Slow decoherence and the radiative decay limit in rare-earth-doped crystals for coherent optical storage

We analyze the material requirements for recording, storage, and processing of optically encoded information using coherent optical transients in resonant solids. We introduce new figures of merit (FOM’s) that explicitly account for the ratio between the rate of the decoherence and the rate of the spontaneous radiative decay. Highest FOM values are achieved when the decoherence rate approaches the fundamental limit set by spontaneous emission under the condition that the total transition oscillator strength is concentrated between a single pair of energy levels. We analyze FOM’s of some of the most promising rare-earth-doped crystals at cryogenic temperatures.     

Selective recovery of gold from secondary sources by Dowex-50-X8 sorbed Rhodamine-B resin

Gold recovery from spent materials has been performed on modified cation-exchange resin. The modified resin was prepared by sorption of Rhodamine-B on Dowex-50-X8 (Na+) resin at pH 2.0. Distribution coefficients of gold ion have been determined with 15% (w/v) potassium chloride in different concentrations of hydrochloric acid. On the basis of Kd values quantitative separation of gold from secondary sources has been achieved. Gold(III) has been selectively separated from gold containing spent materials by column chromatography using modified ionexchange resin and the recovery was more than 92% compared to conventional cyanidation process. The results of the proposed method are suggestive of its applicability to other gold containing secondary sources.     

Time-domain Fresnel-to-Fraunhofer diffraction with photon echoes

A photon echo experiment in Tm(3+):YAG is reported that shows, for the first time to the authors' knowledge, the time-domain equivalent of the transition from near- to far-field diffraction, including Talbot self-imaging effects. The experiment demonstrates the huge dispersion capability of photon echoes and opens the way to further exploration of space-time duality.     

Semigroups satisfying variable identities

The purpose of this note is to generalize a theorem of Tamura’s [3] providing a self-contained and, we think, more elementary proof than Tamura’s in that it avoids using the theory of contents. Tamura’s result states that a semigroup S satisfies an identify xy=f(x,y) with f(x,y) a word of length greater than 2 which starts with y and ends in x if and only if S is an inflation of a semilattice of groups satisfying the same identity. We investigate semigroups as in Tamura’s Theorem, except that we permit f(x,y) to vary with x and y.