Pairing mean-field theory for the dynamics of dissociation of molecular Bose-Einstein condensates

TL;DR

This paper introduces a pairing mean-field theory to model the quantum dynamics of molecular Bose-Einstein condensate dissociation, analyzing effects of dimensionality, correlations, and comparing with exact and stochastic methods.

Contribution

The paper develops a novel pairing mean-field approach for dissociation dynamics and assesses its validity across different dimensions and particle statistics.

Findings

The theory predicts atom production rates influenced by dimensionality and dissociation energy.

Correlation functions between atoms of opposite momenta are calculated and analyzed.

The pairing mean-field results align well with exact and stochastic methods within certain regimes.

Abstract

We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one, two, and three-dimensional geometries and analyze the role of dimensionality on the atom production rate as a function of the dissociation energy. As well as determining the populations and coherences of the atoms, we calculate the correlations that exist between atoms of opposite momenta, including the column density correlations in 3D systems. We compare the results with those of the undepleted molecular field approximation and argue that the latter is most reliable in fermionic systems and in lower dimensions. In the bosonic case we compare the pairing mean-field results with exact calculations using the positive-$P$ stochastic method and estimate the range of validity of the pairing mean-field theory. Comparisons with similar first-principle simulations in the fermionic case are currently not available, however, we argue that the range of validity of the present approach should be broader for fermions than for bosons in the regime where Pauli blocking prevents complete depletion of the molecular condensate.