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arXiv:2407.17901 · Physical review. E

Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential

Ishfaq Ahmad Bhat, Bishwajyoti Dey

Published Aug 15, 2024• 5 citations
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Abstract

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.

DOI
10.1103/physreve.110.024208

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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 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.
We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$ values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional sss-wave scattering lengths through the strength of nonlinear rotation, C\mathit{C}C, such that ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}>0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}=0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity (${\ensuremath{\epsilon}}_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($\ensuremath{\epsilon}$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.
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.
Motivated by recent experiments, we study theoretically a gas of atomic bosons confined in an elliptical harmonic trap, forming a quasi-two-dimensional atomic Bose-Einstein condensate subject to a density-dependent gauge potential which realizes an effective density-angular-momentum coupling. We present exact Thomas-Fermi solutions which allow us to identify the stable regimes of the full parameter space of the model. Accompanying numerical simulations reveal the effect of the interplay of the rigid body and density-angular-momentum coupling for the elliptically confined condensate. By varying the strength of the gauge potential and trap anisotropy, we explore how the superfluid state emerges in different experimentally accessible geometries, while for large rotation strengths dense vortex lattices and concentric vortex ring arrangements are obtained.