Coupled-channel cavity QED model and exact solutions

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Abstract
We present an alternative cavity QED model with three nondegenerate quantized field modes. The atom-field interaction is a cavity analog of Raman scattering, and the three field modes can be associated with pump, Stokes, and anti-Stokes frequencies. Unlike systems based on the Jaynes-Cummings model, this one has two independent channels connecting the two active atomic levels, leading to the possibility of quantum interferences. Despite its complexity, the model has eigenstates and eigenvalues that can be found exactly and fully analytically in finite terms. The most interesting eigenstates have a ‘‘chain’’ character unknown in previous cavity QED models. Both Fock-state and coherent-state solutions are presented for a number of quantities, including complex three-mode variables. Heisenberg operator solutions are demonstrated in a few cases, and an example of fourth-order quantum interferences due to the coupled channels is worked out in full.