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arXiv:1003.2798 · Physical Review A

Hidden vortices in a Bose-Einstein condensate in a rotating double-well potential

Linghua Wen, Hongwei Xiong, Biao Wu

Published Nov 24, 2010• 70 citations
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Abstract

We study vortex formation in a Bose-Einstein condensate in a rotating double-well potential. In addition to the ordinary quantized vortices and elusive ghost vortices, ``hidden'' vortices are found distributed along the central barrier. These hidden vortices are invisible like ghost vortices but carry angular momentum. Moreover, their core size is not given by the healing length, but is strongly influenced by the external potential. We find that the Feynman rule can be well satisfied only after including the hidden vortices. There is no critical rotation frequency for the formation of hidden vortices while there is one for the formation of ordinary visible vortices. Hidden vortices can be revealed in the free expansion of Bose-Einstein condensates. In addition, the hidden vortices in a Bose-Einstein condensate can appear in other external potentials, such as a rotating anisotropic toroidal trap.

DOI
10.1103/physreva.82.053627

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We study vortex formation in a Bose-Einstein condensate in a rotating double-well potential. In addition to the ordinary quantized vortices and elusive ghost vortices, ``hidden'' vortices are found distributed along the central barrier. These hidden vortices are invisible like ghost vortices but carry angular momentum. Moreover, their core size is not given by the healing length, but is strongly influenced by the external potential. We find that the Feynman rule can be well satisfied only after including the hidden vortices. There is no critical rotation frequency for the formation of hidden vortices while there is one for the formation of ordinary visible vortices. Hidden vortices can be revealed in the free expansion of Bose-Einstein condensates. In addition, the hidden vortices in a Bose-Einstein condensate can appear in other external potentials, such as a rotating anisotropic toroidal trap.
We derive analytically the Feynman rule for the vortex number of a Bose-Einstein condensate in a rotating double-well potential. From the numerical simulations of the two-dimensional Gross-Pitaevskii equation we show that the double-well potential gives rise to hidden vortices in addition to the usual visible vortices. The Feynman rule matches with the total number of these two types of vortices. We show that, unlike the isotropic case, the vortex number do not diverge at Ο = 1 for the anisotropic case. We further show that the Feynman rule is also satisfied when the condensate is loaded in a co-rotating optical lattice.
We investigate the dynamics of vortex formation and the structure of vortex lattices in a Bose-Einstein condensate confined within a rotating double-well (DW) potential. The dynamical process is a formation process of ``ghost'' vortices, ``hidden'' vortices, and ``visible'' vortices. The critical rotation frequency for the creation of visible vortex is indicated by a sudden jump in the angular momentum evolution and an inflexion in the energy evolution. Different visible vortex structures can be formed by ruling the rotation frequency. In particular, structural change of visible vortex patterns can be achieved by regulating the anisotropy parameter of the DW potential. This feature allows to flexibly control the distribution of angular momentum in macroscopic quantum systems and study the interplay among rotation, interparticle interaction and external potential in superfluids.
In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.
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 investigate phase separation and hidden vortices in spin-orbit coupled ferromagnetic BoseEinstein condensates with rotation and Rabi coupling. The hidden vortices are invisible in density distribution but are visible in phase distribution, which can carry angular momentum like the ordinary quantized vortices. In the absence of the rotation, we observe the phase separation induced by the spin-orbit coupling and determine the entire phase diagram of the existence of phase separation. For the rotation case, in addition to the phase separation, we demonstrate particularly that the spin-orbit coupling can result in the hidden vortices and hidden vortex-antivortex pairs. The corresponding entire phase diagrams are determined, depending on the interplay of the spin-orbit coupling strength, the rotation frequency, and Rabi frequency, which reveals the critical condition of the occurrence of the hidden vortices and vortex-antivortex pairs. The hidden vortices here are proved to be long-lived in the time scale of experiment by the dynamic analysis. These findings not only provide a clear illustration of the phase separation in spin-orbit coupled spinor Bose-Einstein condensates, but also open a new direction for investigating the hidden vortices in high-spin quantum system.
We have studied the ground state configurations of a rotating Bose—Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.