Superradiant lifetime

Returning to eq. (79) we may try to estimate the new decay time resulting from the cooperative emission in strong superradiance. Such a decay time is also called superradiant lifetime and its inverse is called radiative damping constanf . Calculating this lifetime as (Yariv 1967)... 

The lifetimes of molecular fluorescence emissions are determined by the competition between radiative and nonradiative processes. If the radiative channel is dominant, as in the anthracene molecule, the fluorescence quantum yield is about unity-and the lifetime lies in the nanosecond range. In molecular assemblies, however, due to the cooperative emission of interacting molecules, much shorter lifetimes—in the picosecond or even in the femtosecond range—can theoretically be expected an upper limit has been calculated for 2D excitons [see (3.15) and Fig. 3.7] and for /V-multilayer systems with 100 > N > 2.78 The nonradiative molecular process is local, so unless fluorescence is in resonance by fission (Section II.C.2), its contribution to the lifetime of the molecular-assembly emission remains constant it is usually overwhelmed by the radiative process.118121 The phenomenon of collective spontaneous emission is often related to Dicke s model of superradiance,144 with the difference that only a very small density of excitation is involved. Direct measurement of such short radiative lifetimes of collective emissions, in the picosecond range, have recently been reported for two very different 2D systems ... 

The subject of correlated or collective spontaneous emission by a system of a large number of atoms was first proposed by Dicke [1], who introduced the concept of superradiance that the influence on each atomic dipole of the electromagnetic field produced by the other atomic dipoles could, in certain circumstances, cause each atom to decay with an enhanced spontaneous emission rate. The shortening of the atomic lifetime resulting from the interaction between N atoms could involve an enhancement of the intensity of radiation up to N2. 

For example, a 450-A radius CdS cluster should have a l-ps radiative lifetime observable below 7 K. As the temperature increases, higher states are populated and the superradiant effect disappears. As a result, the radiative lifetime increases with increasing temperature in this size regime. 

For semiconductor clusters with larger Bohr radius, such as CdS and CdSe, the observation of the superradiant effect proves to be more elusive. This is mainly due to the difficulty of preparing high-quality samples of varying sizes of clusters that exhibit exciton luminescence. The spectra and kinetics of the luminescence are usually very complicated, which makes the positive identification of exciton luminescence difficult. For example, sharp band-edge luminescence with well-resolved vibronic structures was observed from 32-A CdSe clusters [60]. The decay kinetics of the luminescence is multiexponential and only the first 100-psec decay is identified with the exciton luminescence. The lifetime of this luminescence, however, is tempera-... 

In the last decade the Wannier exciton emission from direct band gap soniconductors was reconsidered for high count-rate and coincidence-detection scintillation applications and Cul, Hglj, Pbl2, ZnO Ga, and CdS In compounds in powder form were studied (Derenzo et al. 2002). In direct gap semiconductors a favorable combination of a smaller gap and an UV-VIS emission center based on Wannier exciton can provide high scintillation efficiency and subnanosecond radiative lifetimes due to microscopic superradiance effect (Niki 2006, Wilkinson et al. 2004). On the other hand, the Stokes shift of such emission centers is necessarily low (typically below 0.1 eV) and it prevents their usage in the bulk form due to enhanced reabsorption effect, see Figure 4.4. The ZnO Ga has shown the best combination of subnanosecond decay time and emission intensity... 

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