Superradiant decay

Section III deals with the surface excitations of the anthracene crystal, confined in the first (SJ, second (S2) and third (S3) (001) lattice planes. The experimental observations are briefly summarized. A simple model shows how the fast radiative decay arises and how the underlying bulk reflection modulates this superradiant emission, as well as why gas condensation on the crystal surface strongly narrows this emission, thus accounting for the observed structures. An intrinsic process is proposed to explain the surface-to-bulk relaxation at low temperatures, observed in spite of the very weak surface-to-bulk coupling for k 0 states. 

For An> T we have two states with the molecular decay rate rj2. For An< r we have two states with the same real energy (Rez1 0), but with different decay rates (superradiant y > r j2, subradiant y < r/2). We find a sudden qualitative change in behavior for the system for A = T the time decay passes from biexponential for An> T to a decrease with oscillating beats for A < T.153 This transition is not a special feature of the N = 2 case, but even survives in the continuous limit, as we shall see now. 

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. 

The picosecond time-scale observed in these experiments was the first example of superradiance of two-dimensional Frenkel excitons. Relative quantum yield measurements of the photoluminescence from bulk and the photoluminescence from the outermost monolayer indicate that the decay of excitons in the monolayer is purely radiative with a very small contribution from relaxation to the bulk. Later the same phenomenon for a 2D Wannier-Mott exciton in a semiconductor quantum well was observed by Deveaud et al. (4). 

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... 

So the first example of real superradiance was in fact the free induction decay and die decay of the photon echo observed in ruby by Kumit, Abella and Hartmann (1964). When a pulse from a ruby laser was sent onto a ruby crystal, the free induction decay and the echo decay observed were about 50 ns, when compared to the usual Cr " radiative decay time of 4 ms, showing clearly the radiation emission from the macro-dipole. 

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)... 

Since the macro-dipole exists right after excitation, the superradiance shortened decay starts without delay, beginning with the (Ni -N2Y behavior. The only condition is that the dephasing rate is slower than the superradiant one so that the macro-dipole keeps on existing during the transition, that is... 

Superradiance (SR) and R ions. We have seen that superradiance (SR) in solids with radiation damping has been observed in ruby as the accelerated free induction decay of a photon echo experiment (Kumit et al. 1964). Since then many free induction decay and photon echo experiments have been conducted in Pr -doped systems in order to reach the homogeneous width through a T-i measurement (AVhomo=(2jr7 2) ) (Genack et al. 1976, Shelby and Macfarlane 1984, De Voe and Brewer 1983), and in Ho and Er -doped fluorides (Wannemacher et al. 1990, Macfarlane and Shelby 1982). 

This phenomenon of superradiance is used in the photon-echo technique for high-resolution spectroscopy to measure population and phase decay times, expressed by the longitudinal and transversal relaxation times Tj and T2, see (12.1). This technique is analogous to the spin-echo method in Nuclear Magnetic Resonance (NMR) [12.59]. Its basic principle may be understood in a simple model, transferred from NMR to the optical region [12.60]. 

---