Note on Invariants of the Weyl Tensor

Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.Comment: 3 pages, no figures, corrected expression (12

Infinite-Dimensional Estabrook-Wahlquist Prolongations for the sine-Gordon Equation

We are looking for the universal covering algebra for all symmetries of a given pde, using the sine-Gordon equation as a typical example for a non-evolution equation. For non-evolution equations, Estabrook-Wahlquist prolongation structures for non-local symmetries depend on the choice of a specific sub-ideal, of the contact module, to define the pde. For each inequivalent such choice we determine the most general solution of the prolongation equations, as sub-algebras of the (infinite-dimensional) algebra of all vector fields over the space of non-local variables associated with the pde, in the style of Vinogradov covering spaces. We show explicitly how previously-known prolongation structures, known to lie within the Kac-Moody algebra, $A_1^{(1)}$, are special cases of these general solutions, although we are unable to identify the most general solutions with previously-studied algebras. We show the existence of gauge transformations between prolongation structures, viewed as determining connections over the solution space, and use these to relate (otherwise) distinct algebras. Faithful realizations of the universal algebra allow integral representations of the prolongation structure, opening up interesting connections with algebras of Toeplitz operators over Banach spaces, an area that has only begun to be explored.Comment: 46 pages, plain TeX, no figures, to be published in J. Math. Phys

X-Ray Spectral Variability of Extreme BL Lac AGN H1426+428

Between 7 March 2002 and 15 June 2002, intensive X-ray observations were carried out on the extreme BL Lac object H1426+428 with instruments on board the Rossi X-ray Timing Explorer (RXTE). These instruments provide measurements of H1426+428 in the crucial energy range that characterizes the first peak of its spectral energy distribution. This peak, which is almost certainly due to synchrotron emission, has previously been inferred to be in excess of 100 keV. By taking frequent observations over a four-month campaign, which included $\sim$450 ksec of RXTE time, studies of flux and spectral variability on multiple timescales were performed, along with studies of spectral hysteresis. The 3-24 keV X-ray flux and spectra exhibited significant variability, implying variability in the location of the first peak of the spectral energy distribution. Hysteresis patterns were observed, and their characteristics have been discussed within the context of emission models.Comment: accepted for publication in Astrophysical Journa

Probing spin relaxation in an individual InGaAs quantum dot using a single electron optical spin memory device

We demonstrate all optical electron spin initialization, storage and readout in a single self-assembled InGaAs quantum dot. Using a single dot charge storage device we monitor the relaxation of a single electron over long timescales exceeding 40{\mu}s. The selective generation of a single electron in the quantum dot is performed by resonant optical excitation and subsequent partial exciton ionization; the hole is removed from the quantum dot whilst the electron remains stored. When subject to a magnetic field applied in Faraday geometry, we show how the spin of the electron can be prepared with a polarization up to 65% simply by controlling the voltage applied to the gate electrode. After generation, the electron spin is stored in the quantum dot before being read out using an all optical implementation of spin to charge conversion technique, whereby the spin projection of the electron is mapped onto the more robust charge state of the quantum dot. After spin to charge conversion, the charge state of the dot is repeatedly tested by pumping a luminescence recycling transition to obtain strong readout signals. In combination with spin manipulation using fast optical pulses or microwave pulses, this provides an ideal basis for probing spin coherence in single self-assembled quantum dots over long timescales and developing optimal methods for coherent spin control

New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential equation is given. Alternatively, the mentioned first integral can be used in order to provide a first integral of the second-order complex equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in Class. Quantum Gra

Direct Observation of Controlled Coupling in an Individual Quantum Dot Molecule

We report the direct observation of quantum coupling in individual quantum dot molecules and its manipulation using static electric fields. A pronounced anti-crossing of different excitonic transitions is observed as the electric field is tuned. Comparison of our experimental results with theory shows that the observed anti-crossing occurs between excitons with predominant spatially \emph{direct} and \emph{indirect} character. The electron component of the exciton wavefunction is shown to have molecular character at the anti-crossing and the quantum coupling strength is deduced optically. In addition, we determine the dependence of the coupling strength on the inter-dot separation and identify a field driven transition of the nature of the molecular ground state.Comment: 11 pages, 4 figures submitted to Physical Review Letter

Enhanced photoluminescence emission from two-dimensional silicon photonic crystal nanocavities

We present a temperature dependent photoluminescence study of silicon optical nanocavities formed by introducing point defects into two-dimensional photonic crystals. In addition to the prominent TO phonon assisted transition from crystalline silicon at ~1.10 eV we observe a broad defect band luminescence from ~1.05-1.09 eV. Spatially resolved spectroscopy demonstrates that this defect band is present only in the region where air-holes have been etched during the fabrication process. Detectable emission from the cavity mode persists up to room-temperature, in strong contrast the background emission vanishes for T > 150 K. An Ahrrenius type analysis of the temperature dependence of the luminescence signal recorded either in-resonance with the cavity mode, or weakly detuned, suggests that the higher temperature stability may arise from an enhanced internal quantum efficiency due to the Purcell-effect

Recent advances in exciton based quantum information processing in quantum dot nanostructures

Recent experimental developments in the field of semiconductor quantum dot spectroscopy will be discussed. First we report about single quantum dot exciton two-level systems and their coherent properties in terms of single qubit manipulations. In the second part we report on coherent quantum coupling in a prototype "two-qubit" system consisting of a vertically stacked pair of quantum dots. The interaction can be tuned in such quantum dot molecule devices using an applied voltage as external parameter.Comment: 37 pages, 15 figures, submitted to New Journal of Physics, focus issue on Solid State Quantum Information, added reference

Twisting type-N vacuum fields with a group H2H_2

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two non-commuting Killing vectors. We study the case when the homothetic parameter $\phi$ takes the value -1, which is shown to admit a reduction to a third-order real ordinary differential equation for this problem, similar to that previously obtained by one of us when two Killing vectors are present.Comment: LaTeX, 11 pages. To be published in Classical and Quantum Gravit