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Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering

THE STRUCTURE’ VORTEX OF CONDENSED GAS IN TRAPPED CLOUD

Utku Kaya, Abidin Kılıç

Published Dec 6, 2019• 0 citations
Publisher

Abstract

Bose-Einstein condensation, which has a very low particle density and a highly complex quantum structure, has been experimentally proven to date for rubidium, sodium, lithium, hydrogen, metastable helium, cesium and chromium atoms. Due to the differences between the properties and binary interactions of these atoms, experimental studies on condensation have found many impressive results. The structure of a vortex in a trapped environment and the factors affecting it were investigated in this study. Angular Momentum was calculated using Thomas-Fermi Approach.

DOI
10.18038/estubtda.631060

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Bose-Einstein condensation, which has a very low particle density and a highly complex quantum structure, has been experimentally proven to date for rubidium, sodium, lithium, hydrogen, metastable helium, cesium and chromium atoms. Due to the differences between the properties and binary interactions of these atoms, experimental studies on condensation have found many impressive results. The structure of a vortex in a trapped environment and the factors affecting it were investigated in this study. Angular Momentum was calculated using Thomas-Fermi Approach.
The Bose-Einstein condensate, which has very low particle density and a highly complex quantum structure, has been proven experimentally for rubidium, sodium, lithium, hydrogen, metastable helium, cesium and chromium atoms to date. Because of the differences between the properties of these atoms and their binary interactions, many impressive results have been found in experimental work on condensation. The structure of a vortex in the uniform environment and the influencing factors are examined in this study.
The properties of vortex states in a Bose-Einstein-condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods, we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+{\ensuremath{\omega}}^{2}{t}^{2}{)}^{1/2},$ where $\ensuremath{\omega}$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.
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.
In light of the recent experimental observation of Bose-Einstein condensation in dilute 87Rb{}^{87}\mathrm{Rb}87Rb gas cooled to nanokelvin-scale temperatures, we give a quantitative account of the ground-state properties of magnetically trapped Bose gases. Using simple scaling arguments, we show that at large particle number the kinetic energy is a small perturbation, and find a spatial structure of the cloud of atoms and its momentum distribution dependent in an essential way on particle interactions. We also estimate the superfluid coherence length and the critical angular velocity at which vortex lines become energetically favorable.
The structure of vortices in Bose-Einstein condensed atomic gases is studied taking into account many-body correlation effects. It is shown that for excited vortices the particle density in the vortex core increases as the angular momentum of the system increases. The core density can increase by several times with only a few percent change in the angular momentum. This result provides an explanation for the observations in which the measured angular momentum is higher than the estimation based on counting the number of vortices and the visibility of the vortex cores is simultaneously reduced. The calculated density profiles for the excited vortices are in good agreement with experimental measurements of a single vortex.