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Journal of Northeast Normal University

The interaction between contaminants in ideal Bose-Einstein condensates

Yufu Liu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In this paper the interaction between contaminants of the Bose-Einstein condensed system at finite temperature is discussed by using the Thermal Field Dynamics.The system energy and Casimir force between the contaminants are obtained,the relationship of the force with temperature and distance is also discussed.These results will help us further understand the physical effect of contaminants in the Bose-Einstein condensed body and provide certain reference value to Casimir effect and the Bose-Einstein condensation experimental study.

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In this paper the interaction between contaminants of the Bose-Einstein condensed system at finite temperature is discussed by using the Thermal Field Dynamics.The system energy and Casimir force between the contaminants are obtained,the relationship of the force with temperature and distance is also discussed.These results will help us further understand the physical effect of contaminants in the Bose-Einstein condensed body and provide certain reference value to Casimir effect and the Bose-Einstein condensation experimental study.
It is hypothesized that, within Bose-Einstein condensates, contaminants will form a potential that effects the energy state of a condensate. While assuming a system governed by the Gross-Pitaevskii equation, contaminants are modelled as boundary conditions for the wave function of the condensate. It is then found that the energy of the system depends directly upon the distance between contaminants. Energy is minimized as two particles either come together or move apart depending on the nature of the condensate. This is due to the presence of induced standing waves in the condensate between two contaminants, similar to the attractive effect caused by standing electromagnetic waves in a vacuum, the Casimir effect. Quantum calculations are also done to determine the expected strength of the "contaminant in condensate" effect.
We discuss a Casimir force due to zero-temperature quantum fluctuations in an interacting quasi–one-dimensional Bose-Einstein condensate (BEC). For the first time, we can investigate the effect of the trapping potential and the atom-atom interaction simultaneously both of which contribute to the Casimir force. Furthermore, we calculate the Casimir force due to thermal fluctuations at finite temperature. Finally, we speculate on some possible experimental realization and detection of the force in future experiments.
We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that Bose-Einstein(B-E) statistics needs a correction for finite system at ultralow temperatures. As a corrected statistics we introduced a Tsallis type of generalized B-E statistics. The condensate fraction calculated with this generalized B-E statistics, is satisfied well with the experimental result. In the third section we show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached. Our results support the experimental result which was obtained well below the condensation temperature. In the fourth section we concentrate on the thermodynamic Casimir force on the Bose-Einstein condensate. We explored the temperature dependence of the Casimir force.
We discuss a Casimir force due to zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC) with a strong harmonic trap. The results show that the presence of a strong harmonic trap changes the power law behavior of Casimir force due to the dimensional reduction effect. At finite temperature, we calculate Casimir force due to thermal fluctuation and find an exotic temperature dependent behavior in the first order term. Finally, we speculate some possible experimental realization and detection of the force in future experiments.
The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T ⩽ T c (where T c is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T > T c , the Casimir force is an exponential decay function; and when T ≫ T c , the Casimir force vanishes.