Hamiltonian including radiation field

The central feature of QED is that there is a closed system of particles and fields that act on each other, the particles associated with the radiation field being photons. The states of the entire system can be dealt with, and its properties, including rates of transitions in which the number of particles changes, calculated as accurately as desired. Typically in applications to molecules (MQED) the Hamiltonian is written in the form (5.2) with the interaction between molecule and fields separated out as a small term to be treated as a perturbation,... 

Another scheme to calculate and interpret macroscopic nonlinear optical responses was formulated by Mukamel and co-workers [112 114] and incorporated intermolecular interactions as well as correlation between matter and the radiation field in a consistent way by using a multipolar Hamiltonian. Contrary to the local field approximation, the macroscopic susceptibilities cannot be expressed as simple functionals of the single-molecule polarizabilities, but retarded intermolecular interactions (polariton effects) can be included. 

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. 

The total Hamiltonian describing the total interacting many-body problem—Dirac particles + radiation field + nucleus—may be obtained from the T 00-component of the energy-momentum tensor. The part of the Hamiltonian relevant for the relativistic description of the atomic many-body problem in the presence of the external electromagnetic held of the nucleus including radiative corrections and possible interactions... 

H being the total system Hamiltonian, including the radiation field when external charges and currents are absent, and... 

In order to include all types of discrimination we first give a complete hamil-tonian (II. 1), expressed as the sum of the isolated molecule hamiltonians Hs, and H i, their electrostatic interaction H-e, the coupling by radiation, and the hamiltonian for the radiation field. 

In the coupling region, where the electromagnetic field cannot be treated as a weak perturbation, its interaction with the electronic excitations of the solid has to be included in zeroth order. To calculate the energy spectrum of the new particles evolving from this interaction, we have to diagonalize the Hamiltonian of the interacting electron-radiation field system (23,24) ... 

We now add die field back into the Hamiltonian, and examine the simplest case of a two-level system coupled to coherent, monochromatic radiation. This material is included in many textbooks (e.g. [6, 7, 8, 9, 10 and 11]). The system is described by a Hamiltonian having only two eigenstates, i and with energies = and Define coq = - co. The most general wavefunction for this system may be written as... 

Electron spin resonance (ESR) measures the absorption spectra associated with the energy states produced from the ground state by interaction with the magnetic field. This review deals with the theory of these states, their description by a spin Hamiltonian and the transitions between these states induced by electromagnetic radiation. The dynamics of these transitions (spin-lattice relaxation times, etc.) are not considered. Also omitted are discussions of other methods of measuring spin Hamiltonian parameters such as nuclear magnetic resonance (NMR) and electron nuclear double resonance (ENDOR), although results obtained by these methods are included in Sec. VI. 

Thus suppose we had included the interaction of the radiation s magnetic field B with the atomic or molecular electrons and nuclei. The Hamiltonian for this interaction is [Equation (1.268)] -B , where p is the magnetic dipole-moment operator for the system. This gives additional terms in cm that are proportional to... 

Because circular dichroism is a difference in absorption for left and right circularly polarized light, its theoretical description includes subtraction of the transition probabilities induced by left and right circularly polarized radiation. The interaction Hamiltonian that determines transition probability includes electric, , and magnetic, B, fields of electromagnetic circularly polarized radiation, and the electric, /i, and magnetic, m, dipole moments of the molecule. 

Note that by giving to the system an external energy E, excited vibration-rotation and electronic states can be activated (populated too). These states can radiate energy into the field by photon emission or can be populated by photon absorption. The electromagnetic field is considered here as a source or as a sink of energy ensuring energy conservation. The total Hamiltonian must include the... 

---