Formation of Matter-Wave Droplet Lattices in Multi-Color Periodic Confinements

Abstract

In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion.