K-quantum downconversion in the motion of a trapped atom

Summary form only given.The phenomenon of multiquantum downconversion is of great interest in quantum optics. In the limit of a classical driving field it can be described by an interaction Hamiltonian (in the interaction picture). For k=2 an interaction of this type is of interest in the context of squeezing. For multiquantum processes of higher order (k>2), however, the Hamiltonian is known to lead to a divergent dynamics. This problem is resolved by taking into account the quantization of the pump mode. More recently, the realization of similar interactions also became possible in the quantized motion of a trapped atom, where the operator it represents the annihilation of a motional quantum of the center-of-mass motion. For k=2 such a dynamic has been used to generate motional squeezing, and other interactions of that type have been considered.