Abstract
The behavior of a simple theoretical model of a quantum-frequency converter with a time-dependent pump amplitude and phase is analyzed quantum mechanically. A sufficient condition ensuring periodic frequency conversion between the modes is found and exact solutions are given in these cases. The complete time-dependent density matrices which give the most complete statistical description of the system are presented for a variety of initial states of the system. In the general case where the sufficient condition is not satisfied, time-dependent-perturbation-theory results give corrections to the amplitude and the period of the energy exchange between the modes. Comparisons are made between these results and those of other authors.
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