Control of the vibrational dynamics of an atom in a parabolic potential of a trap with the help of a classical electromagnetic field

The model proposed by Blockley, Walls, and Risken for describing the interaction of the center of mass coordinate of an atom captured in a parabolic trap with an electron transition is generalized. This interaction occurs when the atom oscillates in the neighborhood of a node of a classical standing wave resonant with the first vibrational band of the intra-atomic transition. Two methods of controlling the vibrations are considered. In the first method, an exciting one-mode field resonant with the intra-atomic transition transforms the vibrational mode to a coherent state. In the second method, the electron transition is influenced by a two-mode field exciting the vibrational mode to a state squeezed with respect to the coordinate and, under a certain choice of the phase, with respect to the momentum. The transition to the squeezed state is possible if the control field is switched on slowly. The rate at which it is switched on is evaluated depending on the parameters of the problem.