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AIP conference proceedings

Bose-Einstein condensate in a rotating double-well potential: Hidden vortices and Feynman rule

Thudiyangal Mithun, Kuppuswamy Porsezian, Bishwajyoti Dey

Published Jan 1, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.4872508

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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 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.
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 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.
We study the formation of vortices in a dipolar Bose–Einstein condensate in a synthetic magnetic field by numerically solving the Gross–Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.
Abstract We study the vortex formation in coupled atomic and molecular condensates in a rotating double well trap by numerically solving the coupled Gross–Pitaevskii like equations. Starting with the atomic condensate in the double well potential we considered two-photon Raman photo-association for coherent conversion of atoms to molecules. It is shown that the competition between atom-molecule coupling strength and repulsive atom-molecule interaction controls the spacings between atomic and molecular vortices and the rotation frequency of the trap is the key player for controlling the number of visible atomic and molecular vortices. Whereas the Raman detuning controls the spacing between atomic and molecular vortices as well as the number of atomic and molecular vortices in the trap. We have shown by considering the molecular lattices the distance between two molecular vortices can be controlled by varying the Raman detuning. In addition we have found that the Feynman rule relating the total number of vortices and average angular momentum both for atoms and molecules can be satisfied by considering the atomic and molecular vortices those are hidden in density distribution and seen as singularities in phase distribution of the coupled system except for the lattice structure where molecular vortices are overlapped with each other. It is found that although the number of visible/core vortices in atomic and molecular vortex lattices depends significantly on the system parameters the number of atomic and molecular hidden vortices remains constant in most of the cases.