Electrodes constructed from single-crystal sections of rare earth fluorides respond to fluoride ion activity over more than five orders of magnitude and show a high selectivity for fluoride over other common anions. These electrodes can be used for either direct measuremnent of fluoride ion activity or detection of the end point in titration.

Similar coherence between heavy-hole and light-hole excitons has been reported in (33).These are examples of quantum coherence involving a nonradiative superposition of states, which leads to many novel phenomena such as the Hanle effect, dark states, lasing without inversion, electromagnetically induced transparency, and population trapping [see (33) and references therein]. However. unlike the QD system, atomic Zeeman coherence does not necessarily involve two differentiable electrons, in contrast to the experiment we present here.Finally, it is critical to note that while the simple discussion related to Fig. 1 shows the origin of the entanglement, the discussion is considerably over-simplified; it completely disregards the possibility that fast dephasing of the Zeeman coherence could lead to an unobservable effect, even if the single-exciton states themselves were long-lived. In the language of NMR, this is saying that a long T, and T2 associated with the single-exciton states does not guarantee a comparable T2 for the Zeeman coherence. The maptude of the decoherence rate, yij (l/T,), in Eq. 2 can be determined by comparing the relative strength of the coherent and incoherent contribution. The dephasing rate of the radiative coherence was already shown in (24) to be -20 ps and is comparable to the energy relaxation rate, r (lIT,). This measurement fiuther gives the decay rate of the Zeeman coherence as -20 ps, which again is similar to the energy relaxation rate and shows that the pure dephasing of the two-exciton coherence is not significant in QDs. By exchanging the spectral position of the pump and the probe (the polarization has to be changed accordingly, too), the relative time scale of incoherent spin relaxation can also be estimated. As expected, the Zeeman splitting has reduced this process to an unobservable level (>lo0 ps).In summary, we have inferred from our measurements entanglement of an excitonic system in single GaAs QDs and shown the importance of exciton-exciton Coulomb interaction for this observation. Our results are explained by a three-level model in a two-exciton basis. The next step, though more challenging, is to recover the same type of entanglement between coupled QDs [as proposed, for example, in (13, 14)]. This would allow for scaling the experiment to larger systems.

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A new potassium electrode, made from valinomycin, which uses commercially available electrode configurations, responds to potassium ion concentrations from 1 mole per liter to below 10(-6) mole per liter. It is highly selective for potassium ion over sodium ion and divalent ions and can be used for the direct determination of potassium ion in human serumn. No significant complexing of potassiium appears to occur in normal seruin.