A Heisenberg picture mean field model for magneto-association of a quantum degenerate Bose gas close to a Feshbach resonance

Date of Completion

January 2008


Physics, Atomic




We construct a simple quantum optics style mean field model to investigate the behaviour of a zero-temperature untrapped quantum degenerate Bose gas close to a Feshbach resonance. The model allows for both atomic and molecular condensates as well as correlated zero-momentum “BCS” pairs whose provenance would be dissociated zero momentum molecules. Beginning with a second quantized (momentum representation) Hamiltonian and equations conserving total (free and bound) atom number and enforcing an assumption that atoms only appear either in the condensates or pairs and the usual Bogoliubov approximation, the system is numerically and in certain limits, analytically, soluble in the steady state and exhibits a second order phase transition to a pure atomic condensate when the controllable parameters of the coupling Rabi frequency and detuning are varied across an (analytically determined) transition line. Analysis of the thermodynamics of the zero-entropy system shows a negative pressure and hence mechanical instability on both sides of the resonance. A mathematical difficulty arising from an ultra-violet divergence due to the assumption of a zero range interaction is resolved with the help of a simpler, exactly analytically soluble two atom version of the problem. ^