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Journal of the Optical Society of America B

Generation of hyper-bunched light by single Gaussian and non-Gaussian scattering processes

Wolfgang Elsäßer

Published Feb 7, 2024• 0 citations
Publisher

Abstract

We derive theoretically that hyper-bunched light with a central normalized second-order correlation coefficient of six can be realized by a single Gaussian scattering process of parametric down conversion (PDC) light with a central normalized second-order correlation coefficient of three. The Gaussian scattering process is realized by a rotating ground-glass diffuser. We show that the photon counting probability distribution in this case obeys a Tricomi confluent hypergeometric function U [1+ n ,3/2,1/⟨ n ⟩] dependence. Furthermore, we also study non-Gaussian light-scattering probabilities that together with the different impinging light statistics give rise to new photon statistics accompanied by a variety of new values of the second-order correlation coefficient of the scattered light. These theoretical calculations suggest experiments using twin photons from a PDC process and characterizing their photon statistics properties before and after the scattering at the rotating diffuser. These investigations contribute to a more comprehensive understanding of the scattering process, the generated light, and new applications.

DOI
10.1364/josab.510767

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We derive theoretically that hyper-bunched light with a central normalized second-order correlation coefficient of six can be realized by a single Gaussian scattering process of parametric down conversion (PDC) light with a central normalized second-order correlation coefficient of three. The Gaussian scattering process is realized by a rotating ground-glass diffuser. We show that the photon counting probability distribution in this case obeys a Tricomi confluent hypergeometric function U [1+ n ,3/2,1/⟨ n ⟩] dependence. Furthermore, we also study non-Gaussian light-scattering probabilities that together with the different impinging light statistics give rise to new photon statistics accompanied by a variety of new values of the second-order correlation coefficient of the scattered light. These theoretical calculations suggest experiments using twin photons from a PDC process and characterizing their photon statistics properties before and after the scattering at the rotating diffuser. These investigations contribute to a more comprehensive understanding of the scattering process, the generated light, and new applications.
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Parametric down-conversion (PDC) is mostly known in the low-gain (spontaneous) regime, in which the correlated photon pairs are produced. Spontaneous PDC (SPDC) plays a very important role for quantum optics as a variety of quantum states is produced via SPDC. In the high-gain case PDC leads to generation of bright states having up to hundreds mW mean power. With such states almost any nonlinear optical interaction or light-matter interaction becomes more efficient. Even being macroscopically bright, the produced states maintain nonclassical properties as, for example, the fluctuations of electric field quadratures are squeezed below the shot-noise level. The high-gain PDC could be used not only in the same applications as SPDC, it also can provide new ones. Apart from that the high-gain PDC has many remarkable spectral and statistical properties, which are in the focus of this work. The description starts from the PDC generation in normal and anomalous group velocity dispersion ranges. The spectrum and mode content of high-gain PDC is considered as well as their change with the parametric gain are demonstrated. Then, there are the interference effects emerging from the PDC correlations presented, namely the macroscopic analogue of the Hong-Ou-Mandel interference. In addition, it is shown how spatial and temporal walk-off matching could be used for the generation of giant narrowband twin beams. Finally, the statistical properties of high-gain PDC are reviewed as well as their use for multiphoton effects is demonstrated. Photon-number fluctuations of PDC are studied via normalized correlation functions and probability distributions. These fluctuations enhance the generation efficiency for multiphoton effects by orders of magnitude and lead to tremendously fluctuating light described by heavy-tailed photon-number probability distributions.
When a laser beam passes through a rotating ground glass (RGG), the scattered light exhibits thermal statistics. This is extensively used in speckle imaging. This scattering process has not been addressed in the photon picture and is especially relevant if nonclassical light is scattered by the RGG. We develop the photon picture for the scattering process using the Bose statistics for distributing NNN photons in MMM pixels. We obtain an analytical form for the PPP distribution of the output field in terms of the PPP distribution of the input field. In particular, we obtain a general relation for the nthn\mathrm{th}nth-order correlation function of the scattered light, i.e., ${g}_{\text{out}}^{(n)}\ensuremath{\simeq}n!\phantom{\rule{0.16em}{0ex}}{g}_{\text{in}}^{(n)}$, which holds for any order nnn and for arbitrary input states. This result immediately recovers the classical transformation of coherent light to pseudothermal light by RGG.
We discuss two- and three-fold photon statistics for the squeezed light generated by subthreshold degenerate (DPO) and nondegenerate (NDPO) parametric oscillators. In higher-order statistics details of coherence properties are more strongly reflected than in the single-fold statistics. Many experiments use two-fold statistics to extract spectral information about the incident beam. We use phase-space representation to express the operator field variables in terms of independent Gaussian random processes.1 Using the Gaussian property of these field variables and making a Karhunen-Loeve expansion in terms of orthogonal functions, analytical expressions for the two- and three-fold generating functions for the DPO and the NDPO are obtained. From this generating function various statistical quantities such as factorial moments and joint photon counting probability distributions are calculated.
Using the zero time-delay second-order correlation function for studying photon statistics, we investigate how the photon statistics of field-modes generated by the parametric down-conversion (PDC) process depends on the photon statistics of the pump field-mode. We derive general expressions for the zero time-delay second-order correlation function of the down-converted field-modes for both multi-mode and single-mode PDC processes. We further study these expressions in the weak down-conversion limit. We show that for a two-photon two-mode PDC process, in which a pump photon splits into two photons into two separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to twice that of the pump field-mode. Furthermore, for an n -photon n -mode down-conversion process, in which a pump photon splits into n photons into n separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to 2 ( n − 1 ) times that of the pump field- mode. However, in contrast to multi-mode PDC processes, for a single-mode PDC process, in which a pump photon splits into two or more photons into a single mode, the zero time-delay second-order correlation function of the down-converted field-mode is not proportional to that of the pump in the weak down-conversion limit. Nevertheless, we find it to be inversely proportional to the average number of photons in the pump field-mode.