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Physical Review Letters

Renormalized frequency shift of superradiant excitons in thin semiconductor films

Yung-Chang Lee, Der-San Chuu, Wai‐Ning Mei

Published Aug 17, 1992• 9 citations
Publisher

Abstract

The radiative frequency shift of an exciton in a thin semiconductor film, like its radiative level width, is shown to be superradiatively enhanced. Unlike the latter, however, a finite frequency shift can only be obtained after proper renormalization for the correlated system. The shift is found to be inversely proportional to the square of the factor ${\mathit{k}}_{0}$d and proportional to the film thickness T, ${\mathit{k}}_{0}$=${\mathit{E}}_{\mathbf{q}\mathit{n}}$/\ensuremath{\Elzxh}c, ${\mathit{E}}_{\mathbf{q}\mathit{n}}$ being the exciton energy gap and d the lattice constant of the semiconductor. Therefore, the coherent frequency shift can be observed experimentally if one varies the thickness, or the exciton energy gap ${\mathit{E}}_{\mathbf{q}\mathit{n}}$ by imposing high pressure.

DOI
10.1103/physrevlett.69.1081

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Journal of Experimental and Theoretical Physics•Jan 1, 2019•0 citations
The radiative frequency shift of an exciton in a thin semiconductor film, like its radiative level width, is shown to be superradiatively enhanced. Unlike the latter, however, a finite frequency shift can only be obtained after proper renormalization for the correlated system. The shift is found to be inversely proportional to the square of the factor k0{\mathit{k}}_{0}k0​d and proportional to the film thickness T, k0{\mathit{k}}_{0}k0​=Eqn{\mathit{E}}_{\mathbf{q}\mathit{n}}Eqn​/\ensuremath{\Elzxh}c, Eqn{\mathit{E}}_{\mathbf{q}\mathit{n}}Eqn​ being the exciton energy gap and d the lattice constant of the semiconductor. Therefore, the coherent frequency shift can be observed experimentally if one varies the thickness, or the exciton energy gap Eqn{\mathit{E}}_{\mathbf{q}\mathit{n}}Eqn​ by imposing high pressure.
The theory of superradiance of excitons in thin crystal films is presented. While the broken crystal symmetry in the direction normal to the film plane renders the radiative decay of the exciton possible, the remaining crystal symmetry on the film leads to phase coherence between the exciton and the photon fields everywhere on the film. Consequently, a trading between the degrees of freedom of the radiation field and those of the atoms is shown to be responsible for the predicted superradiative enhancement of the exciton decay by a factor ( lambda /d) 2 >>1 in the optical region.
The spontaneous coherent radiation from thin crystal films of nnn layers is studied. By treating each layer as a unit and by employing the method of multiple-time-scale expansion, exact solutions for such systems, with no restriction on the value $\frac{{\ensuremath{\lambda}}_{0}}{d}$, are found. Here ${\ensuremath{\lambda}}_{0}$ is the characteristic radiation wavelength and ddd is the average interparticle spacing. In the limit $\frac{{\ensuremath{\lambda}}_{0}}{d}\ensuremath{\gg}1$, it is seen that there exist correlated states of the film which are exact analog of Dicke's superradiant states. The decay rate for the superradiant states is roughly enhanced by a factor of $n{(\frac{{\ensuremath{\lambda}}_{0}}{d})}^{2}$ compared to the single-atom decay rate ${\ensuremath{\gamma}}_{s}$.
We want to make the best use of the mesoscopic or macroscopic transition dipolemornent of excitons by controling the size and dimension of the materials. First, the semiconductor microcrystallites embedded in insulators or glasses are shown to have the mesoscopic transition dipolemoment of excitons1 . As a result, the exciton in CuC1 microcrystallite with the radius 80 A superradiatively decays in 100 pico-second2. Futhermore, the exciton-exciton interaction and the decay and relaxation of the exciton work effectively in deviating the excitons in the microcrystallite from ideal bosons and this system shows the large third-order optical susceptibility"3 of an order of iO esu when we assume the 0.1% packing of the CuC1 microcrystallites. These predictions have been confirmed expriment ally4'5. Second, the two-dimensional excitons in quantum wells can superradiatively decay in the direction perpendicular to the surfaces2 . This brings about the quick response and the deviation of the excitons from ideal bosons at the same time. The latter effect as well as the two-dimensional macroscopic enhancement of the exction transition dipolemoment enhance the third-order optical susceptibility3. Both the superradiative decay rate and increase as does the coherent length, which is inversely proportional to the square root of the exciton line width6.
Abstract We have studied the nonstationary transmission of two ultrashort laser pulses incident on a thin film. The radiation frequency of one of these pulses is in resonance with the two-photon transition from the ground state of the crystal to the biexciton state, while the other pulse coherently mixes the exciton and biexciton states, leading to strong renormalization of the energy spectrum of the crystal. We have obtained a system of nonlinear equations describing the time evolution of the exciton and biexciton amplitudes and the fields of three pulses transmitted through the film. We have analyzed the effect of amplitudes and widths of incident pulsed and of the time delay between them on the peculiarities of film transmission of these pulses. We have predicted the effect of a substantial time delay in the generation of the pulse transmitted through the film relative to the incident pulse, which is in resonance with the exciton–biexciton transition frequency. The possibility of generation of a precursor, viz., a pulse transmitted through the film sooner than the peak of the incident pulse reaches the film, as well as possibility of generation of a reflected pulse in the absence of the incident pulse, has been proven.