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arXiv:cond-mat/0003451 · Physical Review A

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

Juan José García‐Ripoll, Víctor M. Pérez‐García

Published May 29, 2001• 22 citations
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Abstract

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. With simple arguments, we obtain the velocity field of the quantum fluid for condensates with or without a centered vortex. While the bosons describe open spiraling trajectories, on the frame of reference of the rotating trap, the fluid moves against the trap's rotation. We also find expressions for the angular momentum of linear and Thomas-Fermi solutions for a vortexless state. In these two limits we find the same analytic relation between the shape of the cloud and the rotation speed. Our predictions are supported by numerical simulations of the mean-field Gross-Pitaevskii model and by current experiments with rotating Bose-Einstein condensates (K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, e-print cond-mat/0101051).

DOI
10.1103/physreva.64.013602

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We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. With simple arguments, we obtain the velocity field of the quantum fluid for condensates with or without a centered vortex. While the bosons describe open spiraling trajectories, on the frame of reference of the rotating trap, the fluid moves against the trap's rotation. We also find expressions for the angular momentum of linear and Thomas-Fermi solutions for a vortexless state. In these two limits we find the same analytic relation between the shape of the cloud and the rotation speed. Our predictions are supported by numerical simulations of the mean-field Gross-Pitaevskii model and by current experiments with rotating Bose-Einstein condensates (K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, e-print cond-mat/0101051).
We consider a rotating Bose-Einstein condensate in a harmonic trap and investigate numerically the behavior of the wave function which solves the Gross-Pitaevskii equation. Following recent experiments [P. Rosenbuch, V. Bretin, and J. Dalibard, Phys. Rev. Lett. 89, 200403 (2002)], we study in detail the line of a single quantized vortex, which has a U or S shape. We find that a single vortex can lie only in the $x\ensuremath{-}z$ or $y\ensuremath{-}z$ plane. S-type vortices exist for all values of the angular velocity $\ensuremath{\Omega}$ while U vortices exist for $\ensuremath{\Omega}$ sufficiently large. We compute the energy of the various configurations with several vortices and study the three-dimensional structure of vortices.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.
A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\ensuremath{\Omega}$ to exceed the radial harmonic frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. In the regime $\ensuremath{\Omega}\ensuremath{\gtrsim}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity ${\ensuremath{\Omega}}_{h}$, a central hole appears in the condensate. Numerical studies confirm the predicted value of ${\ensuremath{\Omega}}_{h}$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).
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We study the vortex lattices in a Bose-Einstein condensate in a rotating anisotropic harmonic trap. We first investigate the single-particle wave functions obtained by the exact solution of the problem and give simple expressions for these wave functions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.