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

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

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

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

The Jet-Driven Outflow In The Radio Galaxy SDSS J1517+3353: Implications For Double-Peaked Narrow-Line Active Galactic Nucleus

We report on the study of an intriguing active galaxy that was selected as a potential multiple supermassive black hole merger in the early-type host SDSS J151709.20+335324.7 (z = 0.135) from a complete search for double-peaked [O III] lines from the SDSS spectroscopic quasi-stellar object (QSO) database. Ground-based SDSS imaging reveals two blue structures on either side of the photometric center of the host galaxy, separated from each other by about 5.7 kpc. From a combination of SDSS fiber and Keck/HIRES long-slit spectroscopy, it is demonstrated that, in addition to these two features, a third distinct structure surrounds the nucleus of the host galaxy. All three structures exhibit highly ionized line emission with line ratios characteristic of Seyfert II active galactic nuclei. The analysis of spatially resolved emission-line profiles from the HIRES spectrum reveal three distinct kinematic subcomponents, one at rest and the other two moving at -350 km s(-1) and 500 km s(-1) with respect to the systemic velocity of the host galaxy. A comparison of imaging and spectral data confirm a strong association between the kinematic components and the spatial knots, which implies a highly disturbed and complex active region in this object. A comparative analysis of the broadband positions, colors, kinematics, and spectral properties of the knots in this system lead to two plausible explanations: (1) a multiple active galactic nucleus (AGN) produced due to a massive dry merger, or (2) a very powerful radio jet-driven outflow. Subsequent VLA radio imaging reveals a clear jet aligned with the emission-line gas, confirming the latter explanation. We use the broadband radio measurements to examine the impact of the jet on the interstellar medium of the host galaxy, and find that the energy in the radio lobes can heat a significant fraction of the gas to the virial temperature. Finally, we discuss tests that may help future surveys distinguish between jet-driven kinematics and true black-hole binaries. J1517+3353 is a remarkable laboratory for AGN feedback and warrants deeper follow-up study. In the Appendix, we present high-resolution radio imaging of a second AGN with double-peaked [O III] lines, SDSS J112939.78+605742.6, which shows a sub-arcsecond radio jet. If the double-peaked nature of the narrow lines in radio-loud AGNs are generally due to radio jet interactions, we suggest that extended radio structure should be expected in most of such systems.NSF AST-0507483, AST-0808133University of Texas at AustinAlfred P. Sloan FoundationParticipating InstitutionsNational Aeronautics and Space AdministrationU.S. Department of EnergyJapanese MonbukagakushoMax Planck SocietyAstronom

Ultraviolet spectroscopy of old novae and symbiotic stars

The IUE spectra are presented for two old novae and for two of the symbiotic variables. Prominent emission line spectra are revealed as a continuum whose appearance is effected by the system inclination. These data provide evidence for hot companions in the symbiotic stars, making plausible the binary model for these peculiar stars. Recent IUE spectra of dwarf novae provide additional support for the existence of optically thick accretion disks in active binary systems. The ultraviolet data of the eclipsing dwarf novae EX Hya and BV Cen appear flatter than for the noneclipsing systems, an effect which could be ascribed to the system inclination

Energy-Tunable Quantum Dot with Minimal Fine Structure Created by Using Simultaneous Electric and Magnetic Fields

The neutral biexciton cascade of single quantum dots is a promising source of entangled photon pairs. The character of the entangled state is determined by the energy difference between the excitonic eigenstates known as fine-structure splitting (FSS). Here we reduce the magnitude of the FSS by simultaneously using two independent tuning mechanisms: in-plane magnetic field and vertical electric field. We observe that there exists a minimum possible FSS in each quantum dot which is independent of these tuning mechanisms. However, with simultaneous application of electric and magnetic fields, we show the FSS can be reduced to its minimum value as the energy of emission is tuned over several meV with a 5-T magnet