Factorization of numbers with Gauss sums: I. Mathematical background

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially.Comment: 21 pages, 8 figure

Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.Comment: 22 pages, 7 figure

Microwave-activated conditional-phase gate for superconducting qubits

We introduce a new entangling gate between two fixed-frequency qubits statically coupled via a microwave resonator bus which combines the following desirable qualities: all-microwave control, appreciable qubit separation for reduction of crosstalk and leakage errors, and the ability to function as a two-qubit conditional-phase gate. A fixed, always-on interaction is explicitly designed between higher energy (non-computational) states of two transmon qubits, and then a conditional-phase gate is `activated' on the otherwise unperturbed qubit subspace via a microwave drive. We implement this microwave-activated conditional-phase gate with a fidelity from quantum process tomography of 87%.Comment: 5 figure

Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble

We demonstrate quantum control of a large spin-angular momentum associated with the F=3 hyperfine ground state of 133Cs. A combination of time dependent magnetic fields and a static tensor light shift is used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states, and may lead to improvement of some precision measurements.Comment: 4 pages, 4 figures (color

Probability of the resistive state formation caused by absorption of a single-photon in current-carrying superconducting nano-strips

We have studied supercurrent-assisted formation of the resistive state in nano-structured Nb and NbN superconducting films after absorption of a single photon. In amorphous narrow NbN strips the probability of the resistive state formation has a pronounced spectral cut-off. The corresponding threshold photon energy decreases with the bias current. Analysis of the experimental data in the framework of the generalized hot-spot model suggests that the quantum yield for near-infrared photons increases faster than the photon nergy. Relaxation of the resistive state depends on the photon energy making the phenomenon feasible for the development of energy resolving single-photon detectors.Comment: 9 pages, 9 figures, submitted to Eur. Phys. Journa

On the relationship of polar mesospheric cloud ice water content, particle radius and mesospheric temperature and its use in multi-dimensional models

The distribution of ice layers in the polar summer mesosphere (called polar mesospheric clouds or PMCs) is sensitive to background atmospheric conditions and therefore affected by global-scale dynamics. To investigate this coupling it is necessary to simulate the global distribution of PMCs within a 3-dimensional (3-D) model that couples large-scale dynamics with cloud microphysics. However, modeling PMC microphysics within 3-D global chemistry climate models (GCCM) is a challenge due to the high computational cost associated with particle following (Lagrangian) or sectional microphysical calculations. By characterizing the relationship between the PMC effective radius, ice water content (<i>iwc</i>), and local temperature (<i>T</i>) from an ensemble of simulations from the sectional microphysical model, the Community Aerosol and Radiation Model for Atmospheres (CARMA), we determined that these variables can be described by a robust empirical formula. The characterized relationship allows an estimate of an altitude distribution of PMC effective radius in terms of local temperature and <i>iwc</i>. For our purposes we use this formula to predict an effective radius as part of a bulk parameterization of PMC microphysics in a 3-D GCCM to simulate growth, sublimation and sedimentation of ice particles without keeping track of the time history of each ice particle size or particle size bin. This allows cost effective decadal scale PMC simulations in a 3-D GCCM to be performed. This approach produces realistic PMC simulations including estimates of the optical properties of PMCs. We validate the relationship with PMC data from the Solar Occultation for Ice Experiment (SOFIE)

Use of Sediment Bioassays to Verify Efficacy of Caulerpa taxifolia Eradication Treatments

Infestations of the marine macrophytic alga Caulerpa taxifolia were discovered in Agua Hedionda Lagoon, California in 2000. Rapid response actions included containment under pvc tarps coupled with injection of liquid sodium hypochlorite. To assess the efficacy of these treatments, replicated sediment cores were removed from representative treated sites and transferred to grow-out facilities. Similar cores from uninfested (control) sediments were removed, inoculated with viable explants of C. taxifolia and placed in grow-out facilities. Results from two sampling periods (1 year, 2 years post-treatment) showed that no viable C. taxifolia emerged in cores, and that inoculated “control” sediments supported normal growth. Eelgrass ( Zostera marina L.) seedlings emerged from native seed-banks in “treated” cores, which also supported growth of some invertebrates (annelid worms and hydroids). This study provided essential verification of C. taxifolia eradication efforts, and demonstrates the feasibility of incorporating quality control/quality assurance components in rapid response actions. Results of this study also suggest that seeds of eelgrass are viable for at least two years. (PDF has 9 pages.

Gauss sum factorization with cold atoms

We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.Comment: 4 pages, 5 figure

A concept of an automated function control for ambient aerosol measurements using mobility particle size spectrometers

An automated function control unit was developed to regularly check the ambient particle number concentration derived from a mobility particle size spectrometer as well as its zero-point behaviour. The function control allows unattended quality assurance experiments at remote air quality monitoring or research stations under field conditions. The automated function control also has the advantage of being able to get a faster system stability response than the recommended on-site comparisons with reference instruments. The method is based on a comparison of the total particle number concentration measured by a mobility particle size spectrometer and a condensation particle counter while removing diffusive particles smaller than 20 nm in diameter. In practice, the small particles are removed by a set of diffusion screens, as traditionally used in a diffusion battery. Another feature of the automated function control is to check the zero-point behaviour of the ambient aerosol passing through a high-efficiency particulate air (HEPA) filter. <br><br> The performance of the function control is illustrated with the aid of a 1-year data set recorded at Annaberg-Buchholz, a station in the Saxon air quality monitoring network. During the period of concern, the total particle number concentration derived from the mobility particle size spectrometer slightly overestimated the particle number concentration recorded by the condensation particle counter by 2 % (grand average). Based on our first year of experience with the function control, we developed tolerance criteria that allow a performance evaluation of a tested mobility particle size spectrometer with respect to the total particle number concentration. We conclude that the automated function control enhances the quality and reliability of unattended long-term particle number size distribution measurements. This will have beneficial effects for intercomparison studies involving different measurement sites, and help provide a higher data accuracy for cohort health and climate research studies

Entanglement of two superconducting qubits in a waveguide cavity via monochromatic two-photon excitation

We report a system where fixed interactions between non-computational levels make bright the otherwise forbidden two-photon 00 --> 11 transition. The system is formed by hand selection and assembly of two discrete component transmon-style superconducting qubits inside a rectangular microwave cavity. The application of a monochromatic drive tuned to this transition induces two-photon Rabi-like oscillations between the ground and doubly-excited states via the Bell basis. The system therefore allows all-microwave two-qubit universal control with the same techniques and hardware required for single qubit control. We report Ramsey-like and spin echo sequences with the generated Bell states, and measure a two-qubit gate fidelity of 90% (unconstrained) and 86% (maximum likelihood estimator).Comment: 5 pages, 4 figures. V2: add supplemental material about the Schrieffer-Wolff transformatio