Abstract
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.
Highlights
Following the first observation of second-harmonic generation (SHG) by Franken et al [1], the process has been the subject of a huge amount of theoretical and experimental investigations
We review the simplest quantum description starting from a perturbative approach to the basic interaction Hamiltonian of the process, and we find a series of analytic results on the evolution of the pump field, the SHG probability, and the transformation of the statistics
We investigated the second-harmonic generation process starting from the usual perturbative approach, but aiming to achieve some analytic results
Summary
Following the first observation of second-harmonic generation (SHG) by Franken et al [1], the process has been the subject of a huge amount of theoretical and experimental investigations. We review the simplest quantum description starting from a perturbative approach to the basic interaction Hamiltonian of the process, and we find a series of analytic results on the evolution of the pump field, the SHG probability, and the transformation of the statistics. We retrieve some general results on the generation of second-harmonic (SH) light by inspecting the perturbative evolution of both the photon-number operator and the SH state. Sci. 2019, 9, 1690 supported by the comparison with the classical results and by the quantum description, we move to the analysis of the output statistics by inspecting the Glauber autocorrelation function [12] of the SH field. We analytically retrieve it for the cases of coherent, chaotic, and squeezed light
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