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arXiv:cond-mat/0610797

Theory of Critical Temperature Adiabatic Change for Ideal Gas Bose-Einstein Condensation in Optical Lattices

G. A. Muradyan, A. Zh. Muradyan

Published Oct 28, 2006• 0 citations
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Abstract

We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that the width of the lowest energy band appears as the main parameter determining the critical temperature of condensation. Is obtained a very simple, proportional to 1/3 degree, regularity for this dependence. The fundamental role of tunneling in physics of condensate establishment is underscored.

DOI
10.48550/arxiv.cond-mat/0610797

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We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that the width of the lowest energy band appears as the main parameter determining the critical temperature of condensation. Is obtained a very simple, proportional to 1/3 degree, regularity for this dependence. The fundamental role of tunneling in physics of condensate establishment is underscored.
We calculate the critical temperature of the Bose-Einstein condensation of an ideal Bosegas in the presence of an external periodic potential in one, two, or three directions. A number of assumed approximations enables us to show that the only parameter determining the critical temperature of condensation is the width of the lower energy band with the direct proportionality to the one-third power of this width for each direction of periodicity of the external potential. This also proves the result, obtained earlier by means of numerical calculation, that deepening of the periodic potential (which is known to lead to narrowing of energy bands) leads to lowering of the critical temperature. The fundamental role of quantum tunneling in establishing this regularity is emphasized.
In this paper we develop an analytic expression for the critical temperature for a gas of ideal bosons in a combined harmonic lattice potential, relevant to current experiments using optical lattices. We give corrections to the critical temperature arising from effective mass modifications of the low energy spectrum, finite size effects, and excited band states. We compute the critical temperature using numerical methods and compare to our analytic result. We study condensation in an optical lattice over a wide parameter regime and demonstrate that the critical temperature can be increased or reduced relative to the purely harmonic case by adjusting the harmonic trap frequency. We show that a simple numerical procedure based on a piecewise analytic density of states provides an accurate prediction for the critical temperature.
It is shown that the critical temperature of gas Bose-Einstein condensation decreases in deepening periodic potential, in contrast to common regularity in a separate potential well. The physical explanation of this phenomenon is given. Characteristic scale of potential energies decaying the critical temperature is the quantum recoil energy of periodic potential. The theory represents an alternative and direct approach to the experimental results (C.Orzel et al Science 291, 2386 (2001); M.Greiner et al, Nature 415, 39 (2002)) obtained with BEC in optical lattices and treated as the phase squeezing or Mott transition processes.
We present a theoretical study of Bose-Einstein condensation(BEC) of trapped ideal gas of spin-1 ultracold atoms in tight-binding bands corresponding to simple cubic(SC) optical lattices.Under the constraints that both the total number of atoms (N) and the total magnetization (M) are conserved,we first investigate the phase transitions process of noninteracting spin-1 atomic system,by investigating the critical condensation temperature and condensate fraction,we find BEC with spin degrees of freedom shows richer phase transitions than BEC of scalar atoms.We then extend our studies to the case with a uniform external magnetic field included,the phase transitions for this case make interesting changes again.