Space-time propagation of photon pulses in dielectric media,illustrations with beam splitters

TL;DR

This paper introduces a pulse-based formalism for describing photon propagation in dielectric media, simplifying quantum optical calculations and providing new insights into phenomena like beam splitters and the Hong-Ou-Mandel effect.

Contribution

It develops a localized pulse formulation in bosonic Fock space, offering conceptual and practical advantages over traditional eigenmode expansions in quantum optics.

Findings

No need for vacuum fluctuations in beam splitter analysis

Explicit time-dependent description of Hong-Ou-Mandel effect

Quantum phenomena can be derived from classical Maxwell's equations

Abstract

Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic configurations can be constructed by linear combinations. In this presentation we discuss a formulation constructed in the general formalism of bosonic Fock space, in which the quantum excitation can be constructed directly on localized pulses of arbitrary shape. Although the two formulations are essentially equivalent, the direct formulation in terms of pulses has some conceptual and practical advantages, which we illustrate with some examples. The first one is the passage of a single photon pulse through a beam splitter. The analysis of this formulation in terms of pulses in Fock space shows that there is no need to introduce "vacuum fluctuations entering through the unused port", as is often done in the literature. Another example is the Hong-Ou-Mandel effect. It is described as a time dependent process in the Schr\"odinger representation in Fock space. The analysis shows explicitly how the two essential ingredients of the Hong-Ou-Mandel effect are the same shape of the pulses and the bosonic nature of photons. This formulation shows that all the phenomena involving linear quantum optical devices can be described and calculated on the basis of the time dependent solution of the corresponding classical Maxwell's equations for pulses, from which the quantum dynamics in Fock space can be immediately constructed.