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

TL;DR

This paper models the interaction of a moving three-level atom with two coupled modes in a cavity, analyzing entanglement dynamics and atomic population inversion, with results showing how system parameters influence quantum properties.

Contribution

It introduces a reduced model of a three-level atom interacting with coupled modes, providing analytical solutions for system evolution and entanglement measures.

Findings

Entanglement and population inversion can be controlled by system parameters.

Analytical expressions for system dynamics are derived.

Numerical results demonstrate parameter tuning effects.

Abstract

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 $\Lambda$-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 $p$ and the detuning parameters.