In low density regime, the fluorescence of Frenkel exitons in crystal slab can be studied without the aid of rotating wave and Mackoffian approximation. The equations for the case of double and triple lattice-layers are now solved exactly to give the eigen decay rates, frequency shifts and the statistical properties of the fields.
The fluorescence of Frenkel excitons in low density regime is studied without the aid of rotating wave approximation and Markov approximation. The evolution of the emitted field is derived in terms of its initial conditions. It is found that the usual interaction Hamiltonian of $(e/mc)\mathbf{P}\ensuremath{\cdot}\mathbf{A}$ type leads to unreasonable characteristic equation for decay rates. Only when the term (e2/2mc2)A2 is added to the $(e/mc)\mathbf{P}\ensuremath{\cdot}\mathbf{A},$ the result becomes reasonable. The case of single lattice layer is studied in detail. Different features of statistical properties of the superfluorescence are shown as compared with that of atom aggregate. Double and triple lattice-layer cases are also studied to show the effect of coupling between the excitons of different wave vectors.
We systematically study the fluorescence of low-density Frenkel excitons in a crystal slab containing NT V-type three-level atoms. Based on symmetric quasispin realization of SU(3) in large N limit, the two-mode exciton operators are invoked to depict various collective excitations of the collection of these V-type atoms starting from their ground state. By making use of the rotating-wave approximation, the light intensity of radiation for the single-lattice layer is investigated in detail. As a quantum coherence effect, the quantum beat phenomenon is discussed in detail for different initial excitonic states. We also test the above results analytically without the consideration of the rotating-wave approximation and the self-interaction of radiance field is also included.
A formal, regorous theory of Frenkel excitons interacting with an external electromagnetic field is doveloped within the framework of a two-level-atom model in which the dipole approximation is employed in describing the atom-field (taken as a c-number) interaction. The model exciton Hamiltonian is shown to be identical in form with the Heisenberg model Hamiltonian for S=1/2 spins with anisotropic long-range exchange interactions. Instead of treating excitons as a non-ideal Bose gas, atomic polarization operators and level population defference are taken up as two fundamental quantities to describe Frenkel excitons. A pair of equations satisfied by these two quantities are derived. It is shown that Frenkel excitons are generally expressed as quantum-mechanical nonlinear polarization waves, the nonlinearity being characterized by the level population. A discussion is given on the interrelationship between such polarization waves and those derivable from the classical Drude-Lorentz model. With the aid of several approximation procedures similar to those employed in nonlinear optics, a set of equations describing nonlinear exciton-photon coupled modes are derived. Brief discussion is given on the eigenfrequencies of nonlinear Frenkel excitons and nonlinear polaritons. The existence of nonlinear exciton-photon coupled modes whose properties are different from those of polariton modes is suggested.
Superradiance of high density Frenkel excitons in an R-phycoerythrin single crystal is observed at room temperature for the first time. No fluorescence is observed except the emission at the sharp exciton band when the superradiance of excitons occurs, and the higher the pump density, the sharper the emission bandwidth. A redshift and a blueshift are observed at the rise time and the fall time of the emission pulse, respectively. The experimental results also imply deformed-boson properties of high density Frenkel excitons.