Interaction effects on atomic laboratory trapped Bose-Einstein condensates

Abstract

We discuss the effect of inter-atoms interactions on the condensation temperature $T_c$ of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift $\Delta T_c/T_c^0\approx b_1(a/{\lambda }_{T_c})+b_2(a/{\lambda }_{T_c}{)}^2+\psi [a/{\lambda }_{T_c}]$ with $a$ the s-wave scattering length, ${\lambda }_T$ the thermal wavelength and $\psi [a/{\lambda }_{T_c}]$ a non-analytic function such that $\psi [0]={\psi }^{\prime }[0]=\psi "[0]=0$ and $|\psi {"}^{\prime }[0]|=\infty$. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in $a/{\lambda }_{T_c}$ and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for $b_2\simeq 18.8$ which improves a previous numerical result. We also discuss how the discrepancy between $b_2$ and the empirical value of $b_2=46\pm 5$ may be explained with no need to resort to beyond-mean field effects.

6 pages, to appear in Eur. Phys. J. B (2013)

References in corpus (6)

• Bose-Einstein condensation of chromium
• Effects of Interactions on the Critical Temperature of a Trapped Bose Gas
• Polymer Bose--Einstein Condensates
• Trapped Bose-Einstein condensates with Planck-scale induced deformation of the energy-momentum dispersion relation
• Planck-scale effects on Bose-Einstein condensates
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Cited by in corpus (6)

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• Finite-size effects on the Bose-Einstein condensation critical temperature in a harmonic trap
• Origin of nonlinear contribution to the shift of the critical temperature in atomic Bose-Einstein condensates
• Critical temperature of trapped interacting bosons from large-N based theories
• Weakly interacting Bose-Einstein condensates in temperature-dependent generic traps
• Condensation temperature of strongly interacting ${}^{39}K$ condensates in the mean-field and semi-classical approximations