No abstract

We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-component Bose-Einstein condensates (TBECs) of dilute atomic gases in presence of vortices. In particular, we consider TBECs of Rb hyperfine states, and Rb-Cs mixture. There is an enhancement of the phase-separation when the vortex is present in both condensates. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupy the edges at phase-separation. But, suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the inter-species interactions to propel the TBEC from miscible to immiscible phase, and use the time dependent Gross-Pitaevskii equation to probe the phenomenon of phase-separation. We also examine the effect of higher charged vortex.

We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle θ of the dipolar bosons. At low tilt angles 0 • θ 25 • , the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles 55 • θ 35 • , phases with striped order of supersolid or density wave are preferred. In the intermediate domain 25 • θ 35 • an emulsion or SF phase intervenes the transition between the checkerboard and striped phases. The attractive interaction dominates for θ 55 • , which renders the system unstable and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results.