Quantum dynamics of cavity assisted photoassociation of Bose-Einstein condensed atoms

TL;DR

This paper investigates the quantum dynamics of photoassociation of Bose-Einstein condensates into molecules within an optical cavity, introducing improved theoretical methods that accurately account for quantum noise and cavity feedback effects.

Contribution

It develops an enhanced mean field theory and approximate quantum solutions for atom-molecule conversion in cavity-assisted photoassociation, surpassing traditional approaches.

Findings

Improved mean field theory corrects deficiencies of traditional models.

Approximate quantum solutions match numerical results for weakly driven cavities.

Quantum noise and cavity feedback significantly influence the dynamics.

Abstract

We explore the quantum dynamics of photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. Inside of an optical resonator, photoassociation of quantum degenerate atoms involves the interaction of three coupled quantum fields for the atoms, molecules, and the photons. The feedback created by a high-Q optical cavity causes the cavity field to become a dynamical quantity whose behavior is linked in a nonlinear manner to the atoms inside and where vacuum fluctuations have a more important role than in free space. We develop and compare several methods for calculating the dynamics of the atom-molecule conversion process with a coherently driven cavity field. We first introduce an alternate operator representation for the Hamiltonian from which we derive an improved form of mean field theory and an approximate solution of the Heisenberg-Langevin (HL) equations that properly accounts for quantum noise in the cavity field. It is shown that our improved mean field theory corrects several deficiencies in traditional mean field theory based on expectation values of annihilation/creation operators. Also, we show by direct comparison to numerical solutions of the density matrix equations that our approximate quantum solution of HL equations gives an accurate description of weakly or undriven cavities where mean field theories break down.