Resonant Processes in a Frozen Gas

TL;DR

This paper develops a theoretical framework for understanding resonant dipole-dipole interactions in a frozen atomic gas, providing exact and approximate solutions that explain experimental observations and the system's approach to equilibrium.

Contribution

It introduces a new model combining exact solutions and random spin Hamiltonians to analyze resonant processes in frozen gases, bridging sparse and dense systems.

Findings

Derived exact results for single-atom resonant interactions.

Modeled the system's behavior using a random spin Hamiltonian.

Explained the exponential approach to equilibrium with a specific rate.

Abstract

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.