Collapse and revival phenomenon in the evolution of a resonant field in a Kerr-like medium

A quantum theory of the propagation of a single-mode resonant field through a Kerr-like medium is given. Numerical studies show the existence of the quantum collapses and revivals in the otherwise periodic exchange of energy between the field and the atomic oscillator. Approximate analytical methods are developed to explain the numerical results for the case of weak nonlinearity of the Kerr medium. For large nonlinearity, the correspondence with the Jaynes-Cummings model is discussed