Squeezing in the Jaynes-Cummings model for Large Coherent Fields
Clark W. Woods, Julio R. Gea-Banacloche · Journal of Modern Optics · 1993
We use the recently-established asymptotic solution (AS) for large fields to study squeezing in the Jaynes-Cummings model. Arbitrary initial atomic states (including atomic coherence) are considered. We find that most features of squeezing can be understood from the properties of the asymptotic field states, and from the observation, which we establish numerically, that for large fields the interference between the two branches of the wavefunction does not contribute significantly to the squeezing (not even near the revival times, when the two field states being superposed have very nearly the same phase). We obtain a limit on the time over which the field may show any squeezing and find that it scales as the 3/4 power of the number of photons. We also obtain a bound on the maximum achievable squeezing for a given number of photons, which is an improvement over earlier estimates. Finally, we discuss some of the shortcomings of the AS, and in particular the existence of a small ghost peak in the field Q function for initial conditions where the AS predicts a single peak, which is enough to destroy the squeezing for certain times.