SU(2) linear canonical transformation and dynamics in the multiphoton Jaynes-Cummings interaction
Han-Qian Gong · Physical Review A · 1997
The formulation of the evolution operator for the multiphoton Jaynes-Cummings interaction in the decomposition form is presented, in terms of the SU(2) rotation transformation proposed by the present author [J. Mod. Opt. 39, 2209 (1992)]. The study of the dynamical evolution of the photon statistics for the case of intensity dependent coupling with m-photon atomic transition exhibits a number of novel features (sub-Poissonian and oscillatory distributions). It is shown that for m=1 the field distribution oscillates exactly in a periodic sequence without the limitation of the large mean photon number n-bar, and that for m=2 the oscillatory distributions emerge at one-quarter and three-quarters of the revival time for the initially high boson excitation regardless of the initial condition of the atomic state.