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Bose Einstein condensation of gases in a harmonic potential trap

M. E. Zomorrodian, رمضانعلی سبیلی

Published Mar 1, 2005• 0 citations
OpenAlex

Abstract

One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose – Einstein Condensation (BEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.

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One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose – Einstein Condensation (BEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.
The Bose-Einstein condensation of a dilute gas of rubidium-87 atoms was achieved by cooling a small number of atoms in a magnetic trap. The effective potential of the trap is to lowest order harmonic and under these conditions we estimate the critical temperature and the heat capacity of an ideal gas of Bose particles. Previously this has been estimated within the semiclassical approximation. However, because of the small number of atoms, the resulting TcT_cTc​ deviates slightly from our result obtained by exact numerical calculations. For the gap of the heat capacity at the transition point the deviation is 20%20\%20%.
We study the thermodynamic behavior of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic-oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin approximation. For a finite number of particles there is no phase transition, but there is a well-defined temperature at which the condensation starts. We also consider condensation in lower dimensions, and, for one-dimensional systems, we discuss the dependence of the condensate fraction and heat capacity on the ensemble used.
We present an analysis of Bose-Einstein condensation for a system of non-interacting spin-0 particles in a harmonic oscillator confining potential trap. We discuss why a confined system of particles differs both qualitatively and quantitatively from an identical system which is not confined. One crucial difference is that a confined system is not characterized by a critical temperature in the same way as an unconfined system such as the free boson gas. We present the results of both a numerical and analytic analysis of the problem of Bose-Einstein condensation in a general anisotropic harmonic oscillator confining potential.
Bose–Einstein Condensation (BEC) of both the ideal and the weakly inter-acting cold alkali gases confined by anisotropic harmonic oscillator poten-tials is investigated in this paper. It is shown that the transition point is shifted towards lower temperatures because of the trapped potentials, and the specific heat below the transition point is no longer proportional to T 3/2 . Expressions of modified condensation temperature, internal energy and the specific heat are derived for the ideal trapped gases explicitly. Moreover, the effect of interactions among the atoms on the transition temperature is also given and discussed.
We present an analysis of Bose-Einstein condensation for a system of noninteracting spin-0 particles in a harmonic-oscillator confining potential trap. We discuss why a confined system of particles differs both qualitatively and quantitatively from an identical system which is not confined. One crucial difference is that a confined system is not characterized by a critical temperature in the same way as an unconfined system such as the free boson gas. We present the results of both a numerical and analytic analysis of the problem of Bose-Einstein condensation in a general anisotropic harmonic-oscillator confining potential. \textcopyright{} 1996 The American Physical Society.
The thermodynamic properties of an ideal q-boson gas trapped in an n-dimensional harmonic potential are studied, based on the distribution function of q-bosons. The critical temperature Tc,q of Bose-Einstein condensation (BEC) and the heat capacity C of the system are derived analytically. It is shown that for the q-boson gas trapped in a harmonic potential, BEC may occur in any dimension when q ≠ 1, the critical temperature is always higher than that of an ordinary Bose gas (q = 1), and the heat capacity is continuous at Tc,q for a one-dimensional system but discontinuous at Tc,q for a two- or multi-dimensional system.