Generation of Nonclassical States of the Radiation Field in the System of A Single Trapped Atom in A Cavity Within the First Order of the Lamb-Dicke Approximation

In this paper, we propose a theoretical scheme for the generation of non-classical states of the cavity field in a system of a single trapped atom via controlling the lamb-dicke parameter. by exploiting the super-operator method, we obtain an analytical expression for the density operator of the system by which we examine the dynamical behaviors of the atomic population inversion, the phase-space husimi q-function as well as the von neumann quantum entropy of the cavity-field. the results reveal that at certain periods of time one of the cavity-field quadratures may be squeezed and the two sub-systems of the trapped atom and the cavity field are entangled. moreover, we find that the atomic spontaneous emission and the cavity-field damping destroy the nonclassical characteristics of the cavity field.