Based on the theoretical derivation and experimental data, the declaration that the quantum theory of light can contain the classical electromagnetic theory of light is oppugned, and two dead-points are put forward. One is the nonconservation of the energy of the electromagnetic field before and after quantization due to a number of zero point energy, and the other is that the real electromagnetic wave, as a matter, will lose its real material nature in theory, or only as a substitute of photons. Finally, a crucial experiment is designed to demonstrate and compare the accuracy of quantum theory and classical electromagnetic theory in the classical condition.
Based on the theoretical derivation and experimental data, the declaration that the quantum theory of light can contain the classical electromagnetic theory of light is oppugned, and two dead-points are put forward. One is the nonconservation of the energy of the electromagnetic field before and after quantization due to a number of zero point energy, and the other is that the real electromagnetic wave, as a matter, will lose its real material nature in theory, or only as a substitute of photons. Finally, a crucial experiment is designed to demonstrate and compare the accuracy of quantum theory and classical electromagnetic theory in the classical condition.
The study of light through the centuries has produced a number of theories and experiments. Newton advanced the corpuscular theory, building on the early Greek view of matter composed of atoms. Then Young essentially proved the wave nature of light through the interference experiments. Maxwell provided the firm theoretical basis for the wave nature. During the late 1800s and early 1900s, further experiments showed predictions based on a continuous wave led to the well-known ultraviolet catastrophe. Plank and Einstein originated and developed the notion of the photon as an elementary quantum of propagating electromagnetic (EM) energy. The first half of the 20th century saw the development of the field quantization and the quantum electrodynamics (QED). Feynmann labeled QED as ‘‘the best theory we have’’ to describe the matter-light interaction. The second half of the 20th century witnessed the development of the coherent and squeezed optical states attributable to Glauber and Yuen. The study of light and electromagnetic fields has a long history. This chapter explores the nature of light in terms of quantum optics.
Classically, light is an electromagnetic phenomenon, described by Maxwell's equations. However, under certain conditions, such as low intensity or in the presence of certain nonlinear optical materials, light starts to behave differently, and we have to construct a ‘quantum theory of light’. We can exploit this quantum behaviour of light for quantum information processing, which is the subject of this book. In this chapter, we develop the quantum theory of the free electromagnetic quantum field. This means that we do not yet consider the interaction between light and matter; we postpone that to Chapter 7. We start from first principles, using the canonical quantization procedure in the Coulomb gauge: we derive the field equations of motion from the classical Lagrangian density for the vector potential, and promote the field and its canonical momentum to operators and impose the canonical commutation relations. This will lead to the well-known creation and annihilation operators, and ultimately to the concept of the photon. After quantization of the free electromagnetic field we consider transformations of the mode functions of the field. We will demonstrate the intimate relation between these linear mode transformations and the effect of beam splitters, phase shifters, and polarization rotations, and show how they naturally give rise to the concept of squeezing. Finally, we introduce coherent and squeezed states.
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.
Based on the quantum field theory and classical electromagnetic field theory, the behaviors of the electromagnetic field in the boundary of the classical environment and the quantum environment were studied, and three dead-points and five paradoxes, like Lorentz-Compton paradox, non-conservation of the energy of the electromagnetic field before and after quantization due to a number of zero-point energy, the non-self-consistence of the wave-particle duality, etc, were discovered. Through analyzing these dead-points and paradoxes, we found that these paradoxes are related to each other, and all wrapped together. The core problem is the non-self-consistence in the theoretical system and the ambiguity in the mechanism of the wave-particle duality. Based on resolving the classical electromagnetic field into the electromagnetic element-waves according to the photons, a third kind of wave-particle duality, the particle-like characteristics of the classical electromagnetic field in structure, was put forward, and the structure of &pgr;-shape of three kinds of wave-particle duality was revealed. So, in wave-particle duality, the wave and the particle are staggered in existing time, or in existing form, either in imagination or in reality, and the third kind of wave-particle duality will be combined into a unit with the first kind of wave-particle duality, Einstein's wave-particle duality of light, and the second kind of wave-particle duality, de Broglie's wave-particle duality of matter particle. Hence, a self-consistent picture of wave-particle duality of light was set up, and three dead-points and five paradoxes of the electromagnetic field in the boundary of the classical environment and the quantum environment were dispelled. In the last, a crucial experiment was designed for testing this picture.
Based on the quantum field theory and classical electromagnetic field theory, the behaviors of the electromagnetic field in the boundary of the classical environment and the quantum environment were studied, and three dead-points and five paradoxes, like Lorentz-Compton paradox, non-conservation of the energy of the electromagnetic field before and after quantization due to a number of zero-point energy, the non-self-consistence of the wave-particle duality, etc, were discovered. Through analyzing these dead-points and paradoxes, we found that these paradoxes are related to each other, and all wrapped together. The core problem is the non-self-consistence in the theoretical system and the ambiguity in the mechanism of the wave-particle duality. Based on resolving the classical electromagnetic field into the electromagnetic element-waves according to the photons, a third kind of wave-particle duality, the particle-like characteristics of the classical electromagnetic field in structure, was put forward, and the structure of n-shape of three kinds of wave-particle duality was revealed. So, in wave-particle duality, the wave and the particle are staggered in existing time, or in existing form, either in imagination or in reality, and the third kind of wave-particle duality will be combined into a unit with the first kind of wave-particle duality, Einstein's wave-particle duality of light, and the second kind of wave-particle duality, de Broglie's wave-particle duality of matter particle. Hence, a self-consistent picture of wave-particle duality of light was set up, and three dead-points and five paradoxes of the electromagnetic field in the boundary of the classical environment and the quantum environment were dispelled. In the last, a crucial experiment was designed for testing this picture.
We show in this paper that the quantized energies of light in vacuum can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics, which are just a series of expectation values corresponding to relatively stable statistic distributions of electromagnetic harmonic oscillators. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles. The theory developed in this paper is also used to derive the energy equipartition theorem and the discrete levels of hydrogen atom from classical mechanics.