In classical optics light is considered as an electromagnetic wave, and its dynamical properties are described by the time dependence of amplitude and phase. If a light emerging from a source has random fluctuation of amplitude and phase, this light can be described by a proper ensemble from which the mean and the dispersion of the dynamical variables are calculated. On the other hand, the same light beam can be also considered as a stream of photons in quantum optics, and the wave-particle duality produces nonclassical results in some cases. It is our purpose to clarify the role of wave and particle nature of light and distinguish the classical and quantum effects via the characterization of the dynamical variables when the light goes through a beamsplitter.
In classical optics light is considered as an electromagnetic wave, and its dynamical properties are described by the time dependence of amplitude and phase. If a light emerging from a source has random fluctuation of amplitude and phase, this light can be described by a proper ensemble from which the mean and the dispersion of the dynamical variables are calculated. On the other hand, the same light beam can be also considered as a stream of photons in quantum optics, and the wave-particle duality produces nonclassical results in some cases. It is our purpose to clarify the role of wave and particle nature of light and distinguish the classical and quantum effects via the characterization of the dynamical variables when the light goes through a beamsplitter.
The amplitude and phase of all light fields are subject to fluctuations. Much of this irregularity arises from random and uncontrolled changes that occur in any light source and lead to random changes in the light wave's frequency and amplitude. Most of these factors can in principle be eliminated by a careful design of the light source. Even if all of these defects in the source are removed, however, light fields are still subject to fluctuations arising from the laws of quantum mechanics. Even in a highly stabilized laser, the resulting coherent electromagnetic field has an uncertainty in the phase and magnitude of its amplitude. All conventional sources of light fields have at least this noise level, which, in a fully quantum description, arises from vacuum fluctuations. At one time it was believed that this vacuum or coherent-state noise could not be eliminated.
Abstract The single-mode theory of Chapter 5 is inherently limited to the description of experiments that use time-independent light beams. The light is essentially nonergodic, in that its statistical fluctuations may be described by an ensemble, but these are not apparent in a time series of experiments made on the single member of the ensemble corresponding to a practical realization of the state. Identical measurements always give the same results and there are no time-dependent correlations of the kind considered in the classical theory of Chapter 3. Many of the nonclassical properties of light can be understood in terms of single-mode theory but other properties involve excitations of two or more modes. Practical observations of nonclassical effects are usually made on time-dependent light beams.
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.
The following Master’s thesis is concerned with several aspects of the wave-particle duality of light. It is loosely divided in three parts. In the first part we consider historical, theoretical and experimental aspects of the duality problem. We explain how the notion of duality has developed through the last 400 years. We discuss theoretical underpinnings of the duality emodied by Maxwell’s electromagnetic theory, quantization of electromagnetic modes, Fock’s states and coherent states. We critically review several experiments which serve to demonstrate the corpuscular or undulatory behaviour of light and matter; in particular we present how the photoelectric effect and the Compton effect can be explained using the undulatory model, and we critically review Grangier, Roger and Aspect correlation experiment.\n\nIn the second part we describe two illustrative experiments on the duality of light conducted at Quantum Optics Laboratory at University of Oslo. The results of the experiment allow us to discuss how coincidence measurements can be used to exhibit the corpuscular behaviour of light, and how Mach-Zender interferometry performed at very low intensity can be used to exhibit the undulatory behaviour at\nthe (assumed) single-photon level. In addition, in the second part we review elements of theories closely associated with the experiment and the experimental setup: optical coherence, photocount and photon\nstatistics, beam splitter models and Gaussian beams. A proposition for extending the semiclassical model is given, and shortcomings of the present beam splitter models are discussed.\n\nIn the third part of the thesis we consider first Afshar’s experiment and some of the critical response that it has been met with. Then we discuss how the wave-particle duality is to be understood in the\nstandard interpretation of quantum mechanics, and how it could possibly be explained using either an alternative model for light or an alternative interpretation of quantum mechanics, and what difficulties such explanations present.
In Section 11.5 we showed that, although the complex amplitude of the electromagnetic field has a well-defined value in any coherent state, yet the real and imaginary (Hermitian and anti-Hermitian) parts of the field fluctuate with equal dispersions. The phenomenon of vacuum fluctuations is a manifestation of this effect, because the vacuum state is an example of a particular coherent state. This behavior is quite different from that of an ordinary, classical field. In a squeezed state, which is even more non-classical, as we shall see, one part of the field fluctuates less and another part fluctuates more than in the vacuum state. In general, a squeezed state is one in which the distribution of canonical variables over the phase space has been distorted or ‘squeezed’ in such a way that the dispersion of one variable is reduced at the cost of an increase in the dispersion of the other variable. In the following we shall examine the properties of squeezed states when the two canonical variables are two quadratures of the electromagnetic field. Although the squeezing terminology is sometimes applied to variables other than the two field quadratures, it is less meaningful in those cases. A number of review articles on squeezing have been published and can be consulted for more details (Walls, 1983; Schumaker, 1986; Loudon and Knight, 1987; Teich and Saleh, 1989, 1990; Kimble, 1992).
Quantum mechanical uncertainty After reviewing the main characteristics of the classical description of light, let us discuss those aspects of the quantization of the electromagnetic field which are of relevance for the analysis of the phenomena we are interested in. It seems a reasonable place to start to make clear the fundamental difference between the classical and the quantum mechanical description of nature; we will come across this difference many times when discussing experiments, and it will often give us a headache. We have to deal with the physical meaning of what is called uncertainty. The starting point of the classical description is the conviction that natural processes have a “factual” character. This means that physical variables such as the position or momentum of a particle have, in each single case, a well defined (in general, time dependent) value. However, it will not always be possible to measure all the appropriate variables (for instance, the instantaneous electric field strength of a radiation field); furthermore under normal circumstances we are able to measure only with a finite precision. Hence the basic credo of classical physics should be given in the following form: we are justified in imagining a world with variables possessing well defined values which are not known precisely (or not known at all). In doing this we are not forming any conclusions that contradict our everyday experiences. This is the fundamental concept of classical statistics: we are satisfied with the use of probability distributions for the variables we are interested in, not from fundamental but purely practical reasons.