Time averaged quantities in the Jaynes-Cummings model

Abstract

The Jaynes-Cummings model is one of the most basic systems in quantum optics. It is exactly soluble but the quantities of interest are given by infinite oscillating series which cannot be summed. This leads to problems if one wants to learn about the long-time behavior of the system. On the other hand, the time averages of those quantities can be computed exactly. Infinite time averages give information about behavior which persists for all time. We examine the time averages of the squeezing and the variance of the photon number of the field. We also use time averages to gain information about the inversion. For example, one finds that the fraction of time which the inversion spends far from its mean value decreases as the amplitude of the initial field increases. The importance of periodic behavior in the inversion also decreases as the initial amplitude increases. Finally we examine how long the system must be observed for time averages of quantities to approach their infinite time limits.