arXiv:cond-mat/0111357

Vortices in Bose-Einstein Condensed Na Atoms

Keshav Narain Shrivastava

Published Nov 20, 2001• 0 citations

Abstract

There are surface modes on the Bose-Einstein condensed Na atoms so that the number of vortices diverges when the stirring frequency becomes equal to that of the surface waves. We introduce the finite life time of the surface modes so that the number of vortices becomes finite. Usually the number of vortices is a linear function of the stirring frequency. We find that this linearity is destroyed by the finite life time and a peaked function emerges with several peaks, one for each surface mode. The vortices become normal, as they should be, so that there occurs a phase transition from normal to the superfluid state.

DOI: 10.48550/arxiv.cond-mat/0111357

Related papers

Vortex Nucleation in a Stirred Bose-Einstein Condensate

Chandra Raman, J. R. Abo-Shaeer, J. M. M. J. Vogels +2 more

We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. The vortex cores were observed using time-of-flight absorption imaging. Depending on the stirrer size, either discrete resonances or a broad response was visible as the stir frequency was varied. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices.

arXiv:cond-mat/0106235Physical Review LettersNov 1, 2001389 citations

Vortices in a stirred Bose-Einstein condensate

Kirk W. Madison, Frédéric Chevy, Wendel Wohlleben +1 more

We stir with a focused laser beam a Bose-Einstein condensate of 87Rb atoms confined in a magnetic trap. We observe the formation of a single vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to eleven vortices are simultaneously present. We present measurements of the decay of a vortex array once the stirring laser beam is removed.

arXiv:cond-mat/0004037Journal of Modern OpticsNov 1, 2000151 citations

Quantum vortex dynamics in the counterflowing Bose–Einstein condensate

Sergey K. Nemirovskii

The aim of this paper is to derive the equations of motion of quantum vortices in a weakly non-ideal Bose–Einstein condensate (BEC) at finite temperatures and in the presence of macroscopic superfluid and normal velocities. The motivation for this work is that the dynamics of quantum vortices in superfluid helium has been studied at the phenomenological level, and a number of issues require clarification, which can be addressed by studying the corresponding problem in BEC. In BEC, quantum vortices are located at points where the macroscopic wave function (MWF) ψ(r,T), which describes the BEC dynamics, vanishes ψ(r,T)=0. The intersection of the surfaces Reψ(r,T)=0 and Imψ(r,T)=0 forms a one-dimensional line, which is just the quantum vortex line. During the evolution of the MWF, the position of the zero surfaces changes, that is, the vortex lines move. Conversely, the motion of these vortex filaments determines the evolution of the MWF. Thus, there is a mutual correspondence, and the quantity ψ(r,T) can be considered as a functional of the entire vortex configuration, i.e., {s(ξ,t)}. This viewpoint allows us to derive the equations of motion for vortices from the Gross–Pitaevskii equation (GPE), which describes the dynamics of MWF. The key finding is the confirmation that the equation derived from the fundamental quantum description (the GPE) for a BEC has the same mathematical structure as the equation derived from macroscopic, phenomenological reasoning for superfluid helium.

Physics of FluidsFeb 1, 20260 citations

Vortices in dilute Bose-Einstein condensates

Tapio Simula

Bose-Einstein condensation, first predicted by Bose and Einstein in 1924, was finally realized in dilute, weakly interacting gases of alkali atoms in 1995. A few years later, quantized vortices - intimately related to the phenomenon of superfluidity - were created and observed in these novel quantum many-body systems.\n\nIn this Thesis, vortices in dilute atomic Bose-Einstein condensates are studied theoretically and computationally using microscopic mean-field theory formalisms. Special emphasis is on the structure and the stability of vortices at finite temperatures. The formation of quantized circulation in Bose-Einstein condensates is investigated, as well as multiply quantized vorticity and the adiabaticity of the precessing motion of a vortex.\n\nThis research strongly relies on numerically solving the Gross-Pitaevskii equation for the macroscopic condensate wavefunction and the coupled Bogoliubov equations and their variants for the collective quasiparticle excitation eigenmodes. The computed elementary excitation spectra are used, for instance, in determining the local stability of various condensate states. The vortex formation process is studied at finite temperatures in terms of the surface modes of the condensate providing the Landau critical velocities for the breakdown of superfluidity. Free energy calculations are used for determining the thermodynamic equilibrium states.\n\nSingly quantized, axisymmetric vortex states are found to be locally energetically stable even in the zero-temperature limit within the self-consistent finite-temperature approximations. This would imply for the vortex a precession direction opposite to that observed in the experiment. Adiabatic approximation of quantum mechanics is formulated for Bose-Einstein condensed systems and is applied to a case of a moving vortex line. The experimentally observed precessing motion of the vortex is found to be nonadiabatic. A method to create stable multiply quantized vortices using an additional pinning potential is presented. The computed critical trap rotation frequencies for vortex nucleation at finite temperatures are in agreement with experiments and the predictions of zero-temperature field theories.

Jan 10, 20030 citations

Small numbers of vortices in anisotropic traps

Suzanne McEndoo, Thomas Busch

We investigate the appearance of vortices and vortex lattices in two-dimensional, anisotropic, and rotating Bose-Einstein condensates. Once the anisotropy reaches a critical value, the positions of the vortex cores in the ground state are no longer given by an Abrikosov lattice geometry but by a linear arrangement. Using a variational approach, we determine the critical stirring frequency for a single vortex as well as the equilibrium positions of a small number of vortices.

arXiv:0902.4205Physical Review AMay 12, 200929 citations

Surface Excitations, Shape Deformation, and the Long-Time Behavior in a Stirred Bose–Einstein Condensate

Qing-Li Zhu, Jin An

The surface excitations, shape deformation, and the formation of persistent current for a Gaussian obstacle potential rotating in a highly oblate Bose–Einstein condensate (BEC) are investigated. A vortex dipole can be produced and trapped in the center of the stirrer even for the slow motion of the stirring beam. When the angular velocity of the obstacle is above some critical value, the condensate shape can be deformed remarkably at the corresponding rotation frequency followed by surface wave excitations. After a long enough time, a small number of vortices are found to be either trapped in the condensate or pinned by the obstacle, and a vortex dipole or several vortices can be trapped at the beam center, which provides another way to manipulate the vortex.

arXiv:1802.09347Condensed MatterNov 25, 20182 citations