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arXiv:cond-mat/0106262 · Physical Review Letters

Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential

E. Hodby, Gerald Hechenblaikner, S. A. Hopkins, Onofrio M. Maragò, Christopher J. Foot

Published Dec 19, 2001• 278 citations
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Abstract

We have investigated the formation of vortices by rotating the purely magnetic potential confining a Bose-Einstein condensate. We modified the bias field of an axially symmetric TOP trap to create an elliptical potential that rotates in the radial plane. This enabled us to study the conditions for vortex nucleation over a wide range of eccentricities and rotation rates.

DOI
10.1103/physrevlett.88.010405

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We have investigated the formation of vortices by rotating the purely magnetic potential confining a Bose-Einstein condensate. We modified the bias field of an axially symmetric TOP trap to create an elliptical potential that rotates in the radial plane. This enabled us to study the conditions for vortex nucleation over a wide range of eccentricities and rotation rates.
We report on the observation of vortex formation in a Bose-Einstein condensate of 87Rb^{87}\text{R}\text{b}87Rb atoms. Vortices are generated by superimposing an oscillating excitation to the trapping potential introduced by an external magnetic field. For small amplitudes of the external excitation field we observe a bending of the cloud axis. Increasing the amplitude we observe formation of a growing number of vortices in the sample. Shot-to-shot variations in both vortex number and position within the condensed cloud are observed, probably due to the intrinsic vortex nucleation dynamics. We discuss the possible formation of vortices and antivortices in the sample as well as possible mechanisms for vortex nucleation.
A method to produce a spin-dependent rotating potential using near-resonant circularly polarized laser beams is proposed. It is shown that half-quantum vortices are nucleated in a spinor Bose-Einstein condensate (BEC) with an antiferromagnetic interaction. In contrast to the vortex nucleation in a scalar BEC, the spin-vortex nucleation occurs at a low rotation frequency ($\ensuremath{\simeq}0.1{\ensuremath{\omega}}_{\ensuremath{\perp}}$ with ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ being the radial trap frequency) in a short nucleation time $\ensuremath{\simeq}50\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ without dissipation. A method for nondestructive measurement of half-quantum vortices is discussed.
We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center.
We investigate the rotational properties of a Bose-Einstein condensate (BEC) in an effective magnetic field. The corresponding gauge potential is optically generated, and based on the adiabatic motion of the atoms. We demonstrate that the nucleation of vortices is seeded by instabilities in surface excitations and show that this picture also holds when the applied effective magnetic field is not homogeneous. The eventual configuration of vortices in the cloud depends on the geometry of the applied field.
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.