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, γ₁ ≠ 0, γ₂ ≠ 0, the half atomic inversion operator <σ_Z> 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 of γ₁ and γ₂, the kinetic quantities converge rapidly to stationary solutions.