Automated Synthesis of Dynamically Corrected Quantum Gates

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotations subject to realistic timing and pulse-shaping constraints are provided, which can deliver substantially improved gate fidelity for state-of-the-art experimental capabilities.Comment: 5 pages; further restructure and expansio

Lattice QCD-based equations of state at vanishing net-baryon density

We present realistic equations of state for QCD matter at vanishing net-baryon density which embed recent lattice QCD results at high temperatures combined with a hadron resonance gas model in the low-temperature, confined phase. In the latter, we allow an implementation of partial chemical equilibrium, in which particle ratios are fixed at the chemical freeze-out, so that a description closer to the experimental situation is possible. Given the present uncertainty in the determination of the chemical freeze-out temperature from first-principle lattice QCD calculations, we consider different values within the expected range. The corresponding equations of state can be applied in the hydrodynamic modeling of relativistic heavy-ion collisions at the LHC and at the highest RHIC beam energies. Suitable parametrizations of our results as functions of the energy density are also provided.Comment: Updated journal version with refined EoS-parametrization. July 2014. 8 pp. 4 figs. 3 parametrization-tables and weblink Ref. [45

Keplerian Squeezed States and Rydberg Wave Packets

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments.Comment: accepted for publication in Physical Review

Fluxoid fluctuations in mesoscopic superconducting rings

Rings are a model system for studying phase coherence in one dimension. Superconducting rings have states with uniform phase windings that are integer multiples of 2$\pi$ called fluxoid states. When the energy difference between these fluxoid states is of order the temperature so that phase slips are energetically accessible, several states contribute to the ring's magnetic response to a flux threading the ring in thermal equilibrium and cause a suppression or downturn in the ring's magnetic susceptibility as a function of temperature. We review the theoretical framework for superconducting fluctuations in rings including a model developed by Koshnick$^1$ which includes only fluctuations in the ring's phase winding number called fluxoid fluctuations and a complete model by von Oppen and Riedel$^2$ that includes all thermal fluctuations in the Ginzburg-Landau framework. We show that for sufficiently narrow and dirty rings the two models predict a similar susceptibility response with a slightly shifted Tc indicating that fluxoid fluctuations are dominant. Finally we present magnetic susceptibility data for rings with different physical parameters which demonstrate the applicability of our models. The susceptibility data spans a region in temperature where the ring transitions from a hysteretic to a non hysteretic response to a periodic applied magnetic field. The magnetic susceptibility data, taken where transitions between fluxoid states are slow compared to the measurement time scale and the ring response was hysteretic, decreases linearly with increasing temperature resembling a mean field response with no fluctuations. At higher temperatures where fluctuations begin to play a larger role a crossover occurs and the non-hysteretic data shows a fluxoid fluctuation induced suppression of diamagnetism below the mean field response that agrees well with the models

What Can We Learn from Nighttime Lights for Small Geographies? Measurement Errors and Heterogeneous Elasticities

Nighttime lights are routinely used as a proxy for economic activity when official statistics are unavailable and are increasingly applied to study the effects of shocks or policy interventions at small geographic scales. The implicit assumption is that the ability of nighttime lights to pick up changes in GDP does not depend on local characteristics of the region under investigation or the scale of aggregation. This study uses panel data on regional GDP growth from six countries, and nighttime lights from the Defense Meteorological Satellite Program (DMSP) to investigate potential nonlinearities and measurement errors in the light production function. Our results for high statistical capacity countries (the United States and Germany) show that nightlights are significantly less responsive to changes in GDP at higher baseline level of GDP, higher population densities, and for agricultural GDP. We provide evidence that these nonlinearities are too large to be caused by differences in measurement errors across regions. We find similar but noisier relationships in other high-income countries (Italy and Spain) and emerging economies (Brazil and China). We also present results for different aggregation schemes and find that the overall relationship, including the nonlinearity, is stable across regions of different shapes and sizes but becomes noisier when regions become few and large. These findings have important implications for studies using nighttime lights to evaluate the economic effects of shocks or policy interventions. On average, nighttime lights pick up changes in GDP across many different levels of aggregation, down to relatively small geographies. However, the nonlinearity we document in this paper implies that some studies may fail to detect policy-relevant effects in places where lights react little to changes in economic activity or they may mistakenly attribute this heterogeneity to the treatment effect of their independent variable of interest

Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect

The quantum Hall effect is necessarily accompanied by low-energy excitations localized at the edge of a two-dimensional electron system. For the case of electrons interacting via the long-range Coulomb interaction, these excitations are edge magnetoplasmons. We address the time evolution of localized edge-magnetoplasmon wave packets. On short times the wave packets move along the edge with classical E cross B drift. We show that on longer times the wave packets can have properties similar to those of the Rydberg wave packets that are produced in atoms using short-pulsed lasers. In particular, we show that edge-magnetoplasmon wave packets can exhibit periodic revivals in which a dispersed wave packet reassembles into a localized one. We propose the study of edge-magnetoplasmon wave packets as a tool to investigate dynamical properties of integer and fractional quantum-Hall edges. Various scenarios are discussed for preparing the initial wave packet and for detecting it at a later time. We comment on the importance of magnetoplasmon-phonon coupling and on quantum and thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was originally 3Mbyte and had to be bitmapped for submission to archive; in the process it acquired distracting artifacts, to upload the better version, see http://physics.indiana.edu/~uli/publ/projects.htm

Fluctuation Superconductivity in Mesoscopic Aluminum Rings

Fluctuations are important near phase transitions, where they can be difficult to describe quantitatively. Superconductivity in mesoscopic rings is particularly intriguing because the critical temperature is an oscillatory function of magnetic field. There is an exact theory for thermal fluctuations in one-dimensional superconducting rings, which are therefore expected to be an excellent model system. We measure the susceptibility of many rings, one ring at a time, using a scanning SQUID that can isolate magnetic signals from seven orders of magnitude larger background applied flux. We find that the fluctuation theory describes the results and that a single parameter characterizes the ways in which the fluctuations are especially important at magnetic fields where the critical temperature is suppressed.Comment: Reprinted with permission from AAA

Persistent currents in normal metal rings

The authors have measured the magnetic response of 33 individual cold mesoscopic gold rings, one ring at a time. The response of some sufficiently small rings has a component that is periodic in the flux through the ring and is attributed to a persistent current. Its period is close to h/e, and its sign and amplitude vary between rings. The amplitude distribution agrees well with predictions for the typical h/e current in diffusive rings. The temperature dependence of the amplitude, measured for four rings, is also consistent with theory. These results disagree with previous measurements of three individual metal rings that showed a much larger periodic response than expected. The use of a scanning SQUID microscope enabled in situ measurements of the sensor background. A paramagnetic linear susceptibility and a poorly understood anomaly around zero field are attributed to defect spins.Comment: Journal version. 4+ pages, 3 figures. See http://stanford.edu/group/moler/publications.html for the auxiliary document containing additional data and discussion (Ref. 29). Changes w.r.t. v1: Clarified some details in introduction and regarding experimental procedures, shortened abstract, added references and fixed some typo