Origin of splits inQfunctions for the Jaynes-Cummings model
Kuniaki Matsuo · Physical Review A · 1994
A splitting in the Q distribution functions for the Jaynes-Cummings model is explained, based on the interpretations of the density matrix. It has been shown [J. Eiselt and H. Risken, Phys. Rev. A 43, 346 (1991)] that the Q function splits into two peaks, which counterrotate in phase space and that the collision on the opposite side of the space and the behavior of the Q function are closely connected to the collapse of the Rabi oscillations. This paper reveals the origin of the splitting of the Q distribution functions in terms of the interpretation of the density-matrix formalism. The effects of the initial atomic state on the Q distribution functions and on the quadrature fields are emphasized. It will be shown that the nonrotating Q function is responsible both for the collapse and revival of the Rabi oscillations and for the high-frequency components of the quadrature fields. In this analysis it is assumed that the initial light field of the model is a coherent state and that an atom is prepared in a coherent superposition of the excited and ground states. Three-dimensional figures of the Q distribution functions are presented as a function of the interaction time.