Cluster quasiclassical dynamics in multiphoton scattering models. Analytical results

Abstract

By introducing collective (“cluster”) dynamic variables that explicitly take into account the symmetry of the model Hamiltonians, two new “cluster” (that take into account the quantum mode correlations) types of quasiclassical approximation for the evolution operatorsUH(t) for a wide class of multiphoton scattering models are obtained; the first type treatsUH(t) as the displacement operator of theSU(2)-group with the parameters determined by the solution to the “classical” equations of motion, and the second type gives a spectral expansion ofUH(t) inSU(2)-quasiclassical eigenfunctions. In this framework, an analysis of the dynamics of the most important quantum-statistical characteristics of the models (mean photon numbers and their variances, field quadratures for individual modes, quasiprobability functions, etc.) is given. In particular, the possibility of realization of the two new types of dynamics depending on the initial states (double-periodic harmonic dynamics forSU(2)-coherent initial states and anharmonic dynamics, which leads to such effects as “collapse-revival” of Rabi oscillations, for ordinary coherent states) is revealed.