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

Magnetic field stabilization system for atomic physics experiments

Atomic physics experiments commonly use millitesla-scale magnetic fields to provide a quantization axis. As atomic transition frequencies depend on the amplitude of this field, many experiments require a stable absolute field. Most setups use electromagnets, which require a power supply stability not usually met by commercially available units. We demonstrate stabilization of a field of 14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of $\gtrsim$ 100 nT without any stabilization. The rms noise is measured using a field-dependent hyperfine transition in a single $^{43}$Ca$^+$ ion held in a Paul trap at the centre of the magnetic field coils. For the $^{43}$Ca$^+$ "atomic clock" qubit transition at 14.6 mT, which depends on the field only in second order, this would yield a projected coherence time of many hours. Our system consists of a feedback loop and a feedforward circuit that control the current through the field coils and could easily be adapted to other field amplitudes, making it suitable for other applications such as neutral atom traps.Comment: 6 pages, 5 figure

Precision spectral manipulation of optical pulses using a coherent photon echo memory

Photon echo schemes are excellent candidates for high efficiency coherent optical memory. They are capable of high-bandwidth multi-pulse storage, pulse resequencing and have been shown theoretically to be compatible with quantum information applications. One particular photon echo scheme is the gradient echo memory (GEM). In this system, an atomic frequency gradient is induced in the direction of light propagation leading to a Fourier decomposition of the optical spectrum along the length of the storage medium. This Fourier encoding allows precision spectral manipulation of the stored light. In this letter, we show frequency shifting, spectral compression, spectral splitting, and fine dispersion control of optical pulses using GEM

Efficient measurement of quantum gate error by interleaved randomized benchmarking

We describe a scalable experimental protocol for obtaining estimates of the error rate of individual quantum computational gates. This protocol, in which random Clifford gates are interleaved between a gate of interest, provides a bounded estimate of the average error of the gate under test so long as the average variation of the noise affecting the full set of Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find gate errors that compare favorably with the gate errors extracted via quantum process tomography.Comment: 5 pages, 2 figures, published versio

Stress Balance in Synthetic Serpentinized Peridotites Deformed at Subduction Zone Pressures

Weak serpentine minerals affect the mechanical behavior of serpentinized peridotites at depth, and may play a significant role in deformation localization within subduction zones, at local or regional scale. Mixtures of olivine with 5, 10, 20 and 50 vol. % fraction of antigorite, proxies for serpentinized peridotites, were deformed in axial shortening geometry under high pressures (ca. 2–5 GPa) and moderate temperatures (ca. 350°C), with in situ stress and strain measurements using synchrotron X-rays. We evaluate the average partitioning of stresses at the grains scale within each phase (mineral) of the aggregate and compare with pure olivine aggregates in the same conditions. The in situ stress balance is different between low antigorite contents up to 10 vol. %, and higher contents above 20 vol. %. Microstructure and stress levels suggest the deformation mechanisms under these experimental conditions are akin to (semi)brittle and frictional processes. Unlike when close to dehydration temperatures, hardening of the aggregate is observed at low serpentine fractions, due to an increase in local stress concentrations. Below and above the 10–20 vol. % threshold, the stress state in the aggregate corresponds to friction laws already measured for pure olivine aggregates and pure antigorite aggregates respectively. As expected, the behavior of the two-phase aggregate does not evolve as calculated from simple iso-stress or iso-strain bounds, and calls for more advanced physical models of two-phase mixtures

Recoil polarization and beam-recoil double polarization measurement of \eta electroproduction on the proton in the region of the S_{11}(1535) resonance

The beam-recoil double polarization P_{x'}^h and P_{z'}^h and the recoil polarization P_{y'} were measured for the first time for the p(\vec{e},e'\vec{p})\eta reaction at a four-momentum transfer of Q^2=0.1 GeV^2/c^2 and a center of mass production angle of \theta = 120^\circ at MAMI C. With a center of mass energy range of 1500 MeV < W < 1550 MeV the region of the S_{11}(1535) and D_{13}(1520) resonance was covered. The results are discussed in the framework of a phenomenological isobar model (Eta-MAID). While P_{x'}^h and P_{z'}^h are in good agreement with the model, P_{y'} shows a significant deviation, consistent with existing photoproduction data on the polarized-target asymmetry.Comment: 4 pages, 1 figur

Beam-Normal Single Spin Asymmetry in Elastic Electron Scattering off 28^{28}Si and 90^{90}Zr

We report on a new measurement of the beam-normal single spin asymmetry $A_{\mathrm{n}}$ in the elastic scattering of 570 MeV transversely polarized electrons off $^{28}$Si and $^{90}$Zr at $Q^{2}=0.04\, \mathrm{GeV}^2/c^2$. The studied kinematics allow for a comprehensive comparison with former results on $^{12}$C. No significant mass dependence of the beam-normal single spin asymmetry is observed in the mass regime from $^{12}$C to $^{90}$Zr.Comment: Submitted for publication to Physics Letters

The implausibility of ‘usual care’ in an open system: sedation and weaning practices in Paediatric Intensive Care Units (PICUs) in the United Kingdom (UK)

Background: The power of the randomised controlled trial depends upon its capacity to operate in a closed system whereby the intervention is the only causal force acting upon the experimental group and absent in the control group, permitting a valid assessment of intervention efficacy. Conversely, clinical arenas are open systems where factors relating to context, resources, interpretation and actions of individuals will affect implementation and effectiveness of interventions. Consequently, the comparator (usual care) can be difficult to define and variable in multi-centre trials. Hence outcomes cannot be understood without considering usual care and factors that may affect implementation and impact on the intervention. Methods: Using a fieldwork approach, we describe PICU context, ‘usual’ practice in sedation and weaning from mechanical ventilation, and factors affecting implementation prior to designing a trial involving a sedation and ventilation weaning intervention. We collected data from 23 UK PICUs between June and November 2014 using observation, individual and multi-disciplinary group interviews with staff. Results: Pain and sedation practices were broadly similar in terms of drug usage and assessment tools. Sedation protocols linking assessment to appropriate titration of sedatives and sedation holds were rarely used (9 % and 4 % of PICUs respectively). Ventilator weaning was primarily a medical-led process with 39 % of PICUs engaging senior nurses in the process: weaning protocols were rarely used (9 % of PICUs). Weaning methods were variably based on clinician preference. No formal criteria or use of spontaneous breathing trials were used to test weaning readiness. Seventeen PICUs (74 %) had prior engagement in multi-centre trials, but limited research nurse availability. Barriers to previous trial implementation were intervention complexity, lack of belief in the evidence and inadequate training. Facilitating factors were senior staff buy-in and dedicated research nurse provision. Conclusions: We examined and identified contextual and organisational factors that may impact on the implementation of our intervention. We found usual practice relating to sedation, analgesia and ventilator weaning broadly similar, yet distinctively different from our proposed intervention, providing assurance in our ability to evaluate intervention effects. The data will enable us to develop an implementation plan; considering these factors we can more fully understand their impact on study outcomes