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TURKISH JOURNAL OF PHYSICS

Temperature dependence for the synthetic magnetization of a rotating Bose gas in harmonic trap

Azza M. El-Badry

Published Jan 1, 2013• 1 citation
Publisher

Abstract

In this paper, the temperature dependence for synthetic magnetization \bar M of a rotating Bose gas in harmonic trap and the magnetic field dependence of the critical temperature are investigated. A simple semiclassical approximation for the density of state approach is used in this study. The suggested approach simultaneously gives corrections to quantities which arise from the finite size and interatomic interaction effects. The calculated results show that the critical temperature decreases due to the increase of the synthetic magnetic field. The synthetic magnetization also exhibits a characteristic temperature dependence. It is proportional to T^3 if \bar T < \bar T_c, while it is proportional to T if \bar T > \bar T_c. The calculated results provide a solid theoretical foundation of the current experiments.

DOI
10.3906/fiz-1205-1

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In this paper, the temperature dependence for synthetic magnetization \bar M of a rotating Bose gas in harmonic trap and the magnetic field dependence of the critical temperature are investigated. A simple semiclassical approximation for the density of state approach is used in this study. The suggested approach simultaneously gives corrections to quantities which arise from the finite size and interatomic interaction effects. The calculated results show that the critical temperature decreases due to the increase of the synthetic magnetic field. The synthetic magnetization also exhibits a characteristic temperature dependence. It is proportional to T^3 if \bar T < \bar T_c, while it is proportional to T if \bar T > \bar T_c. The calculated results provide a solid theoretical foundation of the current experiments.
Abstract We have analytically explored both the zero temperature and the finite temperature scaling theory for the collapse of an attractively interacting 3D harmonically trapped Bose gas in a synthetic magnetic field. We have considered short ranged (contact) attractive inter-particle interactions and Hartree–Fock approximation for the same. We have separately studied the collapse of both the condensate and the thermal cloud below and above the condensation point, respectively. We have obtained an anisotropy, artificial magnetic field, and temperature dependent critical number of particles for the collapse of the condensate. We have found a dramatic change in the critical exponent (from α = 1 to 0) of the specific heat ( C v ∝ | T − T c | α ) when the thermal cloud is about to collapse with the critical number of particles ( N = N c ) just below and above the condensation point. All the results obtained by us below and around the condensation point are experimentally testable within the present-day experimental set-up for the ultracold systems in the magneto-optical traps.
We investigate thermodynamic properties of the rotating Bose gas in a trap, taking the charged ideal Bose gas in a magnetic field as an example. The system is equivalent to a neutral gas in a synthetic magnetic field. It is indicated that the Bose—Einstein condensation temperature is irrelevant to the magnetic field, conflicting with established intuition that the critical temperature decreases with the field increasing. The specific heat and Landau diamagnetization also exhibit intriguing behaviors.
We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived based on a semiclassical approximation to the single-particle-energy spectrum and density of states and are compared with exact results obtained by explicitly summing discrete energy levels for a small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to finite spin-orbit coupling. For a large coupling strength and a finite number of particles NNN, the critical temperature scales as N2/5{N}^{2/5}N2/5 and N2/3{N}^{2/3}N2/3 in three and two dimensions, respectively, contrasted to the predictions of N1/3{N}^{1/3}N1/3 and N1/2{N}^{1/2}N1/2 in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.
We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties, particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N → ∞ .
We investigate condensation and finite-temperature magnetic phase transitions in a coherently (Rabi) coupled Bose gas confined in a three-dimensional harmonic trap. For the noninteracting system, we derive analytical expressions for the critical temperature and condensate fraction using a semiclassical description of the single-particle spectrum and density of states. At fixed particle number, coherent coupling enhances the critical temperature relative to the uncoupled system, and this enhancement decreases with increasing particle number NNN. The finite-size correction, in contrast, lowers the transition temperature, with its effect diminishing for larger NNN. We then incorporate repulsive interactions within the Hartree--Fock--Bogoliubov--Popov framework to investigate the finite-temperature phase diagram in the temperature--Rabi coupling plane. The system undergoes successive transitions from a ferromagnetic to a paramagnetic condensate and, at higher temperature, to a thermal gas. The transition boundaries obtained from the vanishing of the condensate fraction show excellent agreement with the analytical Hartree-Fock predictions. We find that the interactions substantially suppress the variation in the condensation temperature with an increase in the coherent coupling.
We report on a superfluid properties of a Bose- Einstein condensate in a rotating harmonic trap. We employ the semiclassical approximation, which is the density of state approach. Our approach provided the finite size effect. The superfluid fraction of bosons and its heat capacity at constant volume are investigated. The calculated results provide a good qualitative agreement with the measured experimental results for superfluid helium 4H. Moreover, furnish useful qualitatively theoretical results for a spectroscopic measurement of the superfluid fraction of an ultracold atomic gas [N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett. 104, 030401 (2010)]. Our results show that both The superfluid fraction of bosons and its heat capacity depend on the number of the atoms. This significant dependence should be considered when the it in situ widths are used in extracting measurable experimental quantities. Our approach can be extended to consider the rotating condensate in optical potential .