Discrete quantum droplets in one-dimensional optical lattices

We consider the dynamical model of quantum droplets (QDs) launched in a deep optical lattice. This setting is modeled by a one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. We find that the hopping rate, C, plays a dominant role in characterizing the properties of the system. The system can be divided into two regions: the quasicontinuum (QC) and tightly-bound (TB) regions. In the QC region, where the hopping rate C>0.21, the discrete QDs can behave similar to their counterparts in the continuous system. In the TB region, where C<0.21, the presence of the Peierls-Nabarro (PN) potential barrier induces multistablity and discreteness. In this region, the curves for 3 characteristics (chemical potential μ, peak values ρ, and effective width W) are no longer continuous, being split into many branches, and most of the solutions on the μ(N) (N is the total norm of the QD) curves violate the Vakhitov-Kolokolov criterion. Analyses are performed to explain these effects, with the results agreeing well with the numerical simulations. By introducing synthetic gauge fields, we create for the first time stable staggered discrete QDs in the current system. The mobilities and collisions of discrete QDs are also discussed, showing that the phenomena of the dynamics in the two regions (TB and QC) are different.