Resonant Processes in a Frozen Gas

Details Resonant Processes in a Frozen Gas Resonant Processes in a Frozen Gas

1998-12-17

arxiv.org/abs/cond-mat/9812313v2

Physical Review A, Volume 59, Number 6, pp. 4358-4367

Physics

Condensed Matter

Disordered Systems and Neural Networks

30 pages, 6 figures

Scientific paper

10.1103/PhysRevA.59.4358

We present a theory of resonant processes in a frozen gas of atoms interacting via dipole-dipole potentials that vary as $r^{-3}$, where $r$ is the interatomic separation. We supply an exact result for a single atom in a given state interacting resonantly with a random gas of atoms in a different state. The time development of the transition process is calculated both on- and off-resonance, and the linewidth with respect to detuning is obtained as a function of time $t$. We introduce a random spin Hamiltonian to model a dense system of resonators and show how it reduces to the previous model in the limit of a sparse system. We derive approximate equations for the average effective spin, and we use them to model the behavior seen in the experiments of Anderson et al. and Lowell et al. The approach to equilibrium is found to be proportional to $\exp (-\sqrt{\gamma_{eq}t}$), where the constant $\gamma _{eq}$ is explicitly related to the system's parameters.

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