Abstract In reporting and explaining the interactions of light with atoms and molecules, a photon-based description is not only appropriate but clearly essential when electronic or other kinds of quantum transition ensue. However, textbook treatments frequently go no further than the Planck relation, in representing the quantum nature of the light itself—often resorting to classical principles when discussing mechanism. Complete consistency and rigour can be achieved by treating both the matter and the radiation in a fully quantised form, which requires the electromagnetic fields to be cast in a quantum field representation. It proves possible to develop a rigorous approach to this theory that is simple to convey and apply, and which lends itself to a significantly enhanced level of appreciation of mechanism. This paper lays a concise foundation and exemplifies the application in three specific cases: absorption, emission and scattering. It is also shown how this formulation affords a basis for applications in higher-order, multiphoton and nonlinear optical processes.
Abstract In reporting and explaining the interactions of light with atoms and molecules, a photon-based description is not only appropriate but clearly essential when electronic or other kinds of quantum transition ensue. However, textbook treatments frequently go no further than the Planck relation, in representing the quantum nature of the light itself—often resorting to classical principles when discussing mechanism. Complete consistency and rigour can be achieved by treating both the matter and the radiation in a fully quantised form, which requires the electromagnetic fields to be cast in a quantum field representation. It proves possible to develop a rigorous approach to this theory that is simple to convey and apply, and which lends itself to a significantly enhanced level of appreciation of mechanism. This paper lays a concise foundation and exemplifies the application in three specific cases: absorption, emission and scattering. It is also shown how this formulation affords a basis for applications in higher-order, multiphoton and nonlinear optical processes.
In this chapter, we discuss a purely quantum approach to the interaction between an atom and the electromagnetic field. In this treatment, the atom and electromagnetic field form a single quantum system, whose evolution is handled globally within a unified formalism. This will thus have the merit of being fully consistent from the theoretical standpoint. But the main advantage in an entirely quantum approach is that it can treat the full range of matter–radiation interaction phenomena. In particular, it provides a rigorous description of the spontaneous emission of light by an excited atom , something that falls outside the scope of the semi-classical framework applied in Chapters 2 and 3, where the lifetime of an excited atomic state had to be fed in phenomenologically. It can describe other phenomena of the same type, such as parametric fluorescence by a nonlinear crystal subjected to pumping radiation (see Chapter 7), which underlies many recent developments in quantum optics. The fully quantum approach also has the merit of allowing a simple interpretation in terms of photons for the various matter–radiation interaction processes, such as absorption, stimulated emission, scattering, and also the basic processes of nonlinear optics. Indeed, it provides a unified framework for both stimulated and spontaneous processes. Finally, it can be used to tackle completely new situations where matter and radiation interact, which lie outside the scope of any semi-classical description, such as cavity quantum electrodynamics or the production of single-photon or entangled-photons states .
Abstract The quantum electrodynamic theory, based on the quantization of the electromagnetic field, introduces the concept of photon and the related photon creation operator, photon annihilation operator, and photon number operator. It is used to describe stimulated Raman scattering, stimulated Kerr scattering, and various multiphoton excitation processes. Within this theoretical regime the light (as a photon field) and molecules are treated as a combined quantum mechanical system. The light emission or absorption is always accompanied by the quantum transition of the whole system from its initial eigenstate to the final eigenstate. The molecular emission or absorption probability rate is determined by the corresponding transition matrix elements of the interaction Hamiltonian operator.
This chapter considers electron–photon interaction, i.e., light–matter coupling. It introduces the theoretical treatment of electron–photon interaction for different and mostly strongly simplified cases. In resonator structures, calculation of the appropriate photon modes is required to allow access to the strength of electron–photon coupling. The general guideline is that light may be treated as a wave when propagating in vacuum, yet it has to be quantized in the case of the interaction with matter. In any ensemble of atoms or molecules in interaction with an electromagnetic field, there are three processes occurring: spontaneous emission, absorption, and stimulated emission. In order to get a flavor of a many-body treatment of electron–photon interaction, the derivation of the semiconductor Bloch equations will be discussed briefly. The strength of the light field at the location of the electron determines the interaction strength between light and matter.
We investigate in this chapter the general problem of the interaction of an atom (or a molecule) and a classical electromagnetic field. Its importance derives firstly from the fact that a large part of our knowledge of atoms is obtained from a study of the radiation they absorb or emit (we shall consider equally visible radiation and radio-frequency and X-rays) and, secondly, that the interaction with matter modifies the propagation of the electromagnetic field itself, notably through absorption, refraction or scattering. The interactions of atoms with light therefore encompass a vast range of physical effects that we could not hope to cover adequately in a single chapter. In this chapter we shall therefore present the fundamental features of the interaction of an atom, which will be treated quantum mechanically, with a classical electromagnetic field, that is an electromagnetic field described by real electric and magnetic vectors obeying Maxwell's equations. A rigorous description of the atom–light interaction would have to take into account the quantum nature of light. This we shall leave to Chapter 6. It turns out, nevertheless, that many important results can be obtained from the semi-classical viewpoint adopted here (although it is perhaps more appropriate to refer to this treatment as ‘semi-quantized’).
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]
Spectroscopy, the study of matter via its interactions with light, is a vast subject that includes many of humanity's principle means of probing the fundamental structure of matter. Though usually understood from the perspective of classical light, important effects arise due to the quantum nature of the electromagnetic field. Additionally, the quantum vacuum can serve as an effective couple between molecules in the system, generating many-body interactions and cooperative processes in the material. While many techniques are well-described classically, quantum-field corrections can dominate the desired signals in certain cases, such as cascading in higher-order n-wave mixing signals, and are key for experimental interpretation. Even spontaneous emission and light scattering are best understood from the perspective of quantum fields. In this thesis, we utilize a systematic procedure, based on the density matrix in Liouville space, to give a rigorous description of elementary quantum-field effects in nonlinear spectroscopy, with specific examples made to ultrafast x-ray and optical techniques.