Correlations in single‐photon experiments

Abstract

Abstract. Correlations of detection events in two photodetectors placed at the opposite sides of a beam splitter are studied in the frame of classical probability theory. It is assumed that there is always only one photon present in the measuring apparatus during one elementary experiment (one measurement act). Due to the conservation of energy, there is always a strict anticorrelation in one elementary experiment, because the photon cannot excite both of the detectors at the same time. It is explicitely shown in several examples that the "bunching" and "anti-bunching" of the counts in serieses of elementary single-photon experiments is governed by the statistical properties of grouping the sequences of the elementary measurements. PACS IntroductionSince Einstein (1905) introduced the concept of "light quanta" (nowadays they are called "photons") there has been a wide-spreading investigation carried out to check whether one photon can interfere with itself, or, perhaps, it can be split. He wrote in the introduction of his path-breaking paper that "According to the assumption to be kept in eye here, by spreading from a point in the outgoing light rays the energy is not distributed continuously to larger and larger spatial regions, but these rays consist of a finite number of energy quanta localized in spatial points which move without falling apart, and they can be absorbed or created only as a whole." This extreme particle picture for the photon (as a point-like singularity), deduced from the thermodynamical study of black-body radiation in the Wien limit, was refined in a later paper by Einstein (1909a) where he derived from the exact Planck law his famous fluctuation formula, which contains both particle-like and wave-like fluctuations. This was the first mathematically correct formula on the wave-particle duality. Einstein (1909b) Varró (2006). The quantization of the radiation field in modern sense was

The role of self‐coherence in correlations of bosons and fermions in linear counting experiments. Notes on the wave‐particle duality

“…The single-quantum experiments have been defined in [36] so that during one elementary measurement act the energy ε of the incoming quantum, available for the absorbers in the measuring apparatus, is enough to excite at most one of the absorbers belonging to the two detectors. In addition we have taciltly assumed linearity, i.e.…”

“…According to our recent study [36], we consider an elementary measurement act (in other words, an elementary experiment) as a ternary process (rather than a binary process) in which either detector A, or detector B is excited, or neither of them. These mutually exclusive but not independent events, A , B and C form a complete set, each with positive probabilities, p , q and r , respectively.…”

“…In our recent study [36] we have worked out a formalism for treating HBT type correlations in single-photon experiments, more precisely, in the extreme case when one degree of freedom is available for the photon (the case of quasi-monochromaticity in one spatial mode with a given polatization) during the detection time. There the emphasize has been put on the proof of the mathematical identity of our final formulae, obtained in the frame of classical probability theory, with the textbook results derived on the basis of second quantization and Glauber's standard quantum coherence functions [37][38].…”

“…In the present paper we give a generalization of our method to treat cases when several spatio-temporal modes can be excited by the quantum. In order to make the paper possibly self-contained, in Section 2, after an introductory discussion of the physical meaning of our basic assumptions, we briefly summarize the relevant formal results presented already in [36], and derive the basic formulas which will be applied in Sections 3 and 4 in the analysis of some illustrative examples.…”

Interference Phenomena and Whispering-Gallery Modes of Synchrotron Radiation in a Cylindrical Wave-Guide

“…In fact, there have already been theoretical results published, according to which the interactions of free electrons with quantized radiation fields lead to non-classical states [18][19][20][21], like squeezed coherent states or number-phase minimum-uncertainty states. Both in theory and in practice, for the characterization of the statistical properties of such radiations, the higher-order correlation functions have to be studied, as is done in Hanbury Brown and Twiss type experiments [22][23]. Recent measurements [24][25] on undulator radiation in the x-ray regime have shown that the spontaneous signal produces positive second order (intensity-intensity) correlation, similar to that of thermal radiation.…”