arXiv:cond-mat/9908210 · Journal of Physics B Atomic Molecular and Optical Physics

The effect of interactions on Bose-Einstein condensation in a quasi two-dimensional harmonic trap

R. K. Bhaduri, S. M. Reimann, S. Viefers, A. Ghose Choudhury, M. K. Srivastava

Published Sep 14, 2000• 43 citations

Abstract

A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed phase as the temperature is lowered. Its density profile and energy are identical to that of an ideal gas obeying the fractional exclusion statistics of Haldane.

DOI: 10.1088/0953-4075/33/19/304

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arXiv:cond-mat/9908210 · Journal of Physics B Atomic Molecular and Optical Physics

The effect of interactions on Bose-Einstein condensation in a quasi two-dimensional harmonic trap

R. K. Bhaduri, S. M. Reimann, S. Viefers, A. Ghose Choudhury, M. K. Srivastava

Published Sep 14, 2000• 43 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0953-4075/33/19/304

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T^{\star}

. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature

T^{\star}

can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.

Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range,

s

-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.

{x}^{2/3}

potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number

N

of atoms, harmonic oscillator length, deformation of the trap,

s

-wave scattering length) fix its thermodynamic behavior in the large

N

limit through two dimensionless scaling parameters. These are the reduced temperature

t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/{T}_{c}^{0}

and the ratio $\ensuremath{\eta}$ between the

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature

{T}_{c}^{0}

of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.