic collision and suffer fragmentation for small and large values of N, respectively.