Influence of the dipole-dipole interaction on velocity-selective coherent population trapping

We analyze the influence of the dipole-dipole interaction between ground and excited state atoms on atomic cooling by velocity-selective coherent population trapping. We consider two three-level atoms in the -configuration, interacting with two counterpropagating laser fields as well as with the electromagnetic vacuum modes. The elimination of these modes in the Born-Markov approximation results in spontaneous decay, which is essential in providing the momentum diffusion necessary for cooling, as well as a two-body dipole-dipole interaction between ground-and excited-state atoms. The corresponding two-body master equation is solved numerically by Monte-Carlo wave-function simulations. Our main result is that although a dark state survives the inclusion of dipole-dipole interactions, the presence of this interaction can significantly slow down the cooling process for sufficiently high atomic densities.Dedicated to H. Walther on the occasion of his 60th birthdayStrictly speaking, VSCPT is not a true cooling mechanism. The final atomic distribution cannot be characterized by a temperature, so that there is some ambiguity in characterizing the cooling efficiency. We return to this point in Sect. 3