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 problem is solved under the condition that the atomic spontaneous emission is included.In the case of no damping,c=0,γ_(1)≠0,γ_(2)≠0,the half atomic inversion operator<σZ>possesses an analytic solution,whereas in the general case c≠0,the problem is reduced to the numerical evaluation of first-order nonlinear differential equations.The final results show that with the increase ofγ_(1) andγ_(2),the kinetic quantities converge rapidly to stationary solutions.