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Introduction to Quantum Optics

Partha Pratim Mondal

Published May 25, 2022• 3 citations
Publisher

Abstract

Light has long been perceived as a wave, or more specifically as an EM wave, and this is valid with respect to everyday observations. However, experiments involving light have produced surprising results that fall outside the realm of the wave nature of light. These experiments for the first time necessitated that light not be perceived as a wave but more like a particle. Some of these observations include photoelectric, Compton, and two-photon effects. In these experiments, light behaves more as an object filling a space just like a particle rather than a continuous entity like a wave. This is surprising given what we have learned in classical optics. In this chapter, we intend to analyze and understand the particle nature of light and its consequences.

DOI
10.1063/9780735424517_005

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Light has long been perceived as a wave, or more specifically as an EM wave, and this is valid with respect to everyday observations. However, experiments involving light have produced surprising results that fall outside the realm of the wave nature of light. These experiments for the first time necessitated that light not be perceived as a wave but more like a particle. Some of these observations include photoelectric, Compton, and two-photon effects. In these experiments, light behaves more as an object filling a space just like a particle rather than a continuous entity like a wave. This is surprising given what we have learned in classical optics. In this chapter, we intend to analyze and understand the particle nature of light and its consequences.
It is evident from the previous chapter that certain quantities that appear continuous at the macroscopic scale does actually exist in a discrete form at the microscopic scale. So, quantization of these entities makes sense and reveals a plethora of information at such length scales. In this book, our key concern lies with the properties of light, and rightfully so, we will explore different states of the optical radiation field. We will learn that light exists in many states that makes it so unique. Experimental evidence shows that light behaves as a particle at the microscopic scale (subject to specific conditions), although it behaves like a wave at the macroscopic scale. In this chapter, we will dwell deep and discuss many characteristics related to the particle nature of light. Specifically, we will consider two important states of light, the Fock and coherent states. These states can be regarded as the most fundamental states of light that enable complex interpretation of quantum features in the radiation field.
Having just described electromagnetic radiation as a wave, it may seem a bit peculiar to embark on a particle description of that radiation. Perhaps it will help to recall from Chapter 2 that our perception of something depends in part on the means we use to perceive it and that we used a specific experiment (interference) to define the wave property. There is no reason to believe that one human-invented experiment is the only one that can be used to describe electromagnetic radiation. In fact, the Einstein photoelectric effect, described next, is consistent with light being a particle.
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
This chapter begins with a survey of early experimental results — the Planck spectrum, the photoelectric effect, and Compton scattering — that are usually presented as evidence for the existence of photons. The photon concept is indeed sufficient to explain these results, but it is not necessary. There are semi-classical models that explain the same data without introducing photons. The crucial experiment, in which light consisting of a single photon reflects from a beam splitter, depends on the essential indivisibility of photons, and it excludes all semi-classical descriptions of light. This discussion is followed by a preview of modern methods of production and detection of individual photons, e.g., spontaneous down conversion and Silicon avalanche-photodiode counters, together with an introduction to the quantum theory of light based on the correspondence principle.
There are two opposing points of view on the nature of light: the first one manifests the wave-particle duality as a fundamental property of the nature; the second one claims that photons do not exist and the light is a continuous classical wave, while the so-called “quantum” properties of this field appear only as a result of its interaction with matter. In this paper we show that many quantum phenomena which are traditionally described by quantum electrodynamics can be described if light is considered within the limits of classical electrodynamics without quantization of radiation. These phenomena include the double-slit experiment, the photoelectric effect, the Compton effect, the Hanbury Brown and Twiss effect, the so-called multiphoton ionisation of atoms, etc. We show that this point of view allows also explaining the “wave-particle duality” of light in Wiener experiments with standing waves. We show that the Born rule for light can easily be derived from Fermi’s golden rule as an approximation for low-intense light or for short exposure time. We show that the Heisenberg uncertainty principle for “photons” has a simple classical sense and cannot be considered as a fundamental limitation of accuracy of simultaneous measurements of position and momentum or time and energy. We conclude that the concept of a “photon” is superfluous in explanation of light-matter interactions.
Quantum field theory describes the particle nature of electromagnetic radiation using the "photon," but has never explained why a fundamental particle exhibits such perfect wave behavior. This paper provides a complete alternative explanation: the photoelectric effect, Compton scattering, and antibunching experiments — landmark experiments considered proof of photon particle nature — require no photon concept. Quantization is not a property of light itself, but of the discrete energy level structure governing how bound electrons emit and absorb energy. Light remains a continuous transverse wave; discreteness results from electrons as "prisoners" in atomic "cages" that can only transition between specific energy steps. Waves propagate continuously and are emitted and absorbed in quantized form — the photon is not a particle, but the name of an energy-exchange event.