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arXiv:cond-mat/0210233 · Physical review. B, Condensed matter

Superradiance of low-density Frenkel excitons in a crystal slab of three-level atoms: The quantum interference effect

Guangri Jin, Peng Zhang, Yu-xi Liu, C. P. Sun

Published Oct 3, 2003• 38 citations
arXivHTMLPDF

Abstract

We systematically study the fluorescence of low-density Frenkel excitons in a crystal slab containing ${N}_{T}$ 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.

DOI
10.1103/physrevb.68.134301

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We systematically study the fluorescence of low-density Frenkel excitons in a crystal slab containing NT{N}_{T}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.
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{(e}^{2}{/2\mathrm{mc}}^{2}){\mathbf{A}}^{2}(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.
A theory on interference effects at high photon densities has been developed for two types of a single three-level atom for which transitions occur: (i) from two different upper levels to a common lower one and (ii) from a common upper level to two different lower levels. The excitation spectrum for the interference effects for the two types of atoms results from the symmetric and antisymmetric interference between the two electronic transitions of the system, respectively. The spectral function for the symmetric modes consists of three Lorentzian lines peaked at the frequencies ω = Δ and ω = Δ ± Ω and having spectral widths of the order of γ0 and 3γ0/4, respectively, where Δ is the beat frequency, Ω is the Rabi frequency, and γ0/2 is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. The antisy mmetric spectrum consists of the peak of ω = Δ, which has a delta-function distribution indicating the stability of the mode in question, and two Lorentzian lines peaked at ω = Δ ± Ω with radiative widths of the order of γ0/2. The excitation spectrum of each type of atom contains also a Lorentzian line describing the very low frequency mode of the system, respectively.
An investigation is made of the influence of quantum interference processes accompanying radiative relaxation of excited states on the population dynamics, total intensity, and spectra of the resonance fluorescence of three-level V -type atoms. Analytic expressions are obtained for the total intensity and spectra of the resonance fluorescence taking into account the off-diagonal nature of the radiative relaxation operator. It is shown that quantum interference process can substantially alter the total spontaneous emission intensity of the atoms and the population dynamics of the atomic levels, as well as the resonance fluorescence spectra.
We investigate the two-time intensity correlation functions of the fluorescence field emitted from a VVV-type three-level atom. We are particularly interested in the manner in which the atom emits photons in the presence of quantum interference. We show that under strong-field excitation quantum interference leads to anticorrelations of photons emitted from the atomic excited levels which can exist for extremely long times. This indicates that the excited atomic levels are not the preferred radiative states. We find that the atom spends most of its time in a superposition of the excited atomic levels from which it emits strongly correlated photons. The strong correlations are present only for a nonzero splitting between the excited levels, and for degenerate levels the correlations reduce to that of a two-level atom. Moreover, we find that the transition from the ground level to the symmetric superposition of the excited levels does not saturate even for a strong driving field. We also calculate the correlation functions for a weak driving field, and find that in this case the photon correlations are not significantly affected by quantum interference, but the atom can emit a strongly correlated pair of photons produced by a three-wave mixing process. Under appropriate conditions, with near-maximal quantum interference, it is possible to make the maximum value of the correlation function extremely large, in marked contrast with the corresponding case with no quantum interference.
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.