An update on the middle levels problem

The middle levels problem is to find a Hamilton cycle in the middle levels, M_{2k+1}, of the Hasse diagram of B_{2k+1} (the partially ordered set of subsets of a 2k+1-element set ordered by inclusion). Previously, the best result was that M_{2k+1} is Hamiltonian for all positive k through k=15. In this note we announce that M_{33} and M_{35} have Hamilton cycles. The result was achieved by an algorithmic improvement that made it possible to find a Hamilton path in a reduced graph of complementary necklace pairs having 129,644,790 vertices, using a 64-bit personal computer.Comment: 11 pages, 5 figure

Observation of the Purcell effect in high-index-contrast micropillar

We have fabricated pillar microcavity samples with Bragg mirrors consisting of alternate layers of GaAs and Aluminium Oxide. Compared to the more widely studied GaAs/AlAs micropillars these mirrors can achieve higher reflectivities with fewer layer repeats and reduce the mode volume. We have studied a number of samples containing a low density of InGaAs/GaAs self assembled quantum dots in a cavity and here report observation of a three fold enhancement in the radiative lifetime of a quantum dot exciton state due to the Purcell effect

Oxide-apertured microcavity single-photon emitting diode

We have developed a microcavity single-photon source based on a single quantum dot within a planar cavity in which wet-oxidation of a high-aluminium content layer provides lateral confinement of both the photonic mode and the injection current. Lateral confinement of the optical mode in optically pumped structures produces a strong enhancement of the radiative decay rate. Using microcavity structures with doped contact layers, we demonstrate a single-photon emitting diode where current may be injected into a single dot

Polarization correlated photons from a positively charged quantum dot

Polarized cross-correlation spectroscopy on a quantum dot charged with a single hole shows the sequential emission of photons with common circular polarization. This effect is visible without magnetic field, but becomes more pronounced as the field along the quantization axis is increased. We interpret the data in terms of electron dephasing in the X+ state caused by the Overhauser field of nuclei in the dot. We predict the correlation timescale can be increased by accelerating the emission rate with cavity-QED

Experimental position-time entanglement with degenerate single photons

We report an experiment in which two-photon interference occurs between degenerate single photons that never meet. The two photons travel in opposite directions through our fibre-optic interferometer and interference occurs when the photons reach two different, spatially separated, 2-by-2 couplers at the same time. We show that this experiment is analogous to the conventional Franson-type entanglement experiment where the photons are entangled in position and time. We measure wavefunction overlaps for the two photons as high as 94 $\pm$ 3%.Comment: Updated to published version, new fig. 4., corrected typo

Double-Peaked Narrow-Line Active Galactic Nuclei. II. The Case Of Equal Peaks

Active galactic nuclei (AGNs) with double-peaked narrow lines (DPAGNs) may be caused by kiloparsec-scale binary AGNs, bipolar outflows, or rotating gaseous disks. We examine the class of DPAGNs in which the two narrow-line components have closely similar intensity as being especially likely to involve disks or jets. Two spectroscopic indicators support this likelihood. For DPAGNs from Smith et al., the "equal-peaked" objects (EPAGNs) have [Ne V]/[O III] ratios lower than for a control sample of non-double-peaked AGNs. This is unexpected for a pair of normal AGNs in a galactic merger, but may be consistent with [O III] emission from a rotating ring with relatively little gas at small radii. Also, [O III]/H beta ratios of the redshifted and blueshifted systems in the EPAGN are more similar to each other than in a control sample, suggestive of a single ionizing source and inconsistent with the binary interpretation.University Cooperative Society of the University of Texas at AustinJane and Roland Blumberg Cenntenial Professorship in AstronomyAlfred P. Sloan FoundationNational Aeronautics and Space AdministrationNational Science FoundationU.S. Department of EnergyJapanese MonbukagakushoMax Planck SocietyUniversity of ChicagoInstitute for Advanced StudyJapan Participation GroupJohns Hopkins UniversityKorean Scientist GroupLos Alamos National LaboratoryMax-Planck-Institute for Astronomy (MPIA)Max-Planck-Institute for Astrophysics (MPA)New Mexico State UniversityUniversity of PittsburghUniversity of PortsmouthPrinceton UniversityUnited States Naval ObservatoryUniversity of WashingtonFermilabAstronom