Phonon-Photon Coupling

Previously we had only considered the optical modes at fc = 0 because the large difference between the momentum of a photon and a phonon would not permit energy and momentum to be conserved otherwise. Obviously, k carmot be exactly zero, so let us explore the region of small fc by developing the dispersion relation o versus fc where the photons can couple with phonons. Rewriting Equation 23.34, 

Dispersion relationship ( o vs. fc) for NaCl in the vicinity of small fc. The dashed diagonal line represents the speed of light in the medium with c(oo) and the dash-dot diagonal line represents the speed of light in a medium with c(0). The horizontal lines at T and ojl are the energy gap. The lattice cannot propagate frequencies between these frequencies. 

Because there is an energy gap between and ot, no photon can enter and propagate in 

Vertically polarized light exciting a longitudinal vibration in a line of diatomic ions. Undisturbed lattice (top) is excited by a vertically polarized photon causing the cations (black) and the anions (gray) to oscillate back-and-forth relative to each other. 

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First, we envisage the weak exciton-photon coupling (which allows an intuitive description of the phonon effects on the nature of the secondary emissions). Therefore we write the hamiltonian of the total system as sums of free photons (Hy), free excitons (He), and free phonons (Hp), with the appropriate interactions Hey (Section I) and Hep (see Sections II, A, B, C.), including intramolecular vibrations too. 

Let us now consider the case of strong exciton-photon coupling, which is that in the singlet state of the anthracene crystal. As shown in Section I, we have to consider as zero-order hamiltonian H that of the polaritons, and the transition between polaritons will be induced by the exciton-phonon coupling Hep. Let us denote by Jf and the hamiltonian of the total system and of its... 

In absorption, the photon couples to the dipole moment induced by the phonon vibration and the absorption spectrum, a(o>), is given approximately by. 

The results from the general theory for the vibrational spectrum of a localized harmonic oscillator, linearly coupled with a noninteracting boson continuum (phonons, photons, electron-hole pairs), can be used to estimate the contribution of different relaxation processes at smfaces. The spectral function of the oscillator obtained by normal-mode analysis at zero temperature is [25]... 

Coupling the motion of the mosaic cell (TLS and boson peak) to phonons is necesssary to explain thermal conductivity therefore the interaction effects discussed later follow from our identification of the origin of amorphous state excitations. The emission of a phonon followed by its absorption by another cell will give an effective interaction, in the same way that photon exchange leads to... 

Note that dra(t)/dt = [H,ra]=(l/ma)[pa-qaA(ra)] and, consequently, the first term in (69) represents the kinetic energy of the system of particles in the presence of the transverse electromagnetic field. Note the analogy between this representation and the dynamical solute-solvent coupling of section 2.6 where the optical phonons are equivalent to electromagnetic photons of low frequency (the acoustical phonons are related to sound waves). 

The electron-phonon operator is a tensor product between the electronic dipole and the nuclear dipole operators. A mixing between the AA and BB via the singlet-spin diradical AB state is possible now. A linear superposition of identical vibration states in AA and BB is performed by the excited state diradical AB. If the system started at cis state, after coupling may decohere by emission of a vibration photon in the trans state furthermore, relaxation to the trans... 

A one-level system e) that can exchange its population with the bath states [/) represents the case of autoionization or photoionization. However, the above Hamiltonian describes also a qubit, which can undergo transitions between the excited and ground states e) and g), respectively, due to its off-diagonal coupling to the bath. The bath may consist of quantum oscillators (modes) or two-level systems (spins) with different eigenfrequencies. Typical examples are spontaneous emission into photon or phonon continua. In the RWA, which is alleviated in Section 4.4, the present formalism applies to a relaxing qubit, under the substitutions... 

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. 

Plasmon-phonon coupling represents mixing of two quasi-particles. The coupling of three quasi-particles has also been observed. The term plasmariton was used by Alfano 45) for a coupled state of a TO phonon and a dressed photon , namely, a photon surrounded by an electron cloud (a coupled state of a plasmon and a photon). The quasi-particle dressed photon is also called a transverse plasmon. Because the coupled state of a photon and a TO phonon has been termed polariton, a plasmariton can also be regarded as coupled state of a plasmon and a polariton. Earlier the term plasmariton was used in a more restricted sense, namely, when a partly transverse character of the plasmon is induced by an external magnetic field. 

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