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Dynamics of three-level atoms coupled to a displaced-plus-squeezed field

An extension of a previous work is presented where we attempt to find the most general conditions that permit exact analytic solutions of a multi-level atom interacting with a single mode quantized field using nonlinear Riccati equation. For the system to be completely separable we find that the complex coupling constants connecting atomic states as well as the different frequencies of the problem have to satisfy certain relations. This method is applied to atom-field coupling where the field is described by displaced-plus-squeezed state, while the atom is given in any arbitrary initial state.