Sodium Bose-Einstein condensates in the F = 2 state in a large-volume optical trap

We have investigated the properties of Bose-Einstein condensates of sodium atoms in the upper hyperfine ground state. Condensates in the high-field seeking [F=2, m(F)=-2> state were created in a large volume optical trap from initially prepared [F=1, m(F)=-1> condensates using a microwave transition at 1.77 GHz. We found condensates in the stretched state [F=2, m(F)=-2> to be stable for several seconds at densities in the range of 10(14) atoms/cm(3). In addition, we studied the clock transition [F=1, m(F)=0> --> [F=2, m(F)=0> in a sodium Bose-Einstein condensate and determined a density-dependent frequency shift of (2.44+/-0.25+/-0.5) x 10(-12) Hz cm(3).     

Expedient synthesis of a highly substituted tropolone via a 3-oxidopyrylium [5+2] cycloaddition reaction

An expedient ten-step synthesis of a substituted tropolone is described. The synthesis involves a 3-oxidopyrylium [5+2] cycloaddition reaction with acrylonitrile as the key step, affording a highly functionalized [3.2.1]-bicycle 10 as a single regioisomer. The nitrile substituent of the reduced cycloadduct 12 permits efficient ether-bridge cleavage and tropolone 15 is obtained after a final bis-oxidation procedure. The pyranulose acetate cycloaddition precursor was derived from 3-methyl-2-furoate.     

Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices

We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.     

On the classical simulation of unimolecular reaction processes

The numerical simulation of the internal motions of a molecule undergoing a unimolecular reaction on an assumed potential energy surface requires the step-by-step solution of a set of simultaneous differential equations. After several thousand time steps, due to differences in the handling of rounding errors in different computing systems, the situation often arises that no two computing machines will give the same result for a given trajectory, even when running the identical algorithm.