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Coherence in Matter and Radiation \\ Matter and Field Interactions

Trever Harborth

Published May 1, 2025• 0 citations
Publisher

Abstract

Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown, however, that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analysis to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level two-photon system but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.

DOI
10.12794/metadc2443190

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Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown, however, that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analysis to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level two-photon system but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes, and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level, two-photon system, but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information.
The refractive index of a system is often viewed as the collective response of a medium to an electromagnetic field. Nevertheless, even if targeted at a single atom, the incoming light undergoes the dispersion. By studying the propagation of a single photon interacting with a two-level atom, we examine the dispersion behavior, calculate the phase and group velocity of the photon wave packet, and further analyze the dispersion experienced by the photon. These findings are critical for advancing long-distance quantum communications.
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The propagation of quantum field interacting with a single two-level atom has been studied. Using the Gaussian quantum mode functions, we calculate evolution of the quantum state that includes atomic and field variable. We demonstrated the phase and group velocities of the single photon propagation that can be of great importance for long quantum communications. The results can be used for controlling quantum field propagation, and for design of optical elements such as a quantum prism and a quantum lens.
In this thesis we present a theoretical analysis of some of the implications of the quantum nature of the electromagnetic field.In particular, we are interested in how atomic dynamics are modified by coupling to a quantized radiation field.In chapter two we review the Jaynes-Cummings model of atom-field interactions.This model consists of a single two-level atom coupled to a single mode of the radiation field.The evolution of the atom depends upon the initial quantum state of the field mode.Chapter three is a review of the quantum theory of dissipation.In chapter four we examine the properties of the thermofield states of the two-mode, quantized radiation fields.We investigate the use of these states as a representation of single mode thermal states.The thermo field representation is used to describe interactions involving thermal averages and in an analysis of two-mode squeezing in parametric amplifiers.Chapters five to seven are concerned with the Rydberg atom maser.In chapter five we review some of the properties of Rydberg atoms in cavities and consider the validity of the Jaynes-Cummings model as a description of the maser.In chapter six we discuss the modification of the atomic dynamics when more than one atom is present in the cavity.We show how the collective atomic inversion is influenced by many-atom effects, as well as the photon statistical effects present in the single atom Jaynes-CHAPTER
In the preceding chapters concerning the interaction of a radiation field with matter, we assumed the field to be classical. In many situations this assumption is valid. There are, however, many instances where a classical field fails to explain experimentally observed results and a quantized description of the field is required. This is, for example, true of spontaneous emission in an atomic system which was described phenomenologically in Chapter 5. For a rigorous treatment of the atomic level decay in free space, we need to consider the interaction of the atom with the vacuum modes of the universe. Even in the simplest system involving the interaction of a single-mode radiation field with a single two-level atom, the predictions for the dynamics of the atom are quite different in the semiclassical theory and the fully quantum theory. In the absence of the decay process, the semiclassical theory predicts Rabi oscillations for the atomic inversion whereas the quantum theory predicts certain collapse and revival phenomena due to the quantum aspects of the field. These interesting quantum field theoretical predictions have been experimentally verified. In this chapter we discuss the interaction of the quantized radiation field with the two-level atomic system described by a Hamiltonian in the dipole and the rotating-wave approximations. For a single-mode field it reduces to a particularly simple form. This is a very interesting Hamiltonian in quantum optics for several reasons. First, it can be solved exactly for arbitrary coupling constants and exhibits some true quantum dynamical effects such as collapse followed by periodic revivals of the atomic inversion.