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arXiv:0810.5275 · Physical Review A

Vortex-lattice pinning in two-component Bose-Einstein condensates

M. P. Mink, C. Morais Smith, R. A. Duine

Published Jan 7, 2009• 13 citations
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Abstract

We investigate the vortex-lattice structure for single- and two-component Bose-Einstein condensates in the presence of an optical lattice, which acts as a pinning potential for the vortices. The problem is considered in the mean-field quantum Hall regime, which is reached when the rotation frequency $\ensuremath{\Omega}$ of the condensate in a radially symmetric trap approaches the (radial) trapping frequency $\ensuremath{\omega}$ and the interactions between the atoms are weak. We determine the vortex-lattice phase diagram as a function of optical-lattice strength and geometry. In the limit of strong pinning the vortices are always pinned at the maxima of the optical-lattice potential, similar to the slow-rotation case. At intermediate pinning strength, however, due to the competition between interactions and pinning energy, a structure arises for the two-component case where the vortices are pinned on lines of minimal potential.

DOI
10.1103/physreva.79.013605

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We investigate the vortex-lattice structure for single- and two-component Bose-Einstein condensates in the presence of an optical lattice, which acts as a pinning potential for the vortices. The problem is considered in the mean-field quantum Hall regime, which is reached when the rotation frequency \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ of the condensate in a radially symmetric trap approaches the (radial) trapping frequency \ensuremathω\ensuremath{\omega}\ensuremathω and the interactions between the atoms are weak. We determine the vortex-lattice phase diagram as a function of optical-lattice strength and geometry. In the limit of strong pinning the vortices are always pinned at the maxima of the optical-lattice potential, similar to the slow-rotation case. At intermediate pinning strength, however, due to the competition between interactions and pinning energy, a structure arises for the two-component case where the vortices are pinned on lines of minimal potential.
We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.
We study the vortex pinning effect on the vortex lattice structure of the rotating two-component Bose-Einstein condensates (BECs) in the presence of impurities or disorder by numerically solving the time-dependent coupled Gross-Pitaevskii equations. We investigate the transition of the vortex lattice structures by changing conditions such as angular frequency, the strength of the inter-component interaction and pinning potential, and the lattice constant of the periodic pinning potential. We show that even a single impurity pinning potential can change the unpinned vortex lattice structure from triangular to square or from triangular to a structure which is the overlap of triangular and square. In the presence of a periodic pinning potential or optical lattice, we observe the structural transition from the unpinned vortex lattice to the pinned vortex lattice structure of the optical lattice. In the presence of a random pinning potential or disorder, the vortex lattice melts following a two-step process by creation of lattice defects, dislocations, and disclinations, with the increase of rotational frequency, similar to that observed for single-component Bose-Einstein condensates. However, for the binary BECs, we show that the two-step vortex lattice melting also occurs with increasing strength of the intercomponent interaction.
We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensates in a rotating double-well trap potential and corotating optical lattice. We show that the vortex number does not diverge when the rotational frequency $\ensuremath{\Omega}\ensuremath{\rightarrow}1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value l/l\sqrt{l}/ll​/l for l=4l=4l=4, which supports the conjecture that surface modes with angular momentum l=4l=4l=4 are excited when the rotating condensate is trapped in a double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning show very interesting features. We show the existence and pinning of hidden vortices whose phase profile is similar to that of the visible vortices.
We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. The onset of these different phases is described by the force balance of a driving force, a pinning force, and vortex-vortex interactions. In particular, when the optical lattice rotates faster than the condensate, an incommensurate effect leads to a vortex-liquid phase supported by the competition between the driving force and the dissipation.
We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.