Second Harmonic Revisited: An Analytic Quantum Approach

We address the second-harmonic generation process in a quantum frame. Starting with a perturbative approach, we show that it is possible to achieve a number of analytic results, ranging from the up-conversion probability to the statistical properties of the generated light. In particular, the moments and the correlations of the photon-number distribution of the second-harmonic light generated by any initial state are retrieved. When possible, a comparison with the results achieved with the classical regime is successfully provided. The nonclassicality of some benchmark states is investigated by inspecting the corresponding autocorrelation function.