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Abstract
By using the Lewis–Riesenfeld quantum invariant theory, an explicit analytical solution for the time evolution operator of the frequency up-conversion system with a driving term is obtained. It is then used to investigate mainly the influence of the driving term, frequency detuning, and the initial states on the quantum statistical properties of the output-coupled fields. It is found that the time evolution for the general up-conversion system can efficiently convert a low-frequency squeezed light into a high-frequency squeezed light, in the case of zero-detuning, but the squeezed effect of the output fields is independent of the driving term. It is also shown that there is an entanglement between the signal and idler output photons for the general up-conversion system.
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