Cavity QED characterization of many-body atomic states in double-well potentials: Role of dissipation

When an incident light beam is scattered off a sample of ultracold atoms trapped in a double-well potential, the statistical properties of the retroreflected field contain information about the quantum state of the atoms, and permit, for example, to distinguish between atoms in a superfluid state and a product of Fock states for each well (Mott-insulator-like state). This paper extends our previous analysis of this problem to include the effects of cavity damping. We use a Monte Carlo wave-function method to determine the two-time correlation function and time-dependent physical spectrum of the retroreflected field. We also analyze quantitatively the entanglement between the atoms and the light field for atoms in these two states.