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arXiv:cond-mat/0211294 · Physical Review A

Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice

Marco Cozzini, S. Stringari

Published Apr 11, 2003• 59 citations
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Abstract

Starting from the equations of rotational hydrodynamics we study the macroscopic behavior of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations, and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al. [Phys. Rev. Lett. 89, 100403 (2002)].

DOI
10.1103/physreva.67.041602

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Starting from the equations of rotational hydrodynamics we study the macroscopic behavior of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations, and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al. [Phys. Rev. Lett. 89, 100403 (2002)].
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We study a rotating Bose-Einstein Condensate (BEC) trapped in a shifted harmonic oscillator and Mexican Hat trap, which approximates the potential of a bubble trap potential in some situations.We determined the vortices configurations that appears in this system by varying the interaction and angular momentum of the atomic cloud.The system phase diagram has the macrovortex configurations for small values of the interaction parameter.The charge of the central vortex increases with increasing rotation.Higher values of the atomic interaction turns the macrovortex unstable.It decays into multiple single-charged vortices that arrange themselves in a lattice.Since the vortices are not always visible in the absorption images, we look for alternative methods to characterize the vortex configuration.More specifically, we search for experimental signatures to determine the transitions in the phase diagram.For that, we study how the BEC's velocity field affects the collective modes of the condensate.The splitting of the modes degenerescence and the increase in the mode frequency with angular velocity, which can be traced to a reduction in the gas compressibility, can be seen as an indirect signature of the presence of the vortices in the trapped BEC.
We study vortex dynamics in a trapped Bose-Einstein condensate with tunable two- and three-body interactions. The dynamics is governed by two-dimensional cubic-quintic Gross-Pitaevskii equation. A time-dependent variational method has been used to obtain critical rotational frequency and surface mode frequency analytically and are compared with numerical simulation results. An imaginary time propagation method and Crank-Nicolson scheme for discretization have been used for numerical simulation. The numerically calculated average value of the angular momentum per particle shows very clearly its dynamical relation with the time development of the vortex formation. The rotational frequency dependence of the variation of average value of the angular momentum per particle with time shows that vortices form much faster in time for higher rotational frequency. Similarly, the vortex forms much faster in time with an increase of the strength of the repulsive three-body interaction. The simulation of the vortex lattice formation in the condensate shows that the presence of the three-body interactions does not alter the vortex lattice pattern but it helps in the shape deformations of the condensate thereby leading to vortex lattice formation. Likewise, the three-body interactions enable the vortex lattice formation in Bose-Einstein condensates even with attractive two-body interactions and in purely quintic BEC.
We study a harmonically confined Bose-Einstein condensate under rotation. Vortex lattice configurations are investigated through a variational approach. Vortices with more than a unit of angular momentum are not stable. We explicitly show that the critical rotational frequency is quite small, as was reported in a recent experiment, with an asymmetric harmonic confining potential. The width of the condensate along the z direction (the anisotropy direction) and in the xy plane and the vortex density are determined as functions of the rotational frequency. The aspect ratio becomes small for large rotational frequencies, making the condensate an effectively two-dimensional system.
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.
We study the formation of vortices in a dilute Bose-Einstein condensate confined in a rotating anisotropic trap. We find that the number of vortices and angular momentum attained by the condensate depend upon the rotation history of the trap and on the number of vortices present in the condensate initially. A simplified model based on hydrodynamic equations is developed, and used to explain this effect in terms of a shift in the resonance frequency of the quadrupole mode of the condensate in the presence of a vortex lattice. Differences between the spin-up and spin-down response of the condensate are found, demonstrating hysteresis phenomena in this system.