Two-dimensional symbiotic solitons and quantum droplets in a quasi-one-dimensional optical lattice

Symbiotic solitons (SS) and quantum droplets (QD) are self-trapped localized modes emerging in binary Bose-gas mixtures with intra-component repulsion and inter-component attraction. We have shown that two-dimensional (2D) SS can be stabilized against collapse or decay by means of a quasi-one-dimensional optical lattice (OL). Mobility of SSs along the free direction of the potential allows us to explore interactions and collisions of SSs moving in the same channel and neighboring channels of the quasi-1D OL. For the case of equal atom numbers in both components of the binary Bose–Einstein condensate (BEC) we have developed a variational approach that showed the stability of SS. For parameter settings when the SS stays on the verge of collapse/decay instability we take into account the Lee–Huang–Yang quantum fluctuations (QF) term in the coupled Gross–Pitaevskii equations (GPE). The QF term in the 2D GPE has the form of nonlinearity with a logarithmic factor, which is repulsive for large amplitude waves and attractive for opposite situations. This property of the governing equation supports stable QDs immersed in a gaseous phase of the larger component in particle-imbalanced Bose-gas mixtures. We explore the peculiar properties of QD such as incompressibility and surface tension, which are inherent to liquids. The proposed model of binary BEC loaded in a quasi-1D OL allows us to demonstrate the manifestations of the incompressibility and surface tension of 2D QDs.