P. Becker

Physikalisch-Technische Bundesanstalt, Brunswyck, Lower Saxony, Germany

Are you P. Becker?

Claim your profile

Publications (124)362.65 Total impact

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Selenium impurities in silicon are deep double donors and their optical and electronic properties have been recently investigated due to their application for infrared detection. However, a singly-ionised selenium donor (Se$^{+}$) possesses an electron spin which makes it potentially advantageous as a silicon-based spin qubit, compared to the more commonly studied group V donors. Here we study the electron spin relaxation $(T_1)$ and coherence $(T_2)$ times of Se$^{+}$ in isotopically purified 28-silicon, and find them to be up to two orders of magnitude longer than shallow group V donors at temperatures above $\sim15~\text{K}$. We further study the dynamics of donor-acceptor recombination between selenium and boron, demonstrating that it is possible to control the donor charge state through optical excitation of neutral Se$^0$.
  • Source
    [Show abstract] [Hide abstract]
    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.
    Physical Review Letters 12/2014; DOI:10.1103/PhysRevLett.113.267604 · 7.73 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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 1015 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 cm3 sample (≈1015 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 64 %. The 31P-T2 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 T1 of the 31P 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.
    Physical Review Letters 12/2014; 113:267604. · 7.73 Impact Factor
  • Source
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We experimentally demonstrate the first 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 (≈ 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 ∼ 64 %. The P-T2 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 T1 of the 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.
  • Source
    [Show abstract] [Hide abstract]
    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.
    Physical Review B 09/2014; 90(12):121203(R). DOI:10.1103/PhysRevB.90.121203 · 3.66 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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.
    Physical Review B 08/2014; 90(19). DOI:10.1103/PhysRevB.90.195204 · 3.66 Impact Factor
  • Source
  • Source
    [Show abstract] [Hide abstract]
    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.
  • Source
    [Show abstract] [Hide abstract]
    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.
    Applied Physics Letters 02/2014; 104(22). DOI:10.1063/1.4881613 · 3.52 Impact Factor
  • [Show abstract] [Hide abstract]
    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. DOI:10.1126/science.1239584 · 31.48 Impact Factor
  • Peter Becker, Detlef Schiel
    [Show abstract] [Hide abstract]
    ABSTRACT: The Avogadro constant, the number of entities in the amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach for the determination of the Avogadro constant by "counting" the atoms in 1 kg single-crystal spheres, which are highly enriched with the Si-28 isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, N-A = 6.02214084(18) x 10(23) mol(-1), is now the most accurate input datum for a new definition of the kilogram.
    International Journal of Mass Spectrometry 09/2013; 349:219-226. DOI:10.1016/j.ijms.2013.03.015 · 2.23 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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; 8(8). DOI:10.1038/nnano.2013.117 · 33.27 Impact Factor
  • Peter Becker
    [Show abstract] [Hide abstract]
    ABSTRACT: The kilogram is the only unit of measure still defined by a physical object. Now, a marathon effort to tie the kilogram to a constant of nature is nearing the finish line. 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, , results were larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, mol–1 is the most accurate input datum for the kilogram redefinition and differs only by from the CODATA 2010 adjusted value. This value is midway between the watt-balance values.
    Contemporary Physics 11/2012; 53(6):461-479. DOI:10.1080/00107514.2012.746054 · 2.03 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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). DOI:10.1103/PhysRevA.87.032326 · 2.99 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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). DOI:10.1103/PhysRevB.86.245301 · 3.66 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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. DOI:10.1126/science.1217635 · 31.48 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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 03/2012; 152(6):455-457. DOI:10.1016/j.ssc.2012.01.008 · 1.70 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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. DOI:10.1038/ncomms1614 · 10.74 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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. DOI:10.1038/nmat3182 · 36.43 Impact Factor