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Abstract: Nonlinear optical media of Kerr type are described by a particular version ofan anharmonic quantum harmonic oscillator. The dynamics of this system can bedescribed using the Moyal equations of motion, which correspond to a quantumphase space representation of the Heisenberg equations of motion. For the Kerrsystem we derive exact solutions of the Moyal equations for a complete set ofobservables formed from the photon creation and annihilation operators. TheseMoyal solutions incorporate the asymptotics of the classical limit in a simpleexplicit form. An unusual feature of these solutions is that they exhibitperiodic singularities in the time variable. These singularities are removed bythe phase space averaging required to construct the expectation value for anarbitrary initial state. Nevertheless, for strongly number-squeezed initialstates the effects of the singularity remain observable.

Autor: T. A. Osborn, Karl-Peter Marzlin


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