Discrete quantum droplets in one-dimensional binary Bose–Einstein condensates

Abstract

We discuss the propagation and interaction of discrete quantum droplets in one-dimensional binary Bose mixtures by variationally and numerically solving the underlying generalized discrete Gross–Pitaevskii equation. Useful analytical expressions are obtained for the energy, the chemical potential, the density profile, and the droplet separation in the regime of a small droplet. We show that for weak lattice coupling, the stationary state of small droplets remains intact and does not display any special structures. An irregular dynamics is observed in both single and dual droplets with flat-top plateau in the limit of relatively strong coupling. Our results reveal also that two droplets interact weakly and cannot form a bound-state due to the intriguing interplay of the discreteness and quantum fluctuations.