The time-dependent invariant of a quantum frequency conversion system in an optical cavity is found from the simple observation that the dynamical evolution of a sum-frequency generation process preserves the total number of the idler photons and the signal photons involved in the process. By using this invariant and the Lewis-Riesenfeld quantum invariant approach, the Schrodinger equation for the coupled system of the two quantized modes of the electromagnetic field is solved under detuned condition. The explicitly analytical formulae of the quantum states and the evolution operators of the s...
