Time-averaged properties of the Jaynes-Cummings model

Exact solutions in the form of infinite series are well known for the Jaynes-Cummings model describing the interaction of a two-level atom with a single-mode field prepared in a coherent state. While these solutions have led to the discovery of many interesting properties of the Jaynes-Cummings model as a function of time, the nature of the solutions is such that it is not a simple matter to make statements of a general nature about the properties of the system. In this paper it is shown that by taking infinite time averages of the series expressions for the atomic inversion and inversion correlation, squeezing, and antibunching, simple closed-form expressions are obtained from which general properties of the Jaynes-Cummings model can be readily inferred. In particular, new conditions are obtained under which the field is significantly squeezed on average, and further information is obtained on the long-time behavior of the revivals in the atomic inversion.