Quantum-statistical enhancement of spontaneous emission in velocity-selective coherent population trapping: Mean-field calculations

We study the mean-field dynamics of atoms in a velocity-selective coherent population trapping (VSCPT) configuration, under the influence of resonant dipole-dipole interactions. By elimination of the transverse electromagnetic field we derive a Heisenberg master equation for an arbitrary atomic operator. A closed equation of motion for the one-particle density matrix can be given by employing a time-dependent Hartree-Fock (TDHF) factorization of the two-particle density matrix, thereby neglecting two-particle correlations, i.e., collisional effects. In the case of bosons, the mean-field evolution mainly shows a quantum-statistical enhancement of the spontaneous emission rates, sensitive to the final-state occupation. The description is specialized to treat atoms with a J=1{→}J^'=1 transition in a one-dimensional σ⁺-σ^- VSCPT configuration. The TDHF equations are integrated numerically. It is shown that for a density at which the gas is optically dense, the number of atoms, trapped in the dark state, is increased and its momentum width is decreased. {} 1996 The American Physical Society.