5.1 Foundations Up until now, we have only considered light propagating essentially in vacuum; this has been used as the basis to describe the effects of reflection, refraction, and transmission in a medium. These essentially passive phenomena, alone, serve as a reminder that nothing is achieved with light, or learned about it, without material interaction. However, a more extensive realm of science centers upon light actively coupling with matter - and many of the systems, in which the photonic aspects of light are most clearly manifest, concern matter in the form of atoms, molecules, or nanoparticles. A quantum analysis of light–matter interactions typically begins with the system Hamiltonian H, the energy operator of the system. In basic quantum mechanics, the "system" simply comprises matter, and the state wavefunctions are secured as eigenstates of the corresponding Hamiltonian Hmat. A quantum formulation of the radiation requires the additional inclusion of a radiation Hamiltonian Hrad. Here, it becomes appropriate to use the representation of quantum electrodynamics (QED): however, because the charges that comprise matter move at significantly sub-luminal speeds in almost all optics and photonics applications, the full relativistic form of QED is unnecessary. To complete the full Hamiltonian for systems in which light and matter are not isolated from each other, an interaction Hamiltonian Hint is also required. The system Hamiltonian can thus be decomposed into three parts: [41]
5.1 Foundations Up until now, we have only considered light propagating essentially in vacuum; this has been used as the basis to describe the effects of reflection, refraction, and transmission in a medium. These essentially passive phenomena, alone, serve as a reminder that nothing is achieved with light, or learned about it, without material interaction. However, a more extensive realm of science centers upon light actively coupling with matter - and many of the systems, in which the photonic aspects of light are most clearly manifest, concern matter in the form of atoms, molecules, or nanoparticles. A quantum analysis of light–matter interactions typically begins with the system Hamiltonian H, the energy operator of the system. In basic quantum mechanics, the "system" simply comprises matter, and the state wavefunctions are secured as eigenstates of the corresponding Hamiltonian Hmat. A quantum formulation of the radiation requires the additional inclusion of a radiation Hamiltonian Hrad. Here, it becomes appropriate to use the representation of quantum electrodynamics (QED): however, because the charges that comprise matter move at significantly sub-luminal speeds in almost all optics and photonics applications, the full relativistic form of QED is unnecessary. To complete the full Hamiltonian for systems in which light and matter are not isolated from each other, an interaction Hamiltonian Hint is also required. The system Hamiltonian can thus be decomposed into three parts: [41]
Although the primarily phenomenological theory of absorption and refraction of light by matter, based on classical models as presented in Chapter 4, is very useful, it is incomplete and often inadequate. A more complete and accurate picture of electrodynamics is given by the theory of quantum optics, and that is the topic of this chapter. The models developed in this chapter are more detailed and therefore more complicated than the phenomenological models of Chapter 4. The most robust models, which are applied in Part II, are presented in this chapter. The quantum models accurately represent experimental data and allow extrapolation and interpolation of such data. Many practical computer based models concerning optical propagation are based on this theory. The theory of elastic scatter as presented in Chapter 4 is consistent with quantum optics and is not presented again. (However, inelastic scatter must address the quantum nature of the scattering medium.) Quantum optics is not completely covered in this chapter. Entire textbooks are devoted to this diverse and comprehensive topic covering optics (see Refs. 5.1–5.3). The emphasis of this book is on absorption and reflection spectroscopy. Now details of internal structure of the medium impacting light–matter interaction are examined. The classical oscillator model is upgraded by semiclassical radiation theory and a quantum oscillator model is developed. Semiclassical radiation theory is based on a quantized medium coupled to a classical field. It is often applied to laser theory, where near-line-center stimulated emission dominates. The quantum oscillator model again utilizes the quantized medium and classical field, but with more attention to detailed balance between absorption and emission. It satisfies causality and the fundamental symmetry relationships established in Chapter 2. These quantum optics models are more complete formalisms and provide solutions to the shortcomings of classical electrodynamics. Of particular interest to propagation in gaseous media is the line shape in the far wing. To achieve long path lengths, propagation near line center of a resonance must be avoided. Line shape models in quantum optics accurately represent much of the frequency and temperature dependence observed in experimental data.
At the beginning of the century doubts were growing about the whole edifice of classical physics, including the laws of mechanics in their Lagrangian and Hamiltonian forms, of statistical thermodynamics, as formulated by Boltzmann and Gibbs, and of optics, namely Maxwell’s and Fresnel’s theory. Einstein proposed that electromagnetic radiation exists in discrete quanta whilst propagating in space as well as during the emission or absorption processes. Scattering by free electrons is a common interaction connected with the absorption of electromagnetic radiation. If the electromagnetic energy is large compared with the ionization energy, the atomic electron can be treated as free. The characteristic features of the scattered radiation have been explained by Compton, on the basis of an elastic collision of a photon with a free electron, where both energy and momentum are conserved. The concept of the matter wavelength holds for both relativistic and non-relativistic particles, provided that the appropriate form of momentum is used.
In modern physics, the investigation of the interaction between light and matter is important from both a fundamental and an applied point of view. Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles where the quantum nature of light photons is significant. The strong interaction between an exciton and cavity photon in a high-finesse microcavity can induce a hybrid light-matter eigenstate which is usually named as polariton in solid-state systems. This strong light-matter interaction can be achieved when this interaction is larger than all broadenings caused by other various factors e.g. electron phonon scattering and cavity loss. The polariton is now stimulating tremendous research interests due to its high potential in cavity quantum electrodynamics (QED) and the achievement of polaritonic devices. Moreover, when the interaction strength between an excitation and the cavity photon, quantified by vacuum Rabi frequency, becomes comparable to or larger than the corresponding electronic transition frequency in a cavity, the system can enter an ultrastrong coupling regime, which has been experimentally observed. In this regime, the standard rotating-wave approximation is no longer valid and the antiresonant term of the interaction Hamiltonian starts to play an important role, giving rise to exciting effects in cavity QED. The Aharonov-Bohm (AB) effect is a fundamental quantum phenomenon that bears the significance of the nature of electromagnetic fields and potentials. Besides its fundamental significance in quantum theory, its importance for applications in interferometric devices is omnipresent. Recently, since the 2D materials have triggered immense interest, some work has been done to integrate the AB effect with the electronic and transport properties of 2D materials. This thesis consists of two parts. In the first part, the light-matter coupling between cyclotron transition and photon is theoretically investigated in some 2-D materials such as the monolayer MoS2, graphene and monolayer black phosphorene (BP) systems. The results show that, in these 2-D materials, the ultrastrong light-matter coupling can be achieved at a high filling factor of Landau levels. Furthermore, we show that, in contrast to the case for conventional semiconductor resonators, the MoS2 system shows a vacuum instability. In monolayer MoS2 resonator, the diamagnetic term can still play an important role in determining magnetopolariton dispersion which is different from monolayer graphene system. The diamagnetic term arises from electron-hole asymmetry which indicates that electron-hole asymmetry can influence the quantum phase transition. Meanwhile, we show that, similar with some other 2D materials such as graphene and MoS2, the monolayer BP system shows a vacuum instability. However, in contrast with other 2D materials, the BP system displays a large energy gap between three branches of polaritons because of its strong anisotropic behavior in the eigenstates of the band structures. For the graphene system, we investigate the coupling of cyclotron transition and a multimode cavity described by a multimode Dicke model. This model exhibits a superradiant quantum phase transition, which we describe exactly in an effective Hamiltonian approach. The complete excitation spectrum in both the normal phase and superradiant phase regimes is given. At last, in contrast to the single mode case, multimode coupling of cavity photon and cyclotron transition can greatly reduce the critical vacuum Rabi frequency required for quantum phase transition, and dramatically enhance the superradiant emission by fast modulating the Hamiltonian. Our study provides new insights in cavity-controlled magneto-transport in these 2-D systems, which could lead to the development of polariton-based devices. The second part is a diversion from the main content of this thesis; readers who are not interested in foundational issues of physics can skip this part. For one charged quantum particle P moving in an electromagnetic vector potential Aˆµ = ( φˆ, - Aˆ ) created by some other charged particles, we can either use the framework of one particle quantum mechanics (OPQM) to calculate the evolutions of P, or we can treat this as an multi-particles problem in the framework of quantum field theory and calculate the evolution of P. These two methods need to be equivalent, i.e., they produce the same result for the evolution of P. One open question is how to describe the evolution of P within the framework of quantum field theory and show that these two methods yield the same result? In chapter 5, we are going to derive the OPQM from the quantum field theory, i.e., the quantum electrodynamics (QED) to be specific. We start with the discussions on the AB effect then raise a plausible interpretation within the QED framework. We provide a quantum treatment of the source of the electromagnetic potential and argue that the underlying mechanism in AB effect can be viewed as interactions between electrons described by QED theory where the interactions are mediated by virtual photons. On further analysis, we show that the framework of one particle quantum mechanics (OPQM) can be given, in general, as a mathematically approximated model which is reformulated from QED theory while the AB effect scheme provides a platform for our derivations. In addition, the classical Maxwell equations are derived from QED scattering process while both classical electromagnetic fields and potentials serve as mathematical tools that are constructed to approximate the interactions among elementary particles described by QED physics. This work opens up a new perspective on the nature of electromagnetic fields and potentials.
"The interaction of light and matter has long history. It evolved from the ancient corpuscular theory, to wave theory, and finally to the quantum theory. Matter is composed of charged particles, among them positively charged nucleus surrounded by electrons that are in motion. Light is an oscillating electromagnetic wave. But light is also particles (photons). The primary objective of this Field Guide to Light-Matter Interaction is to provide the reader with the basic principles of light and matter interaction using classical, semiclassical, and quantum theories. Within this Field Guide, you will find formulae and descriptions of phenomena that are fundamental for an understanding of the present state of the art of light-matter interaction"--
Many dynamical processes of interest are either initiated or probed by light, and their understanding requires some knowledge of this subject. This chapter is included in order to make this text self contained by providing an overview of subjects that are used in various applications later in the text. In particular, it aims to supplement the elementary view of radiation–matter interaction as a time-dependent perturbation in the Hamiltonian, by describing some aspects of the quantum nature of the radiation field. This is done on two levels: The main body of this chapter is an essentially qualitative overview that ends with a treatment of spontaneous emission as an example. The Appendix gives some more details on the mathematical structure of the theory. In elementary treatments of the interaction of atoms and molecules with light, the radiation field is taken as a classical phenomenon.