Bounds on sub-Poissonian statistics in the Jaynes-Cummings model

Abstract

There is a conservation law present in the Jaynes-Cummings model which restricts its dynamics. This means that from a given initial state only a subset of all possible states of the system can be reached. This allows one to place bounds on the expectation values of observables of the system. Using this procedure bounds are found on the extent to which the field statistics can become sub-Poissonian for an initial coherent state. Mandel’s Q parameter, which measures the extent to which the statistics are sub-Poissonian, is shown to be a decreasing function of the initial field amplitude. For an initial thermal field it is found that there is a temperature (which depends on the field frequency) above which the field never becomes sub-Poissonian. These methods can be extended to multiatom systems, and results for such systems are presented.