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arXiv:1212.0921 · Physical Review A

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

Linghua Wen, Yong-Jun Qiao, Yong Xu, Li Mao

Published Mar 4, 2013• 33 citations

Abstract

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 (VAVSSs). We show that different winding numbers of the 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 phases, 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 the respective components, and it is shown that the conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSSs. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSSs allow them to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in the 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 a singly quantized visible vortex, or a hidden vortex, or a ghost vortex, depending on the specific parameters of the system. Finally, a general relationship between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.

DOI: 10.1103/physreva.87.033604

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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 (VAVSSs). We show that different winding numbers of the 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 phases, 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 the respective components, and it is shown that the conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSSs. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSSs allow them to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in the 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 a singly quantized visible vortex, or a hidden vortex, or a ghost vortex, depending on the specific parameters of the system. Finally, a general relationship between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.

We develop a three-dimensional analysis of the phase separation of two-species Bose-Einstein condensates in the presence of vorticity within the Thomas-Fermi approximation. We find different segregation features according to whether the more repulsive component is in a vortex or in a vortex-free state. An application of this study is aimed at describing systems formed by two almost immiscible species of rubidium-87 that are commonly used in Bose-Einstein condensation experiments. In particular, in this work we calculate the density profiles of condensates for the same conditions as the states prepared in the experiments performed at JILA [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)].

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We numerically study the dynamics of quantized vortices in two-dimensional two-component Bose-Einstein condensates (BECs) trapped by a box potential. For one-component BECs in a box potential, it is known that quantized vortices form Onsager vortices, which are clusters of same-sign vortices. We confirm that the vortices of the two components spatially separate from each other-even for miscible two-component BECs-suppressing the formation of Onsager vortices. This phenomenon is caused by the repulsive interaction between vortices belonging to different components, hence, suggesting a new possibility for vortex phase separation.

We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.

The combination of multi-component Bose–Einstein condensates (BECs) and phase imprinting techniques provides an ideal platform for exploring nonlinear dynamics and investigating the quantum transport properties of superfluids. In this paper, we study abundant density structures and corresponding dynamics of phase-separated binary Bose–Einstein condensates with phase-imprinted single vortex or vortex dipole. By adjusting the ratio between the inter-species and intra-species interactions, and the locations of the phase singularities, the typical density profiles such as ball-shell structures, crescent-gibbous structures, Matryoshka-like structures, sector-sector structures and sandwich-type structures appear, and the phase diagrams are obtained. The dynamics of these structures exhibit diverse properties, including the penetration of vortex dipoles, emergence of halfvortex dipoles, co-rotation of sectors, and oscillation between sectors. The pinning effects induced by a potential defect are also discussed, which is useful for controlling and manipulating individual quantum states.

We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac BEC) described by a stationary Dirac Gross-Pitaevskii equations (GPE). We find that the multi-component structure of Dirac equation enables the difference in phase winding of two condensates with respective phase winding number differing by one,

\ell_a - \ell_b = \pm 1

. We observe three classes of vortex states distinguished by their far-field behavior: A ring soliton on either of the two components in combination with a vortex on the other component, and, in the case of strong inter-component interactions, a vortex profile on both components. The latter are multiple core vortices due to the phase winding difference between the components. We also address the role of a Haldane gap on these vortices, which has a similar effect than inter-component by making the occupation on either sublattice more costly. We employ a numerical shooting method to reliably identify vortex solutions and use it to scan large parts of the phase space. We then use a classification algorithm on the integrated wavefunctions to establish a phase diagram of the different topological sectors.