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Wu H.,University of Oxford | Gauger E.M.,University of Oxford | Gauger E.M.,National University of Singapore | George R.E.,University of Oxford | And 8 more authors.
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2013

High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. Manipulation of electron spins 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 introduce an adiabatic geometric phase gate for the electron spin. Benchmarking it against existing dynamic and nonadiabatic geometric gates through simulations and experiments, we show that it 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. © 2013 American Physical Society.


Hubers H.-W.,German Aerospace Center | Hubers H.-W.,TU Berlin | Pavlov S.G.,German Aerospace Center | Lynch S.A.,University of Cardiff | And 11 more authors.
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

The low-temperature (∼5 K) phonon-assisted relaxation of the 2p 0 state of phosphorus donors in isotopically pure, monocrystalline 28Si has been studied in the time domain using a pump-probe technique. The lifetime of the 2p0 state in 28Si:P is found to be 235 ps, which is 16% larger than the lifetime of a reference Si:P sample with a natural isotope composition. The interaction of the 2p0 state with intervalley g-type longitudinal acoustic and f-type transverse acoustic phonons determines its lifetime. This interaction, which depends on the homogeneity of the crystal, becomes weaker in 28Si because of its more perfect crystal lattice compared to natural Si, and this leads to a longer lifetime. The difference between the linewidths of the 1s(A1) → 2p0 transition in 28Si:P and natural Si:P is more than a factor of two. It follows that linewidth broadening due to isotopic composition is an inhomogeneous process. © 2013 American Physical Society.


Knee G.C.,University of Oxford | Simmons S.,University of Oxford | Gauger E.M.,University of Oxford | Gauger E.M.,National University of Singapore | And 10 more authors.
Nature Communications | Year: 2012

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. © 2012 Macmillan Publishers Limited. All rights reserved.


Gumann P.,University of Waterloo | Gumann P.,Harvard University | Patange O.,University of Waterloo | Ramanathan C.,Dartmouth College | And 11 more authors.
Physical Review Letters | Year: 2014

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 1.5×1015 cm-3, 3 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 P31-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 P31 nuclear spins at 1.7 K is extremely long and could not be determined, as no decay was observed even on a time scale of 4.5 h. Optical excitation was performed with a 1047 nm laser, which provided above-band-gap excitation of the silicon. The buildup of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the buildup at 1.7 K showed biexponential behavior with characteristic time constants of 578 and 5670 s. © 2014 American Physical Society.


Sigillito A.J.,Princeton University | Malissa H.,Princeton University | Malissa H.,University of Utah | Tyryshkin A.M.,Princeton University | And 10 more authors.
Applied Physics Letters | Year: 2014

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 (B1) 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 107 spins or 3×104spins/√Hz with averaging. © 2014 AIP Publishing LLC.


Wolfowicz G.,University College London | Wolfowicz G.,University of Oxford | Simmons S.,University College London | Simmons S.,University of Oxford | And 9 more authors.
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

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. Most 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. Importantly, the coherence times we measure follow closely to the calculated field gradients of the transition frequencies (df/dB), providing a strong motivation to explore "clock" transitions where coherence lifetimes could be further enhanced. © 2012 American Physical Society.


Wolfowicz G.,University College London | Wolfowicz G.,University of Oxford | Tyryshkin A.M.,Princeton University | George R.E.,University College London | And 7 more authors.
Nature Nanotechnology | Year: 2013

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. © 2013 Macmillan Publishers Limited. All rights reserved.


Tyryshkin A.M.,Princeton University | Tojo S.,Keio University | Morton J.J.L.,University of Oxford | Riemann H.,Institute For Kristallzuchtung | And 7 more authors.
Nature Materials | Year: 2012

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 28Si 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 28Si material (residual 29Si 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. © 2012 Macmillan Publishers Limited. All rights reserved.


Wolfowicz G.,University College London | Wolfowicz G.,University of Oxford | Urdampilleta M.,University College London | Thewalt M.L.W.,Simon Fraser University | And 5 more authors.
Physical Review Letters | Year: 2014

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. © 2014 American Physical Society.


PubMed | Leibniz Institute for Crystal Growth, Physikalisch - Technische Bundesanstalt, Vitcon Projectconsult GmbH, Simon Fraser University and University College London
Type: Journal Article | Journal: Physical review letters | Year: 2014

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.

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