Bounds from a conservation law in the Dicke model.

Abstract

We study N two-level atoms coupled to a single mode of the electromagnetic field. This system obeys a conservation law that restricts the set of states which can be reached by time evolution from a given initial state. This fact allows one to calculate time-independent bounds for certain observables, in particular, the uncertainty in photon number, \ensuremath{\Delta}n. These bounds can be used to determine how sub- or super-Poissonian the photon statistics can become. This is done for an initial coherent state and an initial thermal state. For the coherent state the number of atoms must be greater than the square root of the initial number of photons for highly sub-Poissonian fields to be possible. On the other hand, for the thermal state N must be greater than the initial photon number for this to occur. In the case of the thermal state, we also find that the field will never become sub-Poissonian if the ratio of the initial photon number to N is greater than a quantity of order 1.