Photons in fock space and beyond
In World Scientific's latest book on "Photons in Fock Space and Beyond", authors Alfred Rieckers and Reinhard Honegger discuss the fact that many actual applications of light perform with mesoscopic material systems, in which the quantum features are combined with classical collective aspects.
The book notes that the emitted radiation consists not only of individual photons but also of classical waves. Usually, the classical part of the radiation is inserted into quantized theoretical models by hand or achieved by the limit h -> 0 of the Planck constant. The experiments display, however, the simultaneous occurrence of both of the radiation parts. Especially in quantum optical communication, the classical signals are accompanied by quantum noise. More subtle intertwinements of quantum mechanical and classical effects show up in optoelectronics and optomechanics in the nano-regime.
In order to include the collective degrees of freedom into the theoretical description, Fock representations alone are no longer sufficient. The present 3-volumes treatise undertakes a reformulation of mesoscopic radiation systems by the use of actual mathematical methods, which generalize widely the quantum optical setup. It begins with a rigorous elaboration of classical electrodynamics (ED), where the fields are enclosed into rather general, possibly not simply connected, cavities. Non-trivial gauge effects arise then already before quantization.
By shaping ED into the form of a commutative Weyl theory, covering also the statistical states of the fields, it is later recognizable as a part of non-relativistic quantum electrodynamics (QED). By going over to a non-commutative Weyl algebra, the photon field observables are introduced in an unambiguous manner, if the representation Hilbert space is selected.
Basic quantum optical notions, like the one-photon wave functions, particle number and phase, as well as coherence and classicality are then clarified by structural reasoning.
The interaction of the photons with matter is newly introduced from scratch. For mesoscopic systems a damping factor is inserted in order to prevent high intensities of the emitted radiation. As a main formal achievement, it is demonstrated by convergent perturbation theory that the setup leads to a well-defined Heisenberg dynamics of the coupled systems, if the photon fields are smeared by appropriate test functions, smoothing out the infrared and ultraviolet singularities. The global dynamics acts not only on the microscopic quantized observables, but moves also the material and photonic collective observables providing a microscopic derivation of Maxwell's theory.
The deduced Maxwell equations contain a magnetic current part, if the rotating wave approximation is applied to the interaction operator. The emitted radiation is realized by the asymptotic many-photon states in the sense of a quantum field theoretic scattering theory. The general approach is especially applied to radiating fluid systems, built on finite-level atoms, and to two-band electronic systems, like semiconductor diodes and Josephson oscillators.
A detailed analysis discloses how the intensity and coherence properties of the radiation depends on the microscopic parameters. The advanced mathematical concepts are called on all over the main text in volumes I and II, the decisive arguments being explained at length where redundancy is not avoided. By offering a systematic exposition of the mathematical background in volume III, conceived in an original manner to the needs of the physical deductions, it is attempted to make the 3-volume treatise as self-contained as possible. By the detailed verbal explanations and repetitions it should be possible to study not only volume I and III for themselves, but also to grasp the main results of volume II—concerning the quantized mesoscopic radiation models—without looking into the other two volumes.
The employed mathematical techniques are advanced, but it is a distinguished feature of the present treatise that they are intimately connected with the physical purposes of the quantum theory of light. They may be considered as paradigmatic for treating also other infinite dimensional physical systems, classical or quantized. Many of the recruited mathematical tools are of use for the quantum field theoretic formulation of elementary particle physics.
The present foundation of radiation theory may be useful for graduate students and researchers interested in one (or more) of the disciplines electrodynamics, quantum optics, quantum field theory, algebraic quantum theory, gauge theory, and general mathematical physics. For mathematicians, the mathematically structured presentation may facilitate the access to the physical applications.
Provided by World Scientific Publishing