Revivals, Fractional Revivals and Tomograms

Abstract

AbstractWe review the basic features of a well known nonclassical effect: wave packet revivals. Revivals of a single mode field occur as a consequence of specific relationships between different frequency parameters in the Hamiltonian. We outline how Gauss sums play a crucial role in the appearance of full and fractional revivals of a single-mode radiation field governed by a Kerr-like Hamiltonian. Using the example of an initial coherent state of light passing through a nonlinear atomic medium, we demonstrate how revivals and fractional revivals are captured in the moments of the field quadratures. The role played by an imperfectly coherent initial state in this regard is demonstrated. We show how optical tomograms mirror the occurrence of revivals and fractional revivals in this case. We illustrate how the presence of more than one time scale blurs this effect, and describe decoherence effects from a tomographic point of view. Using the double-well BEC model as a bipartite example, we explain how revival phenomena are reflected in appropriate tomograms.