Multi-stable quantum droplets in optical lattices

We address the nonlinear dynamics of binary Bose-Einstein condensates with mutually symmetric spinor components trapped in an optical lattice. The interaction between the repulsive Lee-Huang-Yang nonlinearity and the intercomponent attraction as well as Bragg scattering of an optical lattice results in formation of multi-peaked quantum droplets. Even- and odd-symmetric droplets can bifurcate from Bloch modes of the corresponding periodic systems. Linear stability analysis corroborated by direct evolution simulations reveals that even-symmetric droplets with different norms and different number of peaks can evolve stably at the same chemical potential, i.e., multi-stable droplets are possible in the present scheme. Besides the droplets in the semi-infinite gap, the properties of droplets in the first finite bandgap are also discussed. Both even- and odd-symmetric droplets are stable in almost their whole existence domains. We reveal that optical lattice plays an important role for the stabilization of droplets, in sharp contrast to the nonlinear system without a lattice modulation. We, thus, furnish a paradigmatic example of multi-stable quantum droplets held in optical lattices.