Quantum dynamics of collective spin states in a thermal gas

Ensembles of alkali-metal or noble-gas atoms at room temperature and above are widely applied in quantum optics and metrology owing to their long-lived spins. Their collective spin states maintain nonclassical nonlocal correlations, despite the atomic thermal motion in the bulk and at the boundaries. Here we present a stochastic, fully quantum description of the effect of atomic diffusion in these systems. We employ the Bloch-Heisenberg-Langevin formalism to account for the quantum noise originating from diffusion and from various boundary conditions corresponding to typical wall coatings, thus modeling the dynamics of nonclassical spin states with spatial interatomic correlations. As examples, we apply the model to calculate spin noise spectroscopy, temporal relaxation of squeezed spin states, and the coherent coupling between two spin species in a hybrid system.