Radiation field coupling with

The Hamiltonian we adopt is a 2 x 2 matrix of operators. It represents the ground and the excited electronic states within the Born-Oppenheimer approximation, coupled by the radiation field interacting with the dipole operators ... 

As far as spontaneous fluctuations of orientation are concerned, that is within the frame of linear response, this function can be expressed in terms of measured susceptibilities respective to any external field coupled with the orientational degrees of freedom. Such is the case for hertzian electromagnetic radiation that couples with the molecular electric moments. Suitable expressions in terms of the susceptibilities have been proposed, duly incorporating a convenient internal field correction. One among them reads ... 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

This chapter considers the first group of instabilities and introduces the analysis of processes implying an interaction with external flow-field perturbahons. This is exemplified by investigations of coupling between pressure waves and plane flames and also between an external acceleration field and flame fronts. The coupling between flow perturbations and flames giving rise to heat release unsteadiness and coupling with acoushc modes is considered in Chapter 5.2, which deals with the relationship between perturbed flame dynamics and radiated acoustic field, a fundamental process of thermo-acoustic instabilities. 

Photons in quantum optical cavities also constitute excellent qubit candidates [52]. Resonant coupling of atoms with a single mode of the radiation field was experimentally achieved 25 years ago [53], and eventually the coherent coupling of quantum optical cavities with atoms or (simple) molecules was suggested as a means to achieve stable quantum memories in a hybrid quantum processor [54]. There might be a role to play for molecular spin qubits in this kind of hybrid quantum devices that combine solid-state with flying qubits. 

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

The interference process in this collinear approach is, however, different from the interference realized by mixing the local oscillator and the CARS field on a beam splitter. Interference takes place in the sample, which, in the presence of multiple frequencies, mediates the transfer of energy between the beams that participate in the nonlinear process. The local oscillator mixes with the anti-Stokes polarization in the focal volume, and is thus coherently coupled with the pump and Stokes beams in the sample through the third-order polarization of the material. In other words, the material s polarization, and its ability to radiate, is directly controlled in this collinear interferometric scheme. Under these conditions, energy from the local oscillator may flow to the pump and Stokes fields, and vice versa. For instance, when the local oscillator field is rout of phase with the pump/Stokes-induced anti-Stokes polarization in the focal interaction volume, complete depletion of the local oscillator may occur. The energy of the local oscillator field is not redistributed in terms... 

The success of this extended STIRAP scheme can be traced to the fact that the basis of the subset of dressed eigenstates of the coupled matter-radiation field is a stationary state representation. In this representation, all couplings are already taken into account via the identity of and the locations of the energy levels. The contribution of the background states to the population transfer process is then limited to effects associated with nonresonant coupling to the field, and if these background states are far off resonance such effects are small. 

Various theories have been proposed for horizontal transfer at the isoenergetic point. Gouterman considered a condensed system and tried to explain it in the same way as the radiative mechanism. In the radiative transfer, the two energy states are coupled by the photon or the radiation field. In the nonradiative transfer, the coupling is brought about by the phonon field of the crystalline matrix. But this theory is inconsistent with the observation that internal conversion occurs also in individual polyatomic molecules such as benzene. In such cases the medium does not actively participate except as a heat sink. This was taken into consideration in theories proposed by Robinson and Frosch, and Siebrand and has been further improved by Bixon and Jortner for isolated molecules, but the subject is still imperfectly understood. 

The generalization to the control of the dynamics of a molecule with n electronic states is straightforward. For the purpose of deducing the control conditions we will examine the extreme case in which every possible pair of these electronic states is connected via the radiation field and a nonzero transition dipole moment. If the molecule is coupled to a radiation field that is a superposition of individual fields, each of which is resonant with a dipole allowed transition between two surfaces, the density operator of the system can be represented in the form... 

I note, however, the caveat above Our work to date has ignored the possibility of overlapping levels due to the high density of molecular states coupled with the background radiation field. We expect to examine these cases shortly. 

It is very important, in the theory of quantum relaxation processes, to understand how an atomic or molecular excited state is prepared, and to know under what circumstances it is meaningful to consider the time development of such a compound state. It is obvious, but nevertheless important to say, that an atomic or molecular system in a stationary state cannot be induced to make transitions to other states by small terms in the molecular Hamiltonian. A stationary state will undergo transition to other stationary states only by coupling with the radiation field, so that all time-dependent transitions between stationary states are radiative in nature. However, if the system is prepared in a nonstationary state of the total Hamiltonian, nonradiative transitions will occur. Thus, for example, in the theory of molecular predissociation4 it is not justified to prepare the physical system in a pure Born-Oppenheimer bound state and to force transitions to the manifold of continuum dissociative states. If, on the other hand, the excitation process produces the system in a mixed state consisting of a superposition of eigenstates of the total Hamiltonian, a relaxation process will take place. Provided that the absorption line shape is Lorentzian, the relaxation process will follow an exponential decay. 

One of the interesting consequences of eqs. (11-25) and (11-26) is the dependence of the probability of the molecule being in a given nonstationary state on the time correlations in the coupled radiation field. In most experimental studies the radiation field employed consists of a superposition of many frequencies with random phases. It is convenient to represent that form of field in terms of a correlation function d>(t, t"), which is defined in eq. (6-16). Introducing, because of the polychromaticity of the radiation field, the averages of eqs. (11-25) and (11-26), choosing the same representation for the field correlation function as did Bixon and Jortner, and using the conservation of probability, we find for the probability of dissociation of the molecule the relation ... 

The frequency dependence of e and e" and their magnitudes control the extent to which a substance is able to couple with the microwave radiation and therefore are fundamental parameters for interpreting the dielectric heating phenomenon. Although tan 8 is a helpful parameter for comparing the heating rates of a series of dielectrics with similar physical and chemical characteristics, for more complex mixtures expressions, which take into account the complexity of the electric field pattern, the heat capacity of the compound and the density, have been proposed. 

To illustrate this phenomenon, we return to the molecular hydrogen ion H2+. The ground vibrational state of the system is bound in the potential depicted in Figure 1.13. Suppose now that we expose the system to a monochromatic electromagnetic radiation with a frequency radiation field now couples between the ground electronic state and the excited electronic state of the system. The excited electronic state of the hydrogen molecular ion is a dissociative potential curve, which is well approximated by [48] ... 

Note that /ep in Eq. (5.238) is replaced with /Ep for Eq. (5.240), where /Ep is the heat generated by thermal radiation per unit volume and Qap is the heat transferred through the interface between gas and particles. Thus, once the gas velocity field is solved, the particle velocity, particle trajectory, particle concentration, and particle temperature can all be obtained directly by integrating Eqs. (5.235), (5.237), (5.231), and (5.240), respectively. Since the equations for the gas phase are coupled with those for the solid phase, final solutions of the governing equations may have to be obtained through iterations between those for the gas and solid phases. 

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