Influence of an External Classical Field on the Interaction Between a Field and an Atom in Presence of Intrinsic Damping

Abstract

The effect of intrinsic damping on the interaction between a two-level atom and a multi-photon cavity field in the presence of an external classical field is studied. Under certain conditions and use of a transformation, the system is transformed to a generalized Jaynes Cummings model, with the influence of classical field included in the detuning parameter. The temporal evolution of some statistical aspects such as, the atomic inversion, the squeezing phenomena and linear entropy are obtained. In addition, we present the effects of the intrinsic damping and detuning parameters on the above mentioned quantities, for one and two photons. The entropy is used as a measure of the degree of entanglement, and consequently discussed.

Appendix

We derive the formula of the variance squeezing at the initial time. From (4) we get:

$$\begin{array}{@{}rcl@{}} \langle\hat{\sigma}_{x}\rangle &=& \langle\hat{S}_{x} \rangle\cos 2\xi+\langle\hat{S}_{z}\rangle \sin 2\xi\\ \langle\hat{\sigma}_{y}\rangle &=& \langle\hat{S}_{y}\rangle\\ \langle\hat{\sigma}_{z}\rangle &=& \langle\hat{S}_{z} \rangle\cos 2\xi-\langle\hat{ S}_{x} \rangle\sin 2\xi \end{array} $$

(A.1)

then

$$ \langle \hat{\sigma}_{x}^{2} \rangle = 1 \qquad , \qquad \langle \hat{\sigma}_{x} \rangle =\sin 2\xi \qquad \text{and}\qquad \langle \hat{\sigma}_{z} \rangle = \cos 2\xi $$

(A.2)

by using (29) then :

$$ V_{x} = \cos 2\xi -\sqrt{| \cos 2\xi|} $$

(A.3)

Similarly, we can calculate V _y and determine starting point.