Matter-radiation field interactions

AN OVERVIEW OF QUANTUM ELECTRODYNAMICS AND MATTER-RADIATION FIELD INTERACTION... 

To this point, we have considered only the radiation field. We now turn to the interaction between the matter and the field. According to classical electromagnetic theory, the force on a particle with charge e due to the electric and magnetic fields is... 

The high-field output of laser devices allows for a wide variety of nonlinear interactions [17] between tire radiation field and tire matter. Many of tire initial relationships can be derived using engineering principles by simply expanding tire media polarizability in a Taylor series in powers of tire electric field ... 

Let us now consider how electromagnetic radiation can interact with a particle of matter. Quantum mechanics (the field of physics dealing with... 

V(Rl). Finally, 5rad and SGt are the actions of radiation oscillator and that of the interaction between matter and radiation field, respectively [14,15]. 

The dipole moment is the total dipole of the sample, p = Y.i Pi The correlation function describes the response of the system to the weakly coupled radiation field. The effects of the field are modeled by the response of the individual atoms or molecules unaffected by the weak coupling. The Hamiltonian describes the interaction of the field and matter (first-order perturbatiuon theory). The correlation function describes how the perturbed system approaches equilibrium. 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

Given this approximation, we can transform the Hamiltonian of Eq. (1.44) from the velocity gauge to the so-called length gauge in which the matter-radiation interaction term contains only the dot product of the dipole moment and the electric field. In order to do so we choose x [Eq. (1.5)] as... 

The molecule, initially in a state IE), J , Mf), is subjected to two cw fields. Once again J , Mf denote the angular momentum and its projection along the z axis. The matter-radiation interaction term is of the form, ... 

T ) obtain the Schrodinger equation for the interaction of a molecule with the quanted radiation field, that is, the Schrodinger equation for the (matter + radiation) fr steni. we need the quantum analog of 77MR, the matter-radiation interaction, hi the 1,1 pole approximation HMR depends, according to Eq. (1.51), on the transverse... 

Finally, we make a few additional remarks. First, note that a pure number state is a3j= state whose phase 0k is evenly distributed between 0 and 2n. This is a consequence of the commutation relation [3] between Nk and e,0 <. Nevertheless, dipole mafKi w elements calculated between number states are (as all quantum mechanical amplitudes) well-defined complex numbers, and as such they have well-defined phajje j S Thus, the phases of the dipole matrix elements in conjunction with the mode ph f i f/)k [Eq. (12.15)] yield well-defined matter + radiation phases that determine the outcome of the photodissociation process. As in the weak-field domain, if only gJ one incident radiation mode exists then the phase cancels out in the rate expres4<3 [Eq. (12.35)], provided that the RWA [Eqs. (12.44) and (12.45)] is adoptedf However, in complete analogy with the treatment of weak-field control, if we irradh ate the material system with two or more radiation modes then the relative pb between them may have a pronounced effect on the fully interacting state, phase control is possible. 

Therefore, our model of a surface with substrate is based on interactions, of purely retarded type, between surface and bulk dipoles via the radiation field, or, more formally, on a renormalization by the bulk matter of the photon continuum to which the surface is coupled, with consequent modifications of its radiative properties. 

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