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Properties of a Dense Bose–Einstein Condensate

K. Ziegler

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

A grand canonical ensemble of hard-core bosons is considered, subject to thermal fluctuations. We derive a two-fluid theory for this system in which the normal component interacts with the condensate. The latter is described by a complex order parameter field Φ and the total density by a real field φ. The interaction of the condensed and the noncondensed bosons leads to depletion of the condensate. This effect is discussed in a homogeneous and in a trapped Bose gas.

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A grand canonical ensemble of hard-core bosons is considered, subject to thermal fluctuations. We derive a two-fluid theory for this system in which the normal component interacts with the condensate. The latter is described by a complex order parameter field Φ and the total density by a real field φ. The interaction of the condensed and the noncondensed bosons leads to depletion of the condensate. This effect is discussed in a homogeneous and in a trapped Bose gas.
A grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation with fields for occupied and unoccupied sites, an effective field theory is derived in which a complex field corresponds with the order parameter of the condensate and a real field with the total density of bosons. Near the boundary between the normal and the superfluid phase, we obtain the Ginzburg-Landau functional for the superfluid order parameter. A mean-field calculation shows that the critical temperature Tc{T}_{c}Tc​ increases with increasing density up to a maximum and decreases with further increasing density.
The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.
We study the Bose-Einstein condensation (BEC) phenomenon in an interacting trapped Bose gas using the semiclassical two-fluid model and nonextensive statistical mechanics. The effects of nonextensivity characterized by a parameter are explored by calculating the temperature dependent thermodynamic properties, fraction of condensed particles, and density distributions of condensed and thermal components of the system. It is found that nonextensivity in the underlying statistical mechanics may have large effects on the BEC transition temperature.
We consider the Bose-Einstein condensation of atoms in a trap where the density of particles is so high that the low-density approach of Gross [J. Math. Phys. (N.Y.) 4, 195 (1963)] and Pitaevskii (((V. L. Ginsburg and L. P. Pitaevskii, Zh. \'Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 1858 (1958)]))) will not be applicable. For this purpose we use the slave boson representation which is valid for hard-core bosons at any density. This description leads to the same results as the Gross-Pitaevskii approach in the low-density limit, but for higher densities, it predicts the depletion of the condensate in the regions where the density of the atomic cloud is high.