Annihilation operator molecular photonics

Let at(q) and a(q) be the creation and annihilation operators of cavity photons, and B and B, be the creation and annihilation operators of an excitation on the ith molecule . We do not account for the dipole-dipole interactions between different molecules , as we consider the coupling by light to be the principal coupling mechanism. Thus the Hamiltonians of noninteracting cavity photons and molecular excitations are... 

It consists of a lattice of N molecular sites spaced by distance a and comprises the exciton part (an is the exciton annihilation operator on the site n), photon part (bk is the photon annihilation operator with the wavevector k and a given polarization) as well as the ordinary exciton-photon interaction. The cavity photon energy ek is defined by eqn (10.44), e represents the average exciton energy, while en are the on-site exciton energy fluctuations. 

Amplitudes of molecular optical events are proportional to off-diagonal matrix elements of interaction operators between the wavefunctions of the initial, final, and possibly also intermediate states of the molecule, 0), f), and /) respectively. These operators are projections of molecular transition vector and tensor operators onto the polarization directions of photons created or annihilated in the event (Table 1). The amplitudes depend on the wavenumber of the light used and can be real or complex. The probability of an optical event W is proportional to the square of the absolute value of its amplitude (Table 2). The proportionality constant is of no... 

In electronic and vibrational spectroscopy we can neglect both molecular dimensions relative to the wavelength and the effects of the magnetic field of light relative to those of its electric field (electric dipole approximation). Then, the interaction of a single l7-polarized photon with a molecule is described by the projection of the electric dipole moment vector operator M (Table 3) into eP (photon creation) or eP (photon annihilation). Creation... 

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