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arXiv:quant-ph/0607008

Photon wave functions and quantum interference experiments

G. G. Lapaire, John E. Sipe

Published Jul 2, 2006• 2 citations
arXivHTMLPDF

Abstract

We present a general theory to describe two-photon interference, including a formal description of few photon intereference in terms of single-photon amplitudes. With this formalism, it is possible to describe both frequency entangled and separable two-photon interference in terms of single-photon wave functions. Using this description, we address issues related to the physical interpretation of two-photon interference experiments. We include a discussion on how few-photon interference can be interpreted as a bosonic exchange effect, and how this relates to traditional exchange effects with fermions.

DOI
10.48550/arxiv.quant-ph/0607008

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We present a general theory to describe two-photon interference, including a formal description of few photon intereference in terms of single-photon amplitudes. With this formalism, it is possible to describe both frequency entangled and separable two-photon interference in terms of single-photon wave functions. Using this description, we address issues related to the physical interpretation of two-photon interference experiments. We include a discussion on how few-photon interference can be interpreted as a bosonic exchange effect, and how this relates to traditional exchange effects with fermions.
Abstract The main provisions of the construction of the single-particle wave function of a photon in the coordinate representation are expounded and its application to the description of single-photon interference phenomena is discussed. The connection between the concepts of electromagnetic field strengths used in quantum electrodynamics and the characteristics of wave packets in photon quantum mechanics is substantiated. For illustration, we consider the relationship between the structure of the photon wave function in coordinate representation and the polarization of photon in the formalism of quantum transition amplitudes. The meaning of the concept of linear polarization of a photon in the state of a wave packet is explained. The wave function is constructed in the coordinate representation of the state of two entangled photons at the exit from a nonlinear crystal by modeling the polarization vectors and Gaussian momentum distribution for each of the photons.
The formation of an obvious interference pattern in the distribution of the probability of the simultaneous hit of two alone photons radiated synchronously from two independent single-photon sources, playing the slits role of Young's experiment first screen, at different points of the second screen, is demonstrated by modeling the photon coordinate wave function. This function is single-photon wave packet built within the framework of the developed quantum mechanics of the photon in previous authors works, which expresses a superposition of six-component “plane waves with circular polarization” - the eigenfunctions of the operators of photon momentum, of its energy and helicity. The results received make it eventual to justify the description of one-and two-photon interference in framework of “primary” quantization of the electromagnetic field, without resorting to the probability amplitudes of quantum field theory, which, in turn, makes it possible to develop a metaphysical interpretation of experiments with single photons, such as quantum computing, quantum teleportation, quantum cryptography. It seems that this interpretation can serve as an impetus for the development of new practical devices and the setting up of new experiments to reveal the physical nature of quantum interactions through the exchange of photons and, in particular, the physical essence displayed by the idea of quantum object wave function.
The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.
This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical process of spontaneous parametric down-conversion. These entangled photons are then passed through different optical systems to study various aspects of two-photon interference. Firstly, an experimental analysis is made of the high-dimensional entanglement that is present in the orbital angular momentum of the photons. Secondly, we present a comprehensive description of two-photon quantum interference behind a double slit. We demonstrate how to control the quantum correlations and present the first observations of complete two-photon diffraction patterns behind a double slit. Finally, we present pioneering experiments on spatially entangled two-photon states that are scattered of random media. We have observed and theoretically analyzed the structure in the random two-photon interference patterns called two-photon speckle patterns. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments also demonstrate a two-photon interference phenomenon that survives averaging over different realizations of disorder. The latter results are closely related to bosonic, fermionic, and anyonic particle exchange symmetries.
The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we compare our results with the previous ones of correlated photons. The observed TPI fringe can be expressed in the form of three phase terms related to the individual single-photon and two-photon states, and the fringe pattern is strongly affected by the two single-photon-interference fringes and also by their visibilities. With the exception of essential differences such as valid and accidental coincidence events within a given resolving time and the two-photon spectral bandwidth, the interference phenomenon itself exhibits the same features for both correlated and uncorrelated photons in the single-photon counting regime.
A number of recent interference experiments involving multiple photons are reviewed. These experiments include generalized photon bunching effects, generalized Hong-Ou-Mandel interference effects and multi-photon interferometry for demonstrations of multi-photon de Broglie wavelength. The multi-photon states used in these experiments are from two pairs of photons in parametric down-conversion. We find that the size of the interference effect in these experiments, characterized by the visibility of the interference pattern, is governed by the degree of distinguishability among different pairs of photons. Based on this discovery, we generalize the concept of multi-photon temporal distinguishability and relate it to a number of multi-photon interference effects. Finally, we make an attempt to interpret the coherence theory by multi-photon interference via the concept of temporal distinguishability of photons.