Quantization of EM Fields

Art Hobson

Vladimir M. Shalaev

Z. Ficek, Mohamed Ridza Wahiddin

We will begin our journey through the background of quantum optics with an elementary, but quantitative, classical theory of radiative fields.Wewill first briefly outline the electromagnetic (EM) theory of radiation, and describe how the EM radiation may be understood as a wavewhich can be represented by a set of harmonic oscillators. We shall describe how the free or non-interacting EM field may be understood as a collection of harmonic oscillators which is quantized in the standard manner, and whose energy cannot be zero as a consequence of the basic non-commutability of the canonical field variables. This chapter discusses the properties of plane EM waves and normalization of the EM field in one dimension. This is followed by a description of the Hamiltonian and the amplitudes of the EM field in terms of the annihilation and creation operators. Based on this chapter, it is possible to considerably simplify the formulation of the physical basis for the mathematical description of the major problems of quantum optics.

Прохоров Лев Васильевич

Valerică Raicu

ABSTRACT A theoretical framework is introduced for deriving expressions for electromagnetic (EM) potentials and fields of single atomic or molecular emitters modeled as oscillating dipoles, which follows a recently developed method to solve inhomogeneous wave equations for time‐dependent distributions of charge. This framework is first used to evaluate the physical implications of the simplifying assumptions made in the standard approach to the quantization of EM fields and the impact of such assumptions on the predicted energy and momentum quantization. Then, the exact relationships between the potentials and the oscillating (transition) dipole properties derived under the present framework are used to quantize EM fields radiated by single emitters and to achieve agreement with the classical dipole radiation pattern, while maintaining the quantum mechanical description of electromagnetic radiation in terms of the probability distribution of quantum modes. Contributions of the present analysis to the understanding of photon emission from excited atoms or molecules stimulated by light or vacuum field fluctuations are highlighted, and possible experimental tests and practical applications are proposed.

Pierre Meystre