P. Becker

University of Oxford, Oxford, ENG, United Kingdom

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Publications (110)310.64 Total impact

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    ABSTRACT: We present a complete theoretical treatment of Stark effects in doped silicon, whose predictions are supported by experimental measurements. A multi-valley effective mass theory, dealing non-perturbatively with valley-orbit interactions induced by a donor-dependent central cell potential, allows us to obtain a very reliable picture of the donor wave function within a relatively simple framework. Variational optimization of the 1s donor binding energies calculated with a new trial wave function, in a pseudopotential with two fitting parameters, allows an accurate match of the experimentally determined donor energy levels, while the correct limiting behavior for the electronic density, both close to and far from each impurity nucleus, is captured by fitting the measured contact hyperfine coupling between the donor nuclear and electron spin. We go on to include an external uniform electric field in order to model Stark physics: With no extra ad hoc parameters, variational minimization of the complete donor ground energy allows a quantitative description of the field-induced reduction of electronic density at each impurity nucleus. Detailed comparisons with experimental values for the shifts of the contact hyperfine coupling reveal very close agreement for all the donors measured (P, As, Sb and Bi). Finally, we estimate field ionization thresholds for the donor ground states, thus setting upper limits to the gate manipulation times for single qubit operations in Kane-like architectures: the Si:Bi system is shown to allow for A gates as fast as around 10 MHz.
    08/2014;
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    ABSTRACT: The effects of host isotope mass on the hyperfine interaction of group-V donors in silicon are revealed by pulsed electron nuclear double resonance (ENDOR) spectroscopy of isotopically engineered Si single crystals. Each of the hyperfine-split P-31, As-75, Sb-121, Sb-123, and Bi-209 ENDOR lines splits further into multiple components, whose relative intensities accurately match the statistical likelihood of the nine possible average Si masses in the four nearest-neighbor sites due to random occupation by the three stable isotopes Si-28, Si-29, and Si-30. Further investigation with P-31 donors shows that the resolved ENDOR components shift linearly with the bulk-averaged Si mass.
    07/2014;
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    ABSTRACT: We experimentally demonstrate the inductive readout of optically hyperpolarized phosphorus-31 donor nuclear spins in an isotopically enriched silicon-28 crystal. The concentration of phosphorus donors in the crystal was 1.5 x 10$^{15}$ cm$^{-3}$, three orders of magnitude lower than has previously been detected via direct inductive detection. The signal-to-noise ratio measured in a single free induction decay from a 1 cm$^3$ sample ($\approx 10^{15}$ spins) was 113. By transferring the sample to an X-band ESR spectrometer, we were able to obtain a lower bound for the nuclear spin polarization at 1.7 K of 42 %. The $^{31}$P-T$_{2}$ measured with a Hahn echo sequence was 420 ms at 1.7 K, which was extended to 1.2 s with a Carr Purcell cycle. The T$_1$ of the $^{31}$P nuclear spins at 1.7 K is extremely long and could not be determined, as no decay was observed even on a timescale of 4.5 hours. Optical excitation was performed with a 1047 nm laser, which provided above bandgap excitation of the silicon. The build-up of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the build-up at 1.7 K showed bi-exponential behavior with characteristic time constants of 578 s and 5670 s.
    07/2014;
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    ABSTRACT: Electric fields can be used to tune donor spins in silicon using the Stark shift, whereby the donor electron wave function is displaced by an electric field, modifying the hyperfine coupling between the electron spin and the donor nuclear spin. We present a technique based on dynamic decoupling of the electron spin to accurately determine the Stark shift, and illustrate this using antimony donors in isotopically purified silicon-28. We then demonstrate two different methods to use a DC electric field combined with an applied resonant radio-frequency (RF) field to conditionally control donor nuclear spins. The first method combines an electric-field induced conditional phase gate with standard RF pulses, and the second one simply detunes the spins off-resonance. Finally, we consider different strategies to reduce the effect of electric field inhomogeneities and obtain above 90% process fidelities.
    05/2014;
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    ABSTRACT: We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field ($B_{1}$) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported showing a single shot (no signal averaging) sensitivity to $10^{7}$ spins or $3 \times 10^{4}$ spins/$\sqrt{Hz}$ with averaging.
    02/2014;
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    ABSTRACT: Quantum memories capable of storing and retrieving coherent information for extended times at room temperature would enable a host of new technologies. Electron and nuclear spin qubits using shallow neutral donors in semiconductors have been studied extensively but are limited to low temperatures (≲10 kelvin); however, the nuclear spins of ionized donors have the potential for high-temperature operation. We used optical methods and dynamical decoupling to realize this potential for an ensemble of phosphorous-31 donors in isotopically purified silicon-28 and observed a room-temperature coherence time of over 39 minutes. We further showed that a coherent spin superposition can be cycled from 4.2 kelvin to room temperature and back, and we report a cryogenic coherence time of 3 hours in the same system.
    Science 11/2013; 342(6160):830-833. · 31.20 Impact Factor
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    ABSTRACT: A major challenge in using spins in the solid state for quantum technologies is protecting them from sources of decoherence. This is particularly important in nanodevices where the proximity of material interfaces, and their associated defects, can play a limiting role. Spin decoherence can be addressed to varying degrees by improving material purity or isotopic composition, for example, or active error correction methods such as dynamic decoupling (or even combinations of the two). However, a powerful method applied to trapped ions in the context of atomic clocks is the use of particular spin transitions that are inherently robust to external perturbations. Here, we show that such 'clock transitions' can be observed for electron spins in the solid state, in particular using bismuth donors in silicon. This leads to dramatic enhancements in the electron spin coherence time, exceeding seconds. We find that electron spin qubits based on clock transitions become less sensitive to the local magnetic environment, including the presence of (29)Si nuclear spins as found in natural silicon. We expect the use of such clock transitions will be of additional significance for donor spins in nanodevices, mitigating the effects of magnetic or electric field noise arising from nearby interfaces and gates.
    Nature Nanotechnology 06/2013; · 31.17 Impact Factor
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    ABSTRACT: High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. In electron spin resonance, manipulation of the quantum spin is usually achieved with time-dependent microwave fields. In contrast to the conventional dynamic approach, adiabatic geometric phase operations are expected to be less sensitive to certain kinds of noise and field inhomogeneities. Here, we investigate such phase gates applied to electron spins both through simulations and experiments, showing that the adiabatic geometric phase gate is indeed inherently robust against inhomogeneity in the applied microwave field strength. While only little advantage is offered over error-correcting composite pulses for modest inhomogeneities <=10%, the adiabatic approach reveals its potential for situations where field inhomogeneities are unavoidably large.
    Physical Review A 08/2012; 87(3). · 3.04 Impact Factor
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    ABSTRACT: Bismuth (209Bi) is the deepest Group V donor in silicon and possesses the most extreme characteristics such as a 9/2 nuclear spin and a 1.5 GHz hyperfine coupling. These lead to several potential advantages for a Si:Bi donor electron spin qubit compared to the more common phosphorus donor. Previous studies on Si:Bi have been performed using natural silicon where linewidths and electron spin coherence times are limited by the presence of 29Si impurities. Here we describe electron spin resonance (ESR) and electron nuclear double resonance (ENDOR) studies on 209Bi in isotopically pure 28Si. ESR and ENDOR linewidths, transition probabilities and coherence times are understood in terms of the spin Hamiltonian parameters showing a dependence on field and mI of the 209Bi nuclear spin. We explore various decoherence mechanisms applicable to the donor electron spin, measuring coherence times up to 700 ms at 1.7 K at X-band, comparable with 28Si:P. The coherence times we measure follow closely the calculated field-sensitivity of the transition frequency, providing a strong motivation to explore 'clock' transitions where coherence lifetimes could be further enhanced.
    Physical review. B, Condensed matter 07/2012; 86(24). · 3.77 Impact Factor
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    ABSTRACT: A quantum computer requires systems that are isolated from their environment, but can be integrated into devices, and whose states can be measured with high accuracy. Nuclear spins in solids promise long coherence lifetimes, but they are difficult to initialize into known states and to detect with high sensitivity. We show how the distinctive optical properties of enriched (28)Si enable the use of hyperfine-resolved optical transitions, as previously applied to great effect for isolated atoms and ions in vacuum. Together with efficient Auger photoionization, these resolved hyperfine transitions permit rapid nuclear hyperpolarization and electrical spin-readout. We combine these techniques to detect nuclear magnetic resonance from dilute (31)P in the purest available sample of (28)Si, at concentrations inaccessible to conventional measurements, measuring a solid-state coherence time of over 180 seconds.
    Science 06/2012; 336(6086):1280-3. · 31.20 Impact Factor
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    ABSTRACT: a b s t r a c t A new approach for producing high-purity silicon with isotopic enrichment of 28 Si isotope is reported. The methods of centrifugal enrichment were modified to obtain the initial gaseous silicon tetrafluoride with a record-breaking enrichment of 0.99999664(11) with respect to 28 Si. The effective conversion of silicon tetrafluoride into elementary silicon with minimal isotopic dilution was achieved in an electron cyclotron resonance discharge plasma, sustained by gyrotron microwave radiation with a frequency of 24 GHz. We have experimentally demonstrated the deposition of the layers of microcrystalline 28 Si with enrichment of 0.999986 ± 0.000003, which is the best result at the present time.
    Solid State Communications 01/2012; 152:455-457. · 1.53 Impact Factor
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    ABSTRACT: The quantum superposition principle states that an entity can exist in two different states simultaneously, counter to our 'classical' intuition. Is it possible to understand a given system's behaviour without such a concept? A test designed by Leggett and Garg can rule out this possibility. The test, originally intended for macroscopic objects, has been implemented in various systems. However to date no experiment has employed the 'ideal negative result' measurements that are required for the most robust test. Here we introduce a general protocol for these special measurements using an ancillary system, which acts as a local measuring device but which need not be perfectly prepared. We report an experimental realization using spin-bearing phosphorus impurities in silicon. The results demonstrate the necessity of a non-classical picture for this class of microscopic system. Our procedure can be applied to systems of any size, whether individually controlled or in a spatial ensemble.
    Nature Communications 01/2012; 3:606. · 10.02 Impact Factor
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    ABSTRACT: Silicon is one of the most promising semiconductor materials for spin-based information processing devices. Its advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of a (28)Si form with no magnetic nuclei overcomes a primary source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than that achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in pure (28)Si material (residual (29)Si concentration <50 ppm) with donor densities of 10(14)-10(15) cm(-3). We elucidate three mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime T(2) up to 2 s. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. A magnetic field gradient suppresses such interactions, producing an extrapolated electron spin T(2) of 10 s at 1.8 K. These coherence lifetimes are without peer in the solid state and comparable to high-vacuum qubits, making electron spins of donors in silicon ideal components of quantum computers, or quantum memories for systems such as superconducting qubits.
    Nature Material 12/2011; 11(2):143-7. · 35.75 Impact Factor
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    ABSTRACT: Deep luminescence centers in Si associated with transition metals have been studied for decades, both as markers for these deleterious contaminants, as well as for the possibility of efficient Si-based light emission. They are among the most ubiquitous luminescence centers observed in Si, and have served as testbeds for elucidating the physics of isoelectronic bound excitons, and for testing ab-initio calculations of defect properties. The greatly improved spectral resolution resulting from the elimination of inhomogeneous isotope broadening in the recently available highly enriched 28Si enabled the extension of the established technique of isotope shifts to the measurement of isotopic fingerprints, which reveal not only the presence of a given element in a luminescence center, but also the number of atoms of that element. This has resulted in many surprises regarding the actual constituents of what were thought to be well-understood deep luminescence centers. Here we summarize the available information for four families of centers containing either four or five atoms chosen from (Li, Cu, Ag, Au, Pt). The no-phonon transition energies, their isotope shifts, and the local vibrational mode energies presented here for these deep centers should prove useful for the still-needed theoretical explanations of their formation, stability and properties.
    Journal of Applied Physics 10/2011; 110(8):081301-081301-25. · 2.21 Impact Factor
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    ABSTRACT: Electron paramagnetic resonance (EPR) experiments on boron acceptors in isotopically engineered 28Si samples with different degrees of chemical and isotopic purity are reported. The strong suppression of isotope-induced broadening effects in this material allows a direct observation of the linear correlation between the width of the inter-subband Δm = 1 EPR line and the concentrations of carbon, oxygen, and boron point defects down to a total concentration of ≈2 × 1015 cm−3. When the impurity level is decreased further, the linewidth does not fall below 2.3 ± 0.2 mT, for which we discuss possible origins.
    Applied Physics Letters 07/2011; 99(3):032101-032101-3. · 3.79 Impact Factor
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    ABSTRACT: This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.
    Metrologia 03/2011; 48(2):S1. · 1.90 Impact Factor
  • S Valkiers, G Mana, K Fujii, P Becker
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    ABSTRACT: A procedure is described to obtain SI-traceable silicon isotope amount ratios in the BaSiF6 form. On the basis of a gravimetric approach, three synthetic isotope mixtures were made, very similar to natural Si, by blending silicon isotopically enriched with 28Si, 29Si and 30Si. These mixtures served as references to calibrate measurements of (SiF3)+ current ratios. In this way, it was possible to make SI-traceable measurements of silicon isotope amount ratios, without any assumptive correction. The isotopic composition of the natural Si crystal WASO17.2 was remeasured and its molar mass was redetermined.
    Metrologia 03/2011; 48(2):S26. · 1.90 Impact Factor
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    ABSTRACT: We report on electron spin coherence measurements for phosphorus donors in high purity, highly-enriched ^28Si, with residual ^29Si of less than 50 ppm. At this low ^29Si density, spectral diffusion processes by nuclear spin flip-flops are suppressed, and therefore other relaxation processes become prominent. By examining a series of ^28Si crystals with a donor concentration of 1x10^14 to 3x10^15/cm^3, we identified three decoherence mechanisms, all related to dipole interactions between donors: (1) instantaneous diffusion, caused by flips of donor spins induced by the applied microwave pulses; (2) spectral diffusion caused by T1-induced flips of neighboring donors; (3) spectral diffusion caused by donor spin flip-flops. We demonstrate how all three mechanisms can be suppressed, leading to measured coherence times extrapolating to T2˜10 sec. The work was funded by DOE and LPS.
    03/2011;
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    ABSTRACT: Entanglement is the quintessential quantum phenomenon. It is a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing and the strongest forms of quantum cryptography. Spin ensembles, such as those used in liquid-state nuclear magnetic resonance, have been important for the development of quantum control methods. However, these demonstrations contain no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered, phosphorus-doped silicon. We combined high-field (3.4 T), low-temperature (2.9 K) electron spin resonance with hyperpolarization of the (31)P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% relative to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, on 10(10) spin pairs; this fulfils one of the essential requirements for a silicon-based quantum information processor.
    Nature 02/2011; 470(7332):69-72. · 38.60 Impact Factor
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    ABSTRACT: The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.
    Physical Review Letters 01/2011; 106(3):030801. · 7.73 Impact Factor

Publication Stats

992 Citations
310.64 Total Impact Points

Institutions

  • 2011–2013
    • University of Oxford
      • Department of Materials
      Oxford, ENG, United Kingdom
  • 2007–2012
    • Simon Fraser University
      • Department of Physics
      Burnaby, British Columbia, Canada
  • 1981–2012
    • Physikalisch-Technische Bundesanstalt
      Brunswyck, Lower Saxony, Germany
  • 2000
    • University of Wisconsin, Madison
      • Department of Materials Science and Engineering
      Madison, MS, United States
  • 1992
    • University of Antwerp
      Antwerpen, Flanders, Belgium