Moyal phase-space analysis of nonlinear optical Kerr media

John C. Kralik, Michelle S. Malcuit

Mikhail D. Lukin, Philip Hemmer, Marlan O. Scully

T. A. Osborn, Karl-Peter Marzlin

Nonlinear optical media of Kerr type are described by a particular version of an anharmonic quantum harmonic oscillator. The dynamics of this system can be described using the Moyal equations of motion, which correspond to a quantum phase-space representation of the Heisenberg equations of motion. For the Kerr system we derive exact solutions of the Moyal equations for an irreducible set of observables. These Moyal solutions incorporate the asymptotics of the classical limit in a simple, explicit form. An unusual feature of these solutions is that they exhibit periodic singularities in the time variable. These singularities are removed by the phase-space averaging required to construct the expectation value for an arbitrary initial state. Nevertheless, for strongly number-squeezed initial states the effects of the singularity remain observable.

Vladimir I. Man’ko, Giuseppe Marmo, F. Zaccaria

States of nonlinear quantum oscillators (f-oscillators) are considered in the Weyl–Wigner–Moyal representation and the tomographic probability representation, where the states are described by standard probability distributions instead of wave functions or density matrices. The evolving integrals of motion for classical and quantum f-oscillators are found and the solution for the Liouville equation associated with the probability distribution on the phase space for this oscillator is obtained along with the solution of the Moyal equation for the quantum f-oscillator, which provide solutions for the partial case of f-nonlinearity existing in Kerr media. Nonlinear coherent states and the thermodynamics of nonlinear oscillators are studied.

Mostafa Sahrai, Ali Hamrah Gharamaleki

Katarzyna Agnieszka Rutkowska, Yoav Linzon, Boris A. Malomed +1 more

We demonstrate a novel approach to the nonlinear optical collapse control in magneto-optical Kerr media. A suitable and essential interplay between magnetically-induced birefringences is fully described via a superposition of the Cotton-Mouton and Faraday effects.