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Structure of two-component Bose-Einstein condensates with respective vortex-antivortex superposition states

We investigate the phase structure of two-component Bose-Einstein condensates (BECs) with repulsive intra- and interspecies interactions in the presence of respective vortex-antivortex superposition states (VAVSS). We show that different winding numbers of vortex and antivortex and different intra- and interspecies interaction strengths may lead to different phase configurations, such as fully separated phases, inlaid separated phases, asymmetric separated phase, and partially mixed phases, where the density profile of each component displays a petal-like (or modulated petal-like) structure. A phase diagram is given for the case of equal unit winding numbers of the vortex and antivortex in respective components, and it is shown that conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSS. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSS allow to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in respective components, we find that each component in any of the possible phase structures is in a cluster state of vortices and antivortices, where the topological defects appear in the form of singly quantized visible vortex, or hidden vortex, or ghost vortex, depending on the specific parameters of the system. Finally, a general rule between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.