Superstructures, fractional revivals, and optical Schrödinger-cat states in the Jaynes-Cummings model

Abstract

It is shown that if the initial photon distribution is narrow (sub-Poissonian), long-time behavior of the atomic inversion is dominated by very spectacular and almost-periodical superstructures. These superstructures generalize phenomena described previously (fractional revivals). They result from beating of not-nearest-neighbor eigenstates of the system, and we show which beats lead to particular types of revivals. In addition, the cavity field develops macroscopically distinguishable states (optical Schr\"odinger-cat states). These stages emerge when the fractional revivals with a frequency of 2/${\mathit{t}}_{\mathit{R}}$, 3${\mathit{t}}_{\mathit{R}}$, and 4/${\mathit{t}}_{\mathit{R}}$, where ${\mathit{t}}_{\mathit{R}}$ is the single-revival period, appear for the second, fourth, sixth, etc., time in the superstructure pattern.