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Egyptian Journal of Physics

Critical rotation frequency for vortices configuration in a harmonically trapped boson atoms

Alyaa A. Mahmoud, Ahmed S. Hassan, Shemi S.M. Soliman

Published May 10, 2020• 0 citations
Publisher

Abstract

In this paper we suggest a convenient quantum statistical approach to calculate the critical rotation frequency for vortex nucleation in a rotating condensate boson atoms. We extende the quantum mecanices approach for achieving the critical rotation rate to enclode the effect of finite temperature. Dependence of the critical rotation on the interatomic interaction, atoms number and temperature is considered. A simple semiclassical approach is suggested. The calculated results showed that the critical rotation rate α depending crucially on the above mensioned parameters, its change very rapidly at very low temperature. Which means that the vortical configuration is achieved for an accurate rotation rate value α, depends on temperature, interatomic interaction and number of condensate atoms. The obtained results provide useful qualitative theoretical results for future Bose Einstein condensation experiments in rotating traps. Motivated by our work, it will be interesting to study the critical rotation for vortex nucleation of rotating condensate boson atoms in optical lattice.

DOI
10.21608/ejphysics.2020.25523.1036

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In this paper we suggest a convenient quantum statistical approach to calculate the critical rotation frequency for vortex nucleation in a rotating condensate boson atoms. We extende the quantum mecanices approach for achieving the critical rotation rate to enclode the effect of finite temperature. Dependence of the critical rotation on the interatomic interaction, atoms number and temperature is considered. A simple semiclassical approach is suggested. The calculated results showed that the critical rotation rate α depending crucially on the above mensioned parameters, its change very rapidly at very low temperature. Which means that the vortical configuration is achieved for an accurate rotation rate value α, depends on temperature, interatomic interaction and number of condensate atoms. The obtained results provide useful qualitative theoretical results for future Bose Einstein condensation experiments in rotating traps. Motivated by our work, it will be interesting to study the critical rotation for vortex nucleation of rotating condensate boson atoms in optical lattice.
We developed an approach to investigate the temperature dependence of the vortices number for the rotating superfluid Bose-Einstein condensates in a two-dimensional lattice. Our approach enabled us to parametrize the thermal average of the quantum mechanics expectation value and the vortices number in terms of the thermodynamic potential q(T)q(T)q(T) for the system under consideration. The effects of the interatomic interaction, the finite number of atoms, and optical potential depth on the vortices number are investigated. The calculated results show that the vortices number as a function of the rotation rate depends on the normalized temperature, interatomic interaction, optical potential depth, and the number of atoms in the ∈situ{\in situ}∈situ size. These results provide solid theoretical foundations for the measured experimental data for rotating condensate boson in optical lattice such as Williams et. al experiment [R. A. Williams, S. Al-Assam, and C. J. Foot, Phys. Rev. Lett. { 104} (2010) 050404.].
In the present paper we calculate the number of vortices generated in a rotating Bose-Einstein condensate in two-dimensional optical lattice. Our approach enabled us to parametrize the vortices number in terms of the thermodynamic potential q(T)q(T)q(T) for the system under consideration. The thermodynamic potential is calculated using the semiclassical approximation approach. The finite size and the interatomic interaction effects are investigated. The calculated results show that the vortices number as a function of the angular velocity of rotation rate depends on the normalized temperature, number of particles, interatomic interaction, and optical potential.
In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann–Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential [Formula: see text]. The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.
We investigate the thermodynamic stability of quantized vortices in a dilute Bose gas confined by a rotating harmonic trap at finite temperature. Interatomic forces play a crucial role in characterizing the resulting phase diagram, especially in the large NNN Thomas-Fermi regime. We show that the critical temperature for the creation of stable vortices exhibits a maximum as a function of the frequency of the rotating trap, and that the corresponding transition is associated with a discontinuity in the number of atoms in the condensate. Possible strategies for approaching the vortical region are 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.