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On Multistep Bose-Einstein Condensation in Anisotropic Traps

K. Shiokawa

Published Jun 21, 1999• 2 citations
OpenAlex

Abstract

Multistep Bose-Einstein condensation of an ideal Bose gas in anisotropic harmonic atom traps is studied. In the presence of strong anisotropy realized by the different trap frequency in each direction, finite size effect dictates a series of dimensional crossovers into lower-dimensional excitations. Two-step condensation and the dynamical reduction of the effective dimension can appear in three separate steps. When the multistep behavior occurs, the occupation number of atoms excited in each dimension is shown to behave similarly as a function of the temperature. Multistep behaviors can be easily controlled by changing the degree of anisotropy. 1

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Acta Physica Sinica•Jan 1, 2014•1 citation
Multistep Bose-Einstein condensation of an ideal Bose gas in anisotropic harmonic atom traps is studied. In the presence of strong anisotropy realized by the different trap frequency in each direction, finite size effect dictates a series of dimensional crossovers into lower-dimensional excitations. Two-step condensation and the dynamical reduction of the effective dimension can appear in three separate steps. When the multistep behavior occurs, the occupation number of atoms excited in each dimension is shown to behave similarly as a function of the temperature. Multistep behaviors can be easily controlled by changing the degree of anisotropy. 1
Multistep Bose-Einstein condensation of an ideal Bose gas in anisotropic harmonic atom traps is studied. In the presence of strong anisotropy realized by the different trap frequency in each direction, the finite size effect dictates a series of dimensional crossovers into lower-dimensional excitations. Two-step condensation and the dynamical reduction of the effective dimension can appear in three separate steps. When the multistep behaviour occurs, the occupation number of atoms excited in each dimension is shown to behave similarly as a function of the temperature. Multistep behaviours can be easily controlled by changing the degree of anisotropy.
The ideal Bose gas in a highly anisotropic harmonic potential is studied. It is found that Bose-Einstein condensation occurs in two distinct steps as the temperature is lowered. In the first step the specific heat shows a sharp feature, but the system still occupies many one-dimensional quantum states. In the second step, at a significantly lower temperature, the ground state becomes macroscopically occupied. It should be possible to verify these predictions using present-day atom traps. The two-step behavior can occur in a rather general class of anisotropic traps, including the box potential.
Bose-Einstein condensation of a relativistic ideal Bose gas in a rectangular cavity is studied. Finite size corrections to the critical temperature are obtained by the heat kernel method. Using zeta-function regularization of the one-loop effective potential, lower-dimensional critical temperatures are calculated. In the presence of strong anisotropy, the condensation is shown to occur in multisteps. The criteria of this behavior is that critical temperatures corresponding to lower-dimensional systems are smaller than the three-dimensional critical temperature.
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 study Bose-Einstein condensation (BEC) for a non-interacting gas in a very anisotropic trap. Therefore, at enough small temperatures some degrees of freedom "freeze", thus reducing the "effective" dimensionality of the system. We mainly focus in quasi-bidimensional traps characterized by a surface S in the (x, y) plane. We consider two confining mechanisms in the z direction: harmonic and rigid wall potentials. There are not forces parallel to S, excepting the rigid wall at the edges. The most relevant results are: (a) The condensate smoothly sets at T ∼ script O sign(Tc/ log N), where Tc is the tridimensional condensation temperature. (b) When BEC is present, also the low-lying excited states have a macroscopic occupation; this effect is also present in a quasi-onedimensional harmonic "cigar-shape" trap. (c) The condensation process is sensitive to the shape of S.
By defining the characteristic length, the boundary effects of Bose-Einstein condensation in a three-dimensional harmonic trap are investigated using the Euler-MacLaurin formula. Results show that the condensed fraction of particles reduces due to the finite-size effects and the effects of finite particle number; the corrections of the condensation fraction and the condensation temperature have, respectively, a maximum value due to the boundary effect, hence it is very effective to optimize the parameters of the harmonic traps for improving the condensation fraction and the condensation temperature. In the jump of heat capacity exist the boundary effects and the effects of finite particle number, and the jump of heat capacity has a minimum because the parameters of harmonic traps are selected to be reasonable. The equation of state is derived for a finite ideal Bose gas system in a three-dimensional harmonic trap; the anisotropy (or isotropy) of the pressure is determined by the anisotropy (or isotropy) of the frequency of the harmonic potential.