Dynamics of entanglement of a three-level atom in motion interacting with two coupled modes including parametric down conversion

• A moving three-level atom interacts simultaneously with two coupled fields.
• As a result of field–field interaction, parametric down conversion is considered.
• Atomic population inversion as well as quantum entanglement is examined.
• The effects of atomic motion and detuning on the nonclassicality signs are studied.
• The physical quantities may suitably be tuned by field-mode structure parameter.

In this paper, a model by which we study the interaction between a motional three-level atom and two-mode field injected simultaneously in a bichromatic cavity is considered; the three-level atom is assumed to be in a ΛΛ-type configuration. As a result, the atom–field and the field–field interaction (parametric down conversion) will be appeared. It is shown that, by applying a canonical transformation, the introduced model can be reduced to a well-known form of the generalized Jaynes–Cummings model. Under particular initial conditions, which may be prepared for the atom and the field, the time evolution of state vector of the entire system is analytically evaluated. Then, the dynamics of atom by considering ‘atomic population inversion’ and two different measures of entanglement, i.e., ‘von Neumann entropy’ and ‘idempotency defect’ is discussed, in detail. It is deduced from the numerical results that, the duration and the maximum amount of the considered physical quantities can be suitably tuned by selecting the proper field-mode structure parameter pp and the detuning parameters.