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Calculation Indicates Fractional Quantum Decay is Possible for PbSe Quantum Dots in InverseOpal Photonic Crystals Erwin Schrödinger’s famous gedanken experiment involving a cat whose fate is determined by whether or not an atom has radioactively decayed was an early illustration of the oddities of quantum mechanics. In his scenario, the probability of the atom not decaying—and thus of the cat surviving—decreases exponentially with time. However, recent advances in the field of photonic crystals have led a number of researchers to investigate the circumstances under which the timedependence of spontaneous-emission decay in quantum systems can be modified or even eliminated. P. Kristensen at the Technical University of Denmark, A.F. Koenderink at the FOM Institute for Atomic and Molecular Physics in Amsterdam, and their colleagues have developed a measure of so-called “fractional decay,” in which a system never fully decays to its ground state and have theoretically analyzed a realistic physical system in which such an effect should be observed. They report their results in the July issue of Optics Letters (DOI: 10.1364/ OL.33.001557; p. 1557). Spontaneous electronic decay in quantum systems is driven by interaction with the vacuum state of the electromagnetic modes to which the system is coupled. For free space and most materials, this coupling is weak, and the structure of these modes is relatively simple, leading to an exponential time dependence of the decay probability. Recently, several groups have noted that there is a regime in which quantum systems interacting coherently with a highly structured electromagnetic mode spectrum, such as that of a photonic crystal, will not fully decay but instead remain in a superposition of ground and excited states. This “fractional decay” has not yet been observed, and previous theoretical analyses have been very general. The Danish/Dutch group analyzed a specific physical system to determine the parameters under which fractional decay can be expected to occur. In pursuit of this goal, they developed a measure of the extent to which a system undergoes fractional, rather than exponential, decay. Their model system consists of colloidal PbSe quantum dots (QDs) emitting at ω PbSe ≈ 1.3 × 10 15 Hz, placed at the H–symmetry point in the Wigner–Seitz cell of a closed packed Si inverse-opal photonic crystal whose band edge is slightly detuned from ωPbSe. Beginning with a calculation of the local optical density of states in the photonic crystal, the

group analyzed the decay dynamics of the QDs for different amounts of optical loss (absorption) from the Si. While exponential decay dominates for moderate levels of loss, at small but physically realistic loss levels (α ≤ 3 × 10 -4 cm-1), an appreciable fractional decay effect emerges from the analysis. In the complete absence of loss, the fractional decay effect in the model is strong, and the QD system ultimately settles into a superposition of ground and excited states. Given these results, it appears reasonable to hope that fracti