Unified description of inhomogeneities, dissipation and transport in quantum light-atom interfaces

We show how a variety of real-world effects can be incorporated into continuous-variable models of atom-light interfaces within a single, consistent framework. The approach is similar to that of Madsen and Molmer (2004 Phys. Rev. A 70 052324), but uses physical, not canonical, variables. We show how to include spatial and temporal inhomogeneities, external fields, coherent atom-light interactions, loss, decoherence, atomic transport and projective measurements within a covariance-matrix description. The model can be applied to many experimental situations ranging from room temperature vapour cells to sub-mK atomic clouds. As first applications, we calculate the effect of detector time resolution, spatial inhomogeneities and atomic motion on the spin squeezing dynamics of rubidium 87 on the D-2 transition.