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arXiv:0806.4106 · Physical Review A

Formation of vortices in a dense Bose-Einstein condensate

Vicente Pereira de Barros, Ch. Moseley, A. Gammal, K. Ziegler

Published Jul 31, 2008• 2 citations
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Abstract

A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond the Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized nonlinear Schr\"odinger equation with a kinetic term for the rotating condensate. In comparison with previous calculations, based on the Thomas-Fermi approximation, significant improvements are found in regions where the condensate in a trap potential is not smooth. The critical angular velocity of the vortex formation is higher than in the Thomas-Fermi prediction.

DOI
10.1103/physreva.78.013642

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A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond the Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized nonlinear Schr"odinger equation with a kinetic term for the rotating condensate. In comparison with previous calculations, based on the Thomas-Fermi approximation, significant improvements are found in regions where the condensate in a trap potential is not smooth. The critical angular velocity of the vortex formation is higher than in the Thomas-Fermi prediction.
We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.
For a Bose-Einstein condensate placed in a rotating trap and strongly confined along the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas-Fermi regime for an effective two-dimensional (2D) situation in the $x\ensuremath{-}y$ plane. We investigate an asymptotic expansion of the energy, the critical angular velocities of nucleation of vortices with respect to a small parameter $\ensuremath{\varepsilon},$ and the location of vortices. The limit $\ensuremath{\varepsilon}$ going to zero corresponds to the Thomas-Fermi regime. The nondimensionalized energy is similar to the Ginzburg-Landau energy for superconductors in the high-\ensuremath{\kappa} high-field limit and our estimates rely on techniques developed for this latter problem. We also take advantage of this similarity to develop a numerical algorithm for computing the Bose-Einstein vortices. Numerical results and energy diagrams are presented.
Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency ${\ensuremath{\Omega}}_{c}$ is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ${\ensuremath{\Omega}}_{c}$ and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.
We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and, in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several routes to induce vortex lattice formation in a dipolar condensate.
We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.