Second Harmonic Revisited: An Analytic Quantum Approach

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.

Special Issue on Quantum Optics for Fundamental Quantum Mechanics

“…The arguments covered in the previous section are then developed in the research articles, which consist of eight papers, offering a panorama of the present studies in quantum optics and analyzing some specific issues of the different lines of research in which this field is structured. In summary, issues concerning non-locality studies range from the application of the de Broglie-Bohm model to Gauss-Maxwell beams [13] to revisiting complementarity relations in bipartite quantum systems [14]; correlations in atoms are investigated in [15,16], photon emission and statistics in [17,18] and methods in quantum technologies in [19,20] The first paper [13] of this section deals with a Bohmian-based approach to Gauss-Maxwell beams, a particularly appropriate and natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers: a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of the electromagnetic field with that of (electromagnetic) flow or streamline. The described features confer the approach a potential interest in the analysis and description of single-photon experiments.…”

“…The arguments of [17,18] concern photon emission and statistics. The high-frequency electromagnetic emission from non-local wavefunctions is analyzed in [17], where it is shown that, in systems with non-local potentials or other kinds of non-locality, the Landauer-Büttiker formula of quantum transport leads to replacing the usual gauge-invariant current density J with a current J ext , which has a non-local part and coincides with the current of the extended Aharonov-Bohm electrodynamics.…”

“…The process of second harmonic generation is addressed in a quantum frame in [18]: the analysis here starts with a perturbative approach, showing how it is possible to achieve a number of analytic results, ranging from the up-conversion probability to the statistical properties of the generated light. Moreover, the authors investigate the nonclassicality of some benchmark states by inspecting the corresponding autocorrelation function.…”

Photon pumping, photodissociation and dissipation at interplay for the fluorescence of a molecule in a cavity

“…Often, classical radiation fields are used, which is appropriate in the strong field limit. However, highly interesting effects in SHG (and fluorescence in general) appear in the low photon regime [20][21][22][23], where quantum effects generally dominate [24] and the so-called rotating wave approximation (RWA) [25][26][27][28][29] may be inadequate [30][31][32].…”