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arXiv:cond-mat/0210217

Atomic-Molecular Condensates with Large Positive Scattering Length

Aurel Bulgac, Paulo F. Bedaque

Published Oct 9, 2002• 0 citations
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Abstract

We show that in the limit of large and positive atom--atom scattering length the properties of an atomic--molecular Bose--Einstein Condensate (amBEC) are determined by an universal energy density functional (EDF). We find that the optimal conditions for the formation of a stable amBEC are in the regime where there are no shallow trimers and the atom--dimer scattering length is negative and comparable in magnitude with the atom--atom scattering length. At temperatures lower than $T_c$ the chemical potentials for the atoms and molecules can be specified independently. Besides three--body recombinations processes into dimers of large size, inelastic processes involving the formation of deeply bound small size molecular states are possible. These inelastic processes do not lead to an efficient heating of the amBEC and can be used for its mostly non--destructive monitoring.

DOI
10.48550/arxiv.cond-mat/0210217

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We derive a universal formula for the rate constant $\ensuremath{\beta}$ for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length aaa. We show that $\ensuremath{\beta}$ is determined by aaa and by 2 three-body parameters that also determine the binding energies and widths of Efimov states. The rate constant $\ensuremath{\beta}$ scales like $\ensuremath{\hbar}a∕m$ near the resonance, but the coefficient is a periodic function of ln(a)\mathrm{ln}(a)ln(a) that may have resonant enhancement at values of aaa that differ by multiples of 22.7.
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We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.