Bose-Einstein condensation temperature of a gas of weakly dissociated diatomic molecules

TL;DR

This paper investigates how the Bose-Einstein condensation temperature of a weakly dissociated diatomic molecular gas depends on atom-atom interactions, considering dissociation effects and scattering, especially across the BEC-BCS crossover.

Contribution

It provides a detailed calculation of the condensation temperature dependence on scattering length, including effects of dissociation and scattering, and discusses behavior in different trapping conditions.

Findings

Condensation temperature increases with less binding in broad Feshbach resonances.

Maximum transition temperature occurs in the BEC-BCS crossover.

In harmonic traps with narrow resonances, temperature decreases with increasing scattering length.

Abstract

We consider the properties of a gas of bosonic diatomic molecules in the limit when few of the molecules are dissociated. Taking into account the effects of dissociation and scattering among molecules and atoms, we calculate the dispersion relation for a molecule, and the thermal depletion of the condensate. We calculate the dependence of the Bose-Einstein condensation temperature of a uniform gas on the atom-atom scattering length, and conclude that, for a broad Feshbach resonance, the condensation temperature increases as the molecular state becomes less strongly bound, thereby giving rise to a maximum in the transition temperature in the BEC-BCS crossover. We also argue on general grounds that, for a gas in a harmonic trap and for a narrow Feshbach resonance, the condensation temperature will decrease with increasing scattering length.