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Number of vortices generated in a rotating Bose-Einstein condensates in two-dimensional optical lattice

Adel M. Mohammedein, Adel A. Ghoneim, Reem S. Altawash

Published May 15, 2020• 0 citations
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Abstract

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 $q(T)$ 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.

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arXiv:1001.0865•Physical Review Letters•Feb 5, 2010•112 citations
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.
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 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.
In this work, we investigated the thermodynamic behavior of a rotating Bose-Einstein condensation with non-zero interatomic interactions in one-dimensional optical lattice theoretically. Our system is formed by loading three dimensional boson-clouds into 1D optical lattice and subjected to rotate with angular velocity ɷ about the z axis. We employed the semiclassical Hartree-Fock approach to calculate the condensate fraction, critical temperature, entropy and the heat capacity of the system. Thereby, we investigated the effect of the rotation rate, optical potential depth and the interactions parameter on these parameters. The obtained results provide a solid theoretical foundation for the current experiments of rotating interacting Bose-Einstein condensation produced or transferred in optical lattices.
In this paper, we suggest a conventional semiclassical approximation to calculate several thermodynamic quantities of a rotating Bose-Einstein condensation in a deep optical lattice. Expressions for the condensation fraction, critical temperature, and heat capacity are derived analytically. These expressions are obtained by considering the standard harmonic approximation of the deep optical lattice potential. The suggested approach is able to include the the finite size and the positive chemical potential effects simultaneously. The advantage of our suggested approach is in its simplicity, in comparison to the quantum-mechanical calculations (Bose-Hubbard model). Moreover, its generality allows the treatment of a finite temperature regime
In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.
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.