Ground state cooling of a nanomechanical resonator in the weak-confinement regime via quantum interference

Ground state cooling of a nanomechanical resonator coupled to a superconducting flux qubit is discussed. We show that by inducing quantum interference to cancel detrimental carrier excitations, ground state cooling becomes possible in the weak-confinement or non-resolved regime. The qubit is modelled as a three-level system in lambda configuration, and the driving fluxes are applied such that the qubit absorption spectrum exhibits electromagnetically induced transparency, thereby cancelling the unwanted carrier excitation. As our interference-based scheme allows to apply strong cooling fields, fast and efficient cooling can be achieved

X-ray quantum optics with M\"ossbauer nuclei embedded in thin film cavities

A promising platform for the emerging field of x-ray quantum optics are M\"ossbauer nuclei embedded in thin film cavities probed by near-resonant x-ray light, as used in a number of recent experiments. Here, we develop a quantum optical framework for the description of experimentally relevant settings involving nuclei embedded in x-ray waveguides. We apply our formalism to two settings of current experimental interest based on the archetype M\"ossbauer isotope 57Fe. For present experimental conditions, we derive compact analytical expressions and show that the alignment of medium magnetization as well as incident and detection polarization enable the engineering advanced quantum optical level schemes. The model encompasses non-linear and quantum effects which could become accessible in future experiments.Comment: 13 pages, 6 figure

Collective effects between multiple nuclear ensembles in an x-ray cavity-QED setup

The setting of Moessbauer nuclei embedded in thin-film cavities has facilitated an aspiring platform for x-ray quantum optics as shown in several recent experiments. Here, we generalize the theoretical model of this platform that we developed earlier [Phys. Rev. A 88, 043828 (2013)]. The theory description is extended to cover multiple nuclear ensembles and multiple modes in the cavity. While the extensions separately do not lead to qualitatively new features, their combination gives rise to cooperative effects between the different nuclear ensembles and distinct spectral signatures in the observables. A related experiment by Roehlsberger et al. [Nature 482, 199 (2012)] is successfully modeled, the scalings derived with semiclassical methods are reproduced, and a microscopic understanding of the setting is obtained with our quantum mechanical description.Comment: 18 pages, 6 figure

Dynamic formation of Rydberg aggregates at off-resonant excitation

The dynamics of a cloud of ultra-cold two-level atoms is studied at off-resonant laser driving to a Rydberg state. We find that resonant excitation channels lead to strongly peaked spatial correlations associated with the buildup of asymmetric excitation structures. These aggregates can extend over the entire ensemble volume, but are in general not localized relative to the system boundaries. The characteristic distances between neighboring excitations depend on the laser detuning and on the interaction potential. These properties lead to characteristic features in the spatial excitation density, the Mandel $Q$ parameter, and the total number of excitations. As an application an implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is discussed. The gate not only exploits the Rydberg blockade, but also utilizes the special features of an asymmetric geometric arrangement of the three atoms. We show that continuous-wave off-resonant laser driving is sufficient to create the required spatial arrangement of atoms out of a homogeneous cloud.Comment: 8 pages, 7 figure

Pulse-splitting in light propagation through NN-type atomic media due to an interplay of Kerr-nonlinearity and group velocity dispersion

We investigate the spatio-temporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe-and control fields, weaker probe pulses may propagate through the medium with low absorption and pulse shape distortion. In contrast, we find that increasing the probe pulse intensity leads to a splitting of the initially Gaussian pulse into a sequence of subpulses in the time domain. The number of subpulses arising throughout the propagation can be controlled via a suitable choice of the probe and control field parameters. Employing a simple theoretical model for the nonlinear pulse propagation, we conclude that the splitting occurs due to an interplay of Kerr nonlinearity and group velocity dispersion.Comment: 9 pages, 7 figure

Paradoxes of leadership: Contingencies and critical learning

No Abstract.South African Journal of Education Vol. 27(3) 2007: pp. 377-39

Data compression and regression based on local principal curves.

Frequently the predictor space of a multivariate regression problem of the type y = m(x_1, …, x_p ) + ε is intrinsically one-dimensional, or at least of far lower dimension than p. Usual modeling attempts such as the additive model y = m_1(x_1) + … + m_p (x_p ) + ε, which try to reduce the complexity of the regression problem by making additional structural assumptions, are then inefficient as they ignore the inherent structure of the predictor space and involve complicated model and variable selection stages. In a fundamentally different approach, one may consider first approximating the predictor space by a (usually nonlinear) curve passing through it, and then regressing the response only against the one-dimensional projections onto this curve. This entails the reduction from a p- to a one-dimensional regression problem. As a tool for the compression of the predictor space we apply local principal curves. Taking things on from the results presented in Einbeck et al. (Classification – The Ubiquitous Challenge. Springer, Heidelberg, 2005, pp. 256–263), we show how local principal curves can be parametrized and how the projections are obtained. The regression step can then be carried out using any nonparametric smoother. We illustrate the technique using data from the physical sciences

Exact relations between multifractal exponents at the Anderson transition

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with indices $q1/2$. The second relation connects the wave function multifractality to that of Wigner delay times in a system with a lead attached.Comment: 4 pages, 3 figure