We present a critical review of the works related to the statisticalproperties of biological ultra-weak photon emission (UPE) and in particular toits coherence properties. Starting with a brief description of the concept ofcoherence in quantum and classical physics, we then review models used toanalyze photon distributions obtained from measurements of UPE. Moreover,we review experiments focused on statistical properties of UPE and try toassess them from the point of view of current understanding of physics andbiophysics. A critical study of the results and their interpretations leads us toconclude that there is no undoubted proof of the coherence of UPE. We highlightparticular problems of past research with respect to data interpretationor hypothesis building when looking for coherent light sources or emission anddiscuss the application of standard quantum optical methods for assessing thecoherence of an optical field. Since emerging studies show that not only coherenceproperties but also fractal and chaotic properties of UPE time seriessignals can be analyzed, we outline briefly these fractal and chaotic propertiesof UPE time series presenting them as a possible new avenue for UPE signalanalysis.
We present a critical review of the works related to the statisticalproperties of biological ultra-weak photon emission (UPE) and in particular toits coherence properties. Starting with a brief description of the concept ofcoherence in quantum and classical physics, we then review models used toanalyze photon distributions obtained from measurements of UPE. Moreover,we review experiments focused on statistical properties of UPE and try toassess them from the point of view of current understanding of physics andbiophysics. A critical study of the results and their interpretations leads us toconclude that there is no undoubted proof of the coherence of UPE. We highlightparticular problems of past research with respect to data interpretationor hypothesis building when looking for coherent light sources or emission anddiscuss the application of standard quantum optical methods for assessing thecoherence of an optical field. Since emerging studies show that not only coherenceproperties but also fractal and chaotic properties of UPE time seriessignals can be analyzed, we outline briefly these fractal and chaotic propertiesof UPE time series presenting them as a possible new avenue for UPE signalanalysis.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.
We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-A and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the n state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the n state.
This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams.
The concepts listed in the title are introduced and clarified. The relations among them are pointed out. It is shown that the corresponding optical phenomena are definitely of a quantum nature. The basic quantities which are measured in correlation optical experiments are discussed. Manifestations of photon antibunching and of sub-Poisson photon statistics in the recording of delayed coincidences, in the distribution of photon counts, and in intensity fluctuation spectra are analyzed. (More precisely, what is involved is the spectrum of fluctuations in the photocurrent; all the results of the theoretical analysis in this review are expressed in terms of directly measurable quantities.) A diagram technique for calculating the correlation characteristics of the radiation from a polyatomic system is outlined. Photon correlations in nonlinear resonance fluorescence are analyzed. There is a discussion of approaches to the development of macroscopic sources of radiation with sub-Poisson photon statistics: the production of a squeezed state of a field in phase-sensitive parametric effects in nonlinear optics and the introduction of repulsive statistics in luminescence excitation events and in the pumping of a laser. Experiments in these directions which had been reported through April 1986 are discussed. The practical importance of reducing the quantum noise in radiation for extremely precise measurements and for optical data transmission is pointed out.
Developments in quantum technologies lead to new applications that require radiation sources with specific photon statistics. A widely used Poissonian statistics are easily produced by lasers; however, some applications require super- or sub-Poissonian statistics. Statistical properties of a light source are characterized by the second-order coherence function g^(2)(0). This function distinguishes stimulated radiation of lasers with g^(2)(0)=1 from light of other sources. For example, g^(2)(0)=2 for black-body radiation, and g^(2)(0)=0 for single-photon emission. One of the applications requiring super-Poissonian statistics (g^(2)(0)>1) is ghost imaging with thermal light. Ghost imaging also requires light with a narrow linewidth and high intensity. Currently, rather expensive and inefficient light sources are used for this purpose. In the last year, a superluminescent diode based on amplified spontaneous emission (ASE) has been considered as a new light source for ghost imaging. Even though ASE has been widely studied, its photon statistics has not been settled - there are neither reliable theoretical estimates of the second-order coherence function nor unambiguous experimental data. Our computer simulation clearly establishes that coherence properties of light produced by ASE are similar to that of a thermal source with g^(2)(0)=2 independent of pump power. This result manifests the fundamental difference between ASE and laser radiation.
A review is presented of various investigations on coherence and fluctuations of light which have been carried out within the last few years. In particular some of the research carried out at the University of Rochester and related investigations undertaken elsewhere are described. This research is mainly concerned with the following topics: classical and quantum description of higher order coherence effects, photon correlation and coincidence experiments, stellar correlation interferometry, photon bunching, and the determination of the statistical properties of light from photoelectric counting experiments.