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Algebraic Structure and Analytic Solutions of a Moving V-Type Three-Level Atom Interacting with a Two-Mode Cavity Field

In the framework of algebraic dynamics, the dynamics of a V-type three-level atom interacting with a two-mode of the quantized cavity field is considered with atomic center-of-mass motion included. The general analytical expressions for the linearized Hamiltonian and the reduced density operator are derived, which can be used to calculate the expectation values of any system operators. As an illustration, analytical expressions for the optical forces are obtained.