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.