Damped Jaynes-Cummings model including spontaneous emission

As a continuation of the previous paper 'Collapse and revival in the damped Jaynes-Cummings model' [Chin. Phys. Lett. 16 (1999) 895], at present the p roblem is solved under the condition that the atomic spontaneous emission i s included. In the case of no damping, c = 0, gamma (1) not equal 0, gamma (2) not equal 0, the half atomic inversion operator (sigma (z)) possesses a n analytic solution, whereas in the general case c not equal 0, the problem is reduced to the numerical evaluation of first-order nonlinear differenti al equations. The final results show that with the increase of gamma (1) an d gamma (2), the kinetic quantities converge rapidly to stationary solution s.