Role of spatial inhomogeneity in dissociation of trapped molecular condensates

TL;DR

This paper provides an analytical and numerical study of how spatial inhomogeneity in trapped molecular condensates influences dissociation dynamics and atom-atom correlations, revealing degradation of correlations with smaller condensate sizes.

Contribution

It introduces explicit analytic results for correlation functions considering spatial inhomogeneity and compares them with numerical simulations for different dimensions.

Findings

Correlation strength decreases with smaller condensate size.

Analytic results effectively describe dissociation dynamics up to 10% conversion.

Spatial inhomogeneity significantly impacts atom-atom correlations.

Abstract

We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair correlations in the short-time limit. Both fermionic and bosonic statistics of the constituent atoms are considered. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the asymptotic behavior of the second-order correlation functions and for the relative number squeezing between the dissociated atoms in one, two and three spatial dimensions. Comparison with the numerical results shows that the analytic approach employed here captures the main underlying physics and provides useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate.