Much confusion has resulted from the failure to recognise the different concepts embodied in the single word "phase" as applied to a quantized electromagnetic field mode. In this paper we describe three conceptions of phase and the connections between them.
One of the most delicate problems in quantum optics is the proper description of the phase of a single-mode radiation field. One has first to devise an experimental scheme for phase measurement, thus giving an operational definition of phase, and afterwards search for the proper quantum-mechanical description of the experimental procedure. Several such schemes which differ distinctly in their experimental setup have already been proposed and even partly realized. In this paper, I will describe them in some detail and present the outlines of their theoretical analysis.>
Bohmian mechanics is a deterministic theory of point particles in motion. While avoiding all the paradoxes of nonrelativistic quantum mechanics, it yields the quantum formalism itself---especially the role of self-adjoint operators---as a macroscopic measurement formalism. As an "application" it is shown that much of the confusion connected with the phase operator for the electromagnetic field arises from a misunderstanding of the role of operators in quantum theory. 1 Introduction We would like to apologize for the bad title: we will try to explain why the casual use of the words "observables" and "measurements," which are on John Bell's list of bad words in his article "Against Measurement"[1], "measurement" being the worst of all, leads to much unnecessary confusion concerning the meaning of the quantum formalism. But first we introduce an even worse word: following Bell we will use the abbreviation "FAPP" for "for all practical purposes." Quantum mechanics suffers from its irreduc...
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.