The ground states and spin textures of rotating two-component Bose–Einstein condensates in an annular trap

Abstract

We investigate the ground states and spin textures of rotating two-component Bose–Einstein condensates (BECs) confined in an annular potential. For the two-component miscible BECs, we analytically give the critical angular velocity of each component with the Thomas–Fermi approximation (TFA), at which the density profile changes from a disc shape into an annulus shape, forming a giant vortex. We present a phase diagram showing three kinds of density profiles of the ground states that are two disc shaped, one disc and another annulus shaped, and two annulus shaped. For the two-component immiscible BECs with particle number grave imbalance, we also discuss their ground states using the TFA, and three kinds of symmetrical structures of the density profiles are classified analytically. The spin textures of the two-component immiscible BECs have been studied and we find three kinds of symmetrical structures of the spin textures in the annular trap. One of these textures is an annular skyrmion which has been observed in harmonic potentials. Both of the other spin textures contain a new structure composed of concentric double-annulus skyrmion whose topological charge is the sum of the ones of two annular skyrmions, and the topological charge of each annular skyrmion is equal to the absolute value of the difference between the quantum numbers of circulation of two components inside this annular skyrmion. We also prove that these new textures are robust by investigating the dynamical behaviours of the system under external disturbances.