Programme and abstracts Silicon Quantum Information ......Spin qubits in silicon are excellent candidates for scalable quantum information processing (QIP) due to their long coherence

20 September 2013 University of Surrey, Surrey, UK

Silicon Quantum Information Processing Meeting (SiQiP) 2013

Programme and abstracts

Organised by the IOP BRSG Group: The Magnetic Resonance Group www.iop.org/conferences

Silicon Quantum Information Processing Meeting (SiQiP) 2013 1

Programme

09:30 Registration (foyer)

Location: Lecture Theatre F, First Floor, Lecture Theatre Block

09:45 Welcome, B Murdin, University of Surrey, UK (conference chair)

09:50 Electrical detection via photoionisation of a single Er centre in an ion-implanted Si transistor N Stavrias, FELIX Facility, Radboud University, Netherlands

10:10 A donor molecule in silicon F Gonzalez-Zalba, Hitachi Cambridge Laboratory, UK

10:30 Single-hole tunneling through a two-dimensional hole gas in intrinsic silicon P C Spruijtenburg, University of Twente, Netherlands

10:50 Plenary: Single atom spin qubits in silicon A Dzurak, UNSW, Australia

11:35 Coffee (foyer of Lecture theatre block)

12:00 An automated atomic precision lithography tool for Si-based QIP device fabrication J Owen, Zyvex Labs, USA

12:20 Real time electrical detection of coherent spin oscillations in silicon M Brandt, Walter Schottky Institut, Germany

12:40 Lunch, exhibition and posters (foyer of Lecture theatre block)

13:55 Silicon hybrid qubit: effective model and single qubit operations E Ferraro, Laboratorio MDM, IMM-CNR, Italy

14:15 Quantum dot spin cellular automata for realizing a quantum processor A Bayat, University College London, UK

14:35 Modeling and optimizing donor-dot exchange in a Si:Bi system for implementation of a surface code architecture G Pica, Heriot-Watt University, UK

14:55 Exhibition, posters and coffee (foyer of Lecture theatre block)

16:40 Plenary: The unique optical properties of highly enriched 28Si from the perspective of Si-based quantum information M Thewalt, Simon Fraser University, Canada

17:25 Closing remarks

17:30 Depart

2 Silicon Quantum Information Processing Meeting (SiQiP) 2013

Poster programme

P.01 Modelling of coupled silicon hybrid qubits and synthesis of two qubit operations for quantum information processing and communication M De Michielis, Laboratorio MDM, IMM-CNR, Italy

P.02 209Bi in 28Si for high-fidelity quantum storage of microwave photons J Pla, London Centre for Nanotechnology, University College London, UK

P.03 Laboratory Evidence for Extreme Magnetic Fields (105 T) on White Dwarf Stars J Li, University of Surrey, UK

P.04 Reversible logic gates using time-independent Hamiltonians B Antonio, University College London, UK

P.05 The magneto-optics of the donor bound exciton in silicon K Litvinenko, ATI, University of Surrey, UK

P.06 Charge motion in a two isolated silicon double quantum dot structure S Das, Hitachi Cambridge Lab, UK

P.07 Doped silicon quantum dots in high magnetic fields F Gonzalez-Zalba, Hitachi Cambridge Laboratory, UK

P.08 Electrostatic definition of quantum dots in intrinsic silicon M K Husain, University of Southampton, UK

P.09 Printed circuit board metal powder filters for low electron temperatures F Mueller, University of Twente, Netherlands

P10 Electrical detection of orbital donor states E Bowyer, University of Surrey, UK

P11 Theoretical analysis of spin qubit decoherence in mixed electronic-nuclear systems S Balian, University College London, UK

P12 Investigating individual arsenic dopant atoms in silicon using low-temperature scanning tunneling microscopy K Sinthiptharakoon, University College London, UK

P13 Simulation of charge-based qubit dynamics in double quantum dots J Mosakowski, University of Cambridge, UK


Oral abstracts Electrical detection via photoionisation of a single Er centre in an ion-implanted Si transistor

C Yin1, M Rancic2, G G de Boo1, N Stavrias3,4, J C McCallum3, M J Sellars2 and S Rogge1 1University of New South Wales, Australia, 2Australian National University, Australia, 3University of Melbourne, Australia, 4Current address: Radboud University, FELIX Facility, Netherlands A major goal for solid state quantum information processing is the measurement of a single charge or spin state. Here we present recently published results [1] on the detection of an electron spin associated with a single erbium defect in silicon. Devices were produced via the ion-implantation of Er into a pre-formed Fin-FET channel with subsequent annealing to activate the ions. By applying light onto the device which was resonant to an Er3+ transition, photoionisation of single Er centres was detected electrically using the transistor channel as a charge sensor. Optical excitation offers a high resolution probe and electrical detection is extremely sensitive to changes in the charge state of the centre making this hybrid approach an ideal method to study such systems. The Zeeman and hyperfine splitting of single Er centres were also measured. This work could lead to the development of interconnects between optical based and Si quantum technologies.

[1] Yin C. et al. Optical addressing of an individual erbium ion in silicon. Nature, 497, 91-94, (2013).

A Donor molecule in silicon

M F Gonzalez-Zalba1, A Saraiva2, B Koiller2, M J Calderon3, D Heiss4 and A J Ferguson4 1Hitachi Cambridge Laboratory, UK, 2Universidade Federal do Rio de Janeiro, Brazil , 3Instituto de Ciencia de Materiales, Spain, 4University of Cambridge, UK

A minute concentration of impurities has the ability to dramatically alter the electrical properties of semiconductors. As current generations of devices are reaching dimensions of the order of a few tens of nanometres the discreteness of the doping has become evident in the random performance variation of nominally identical devices [1]. The ability to detect and charaterise a single impurity is therefore of great importance and could be the basis of new computational paradigms such as non-Boolean [2] and quantum computation [3]. Several groups have achieved this goal by performing electrical transport through nanoscale FETs [1, 4, 5] and observed that several competing effects modify the donor electrostatic properties at the interface. Understanding these systems is also likely to provide deeper information on the electronic structure of strongly interacting donor pairs -- a challenge from the experimental and theoretical points of view.

Here we report transport spectroscopy of a pair of strongly interacting As donors in a planar double-gated silicon MOSFET. The spin configuration as well as the energy spectrum has been determined revealing discrepancies with the expected values for single dopants. Enhanced binding energies and charging energy (Ec=73 meV) find no match in donors in bulk silicon. To confirm that this is a giant effective molecule with properties qualitatively analogue to a H2 molecule we present a quantitative theoretical description of the observed energy and spin spectrum. The pair geometry within the lattice is inferred by comparison of the measured spectrum with the one calculated in an effective mass theory incorporating the Bloch states multiplicity in Si, a central cell corrected donor potential and full configuration interaction. Our theoretical calculations- free of fitting parameters- are also adopted to give insight on the electronic structure of these dopant molecule systems in other regimes. These measurements gather the first combined theoretical and experimental evidence of detection of a strongly interacting donor pair in silicon.

[1] Pierre, M. et al. Nature Nanotechnology 5 133 [2] Mol, J. A. et al. PNAS 108 13969 [3] Kane, B. E. et al. Nature 393 133 [4] Lansbergen, G. et al. Nature Physics 4 656 [5] Ono, Y. et al, App. Phys. Lett., 90 102106


Single-hole tunneling through a two-dimensional hole gas in intrinsic silicon

P C Spruijtenburg

University of Twente, Netherlands

We report single-hole tunneling through a quantum dot in a two-dimensional hole gas, situated in a narrow-channel field-effect transistor in intrinsic silicon. Two layers of aluminum gate electrodes are defined on Si/SiO2 using electron-beam lithography. Fabrication and subsequent electrical characterization of different devices yield reproducible results, such as typical MOSFET turn-on and pinch-off characteristics. Additionally, linear transport measurements at 4 K result in regularly spaced Coulomb oscillations, corresponding to single-hole tunneling through individual Coulomb islands. These Coulomb peaks are visible over a broad range in gate voltage, indicating very stable device operation. Energy spectroscopy measurements show closed Coulomb diamonds with single-hole charging energies of 5-10 meV and lines of increased conductance as a result of resonant tunneling through additional available hole states. Published Appl. Phys. Lett. 102, 192105 (2013)

Plenary: Single-atom spin qubits in silicon

A Dzurak

University of New South Wales, Australia

Spin qubits in silicon are excellent candidates for scalable quantum information processing (QIP) due to their long coherence times and the enormous investment in silicon MOS technology. Here I discuss qubits based upon single phosphorus (P) dopant atoms in Si [1]. Projective readout of such qubits had proved challenging until single-shot measurement of a single donor electron spin was demonstrated [2] using a silicon single electron transistor (Si-SET) and the process of spin-to-charge conversion. The measurement gave readout fidelities > 90% and spin lifetimes T1 > 6 seconds [2], opening the path to demonstration of electron and nuclear spin qubits in silicon.

Integration of an on-chip microwave transmission line enables single-electron spin resonance (ESR) of the P donor electron. We used this to demonstrate Rabi oscillations of the electron spin qubit, while a Hahn echo sequence revealed electron spin coherence times T2 > 0.2 ms [3]. We also achieved single-shot readout of the

31P nuclear spin (with fidelity > 99.8%) by monitoring the two hyperfine-split ESR lines of the P donor system. By applying (local) NMR pulses we demonstrated coherent control of the nuclear spin qubit, giving a coherence time T2 > 60 ms [4]. Finally, I will discuss recent experiments on single-atom qubits in isotopically enriched 28Si devices, in which the near elimination of the background 29Si nuclear spin bath allows for significantly longer spin coherence times. [1] B.E. Kane, Nature 393, 133 (1998). [2] A. Morello et al., Nature 467, 687 (2010). [3] J.J. Pla et al., Nature 489, 541 (2012). [4] J.J. Pla et al., Nature 496, 334 (2013).

An automated atomic precision lithography tool for Si-based QIP device fabrication

J H G Owen, J Ballard, E Fuchs, J Alexander, W Owen, J N Randall and J R Von Ehr

Zyvex Labs LLC, USA

H depassivation lithography (HDL) of a Si(001) surface by an STM tip was first demonstrated in 1994 by Lyding et al.[1], but the first practical application of this technique has been to create patterns for PH3 deposition, leading to atomic-scale devices such as the recent ‘Single Atom Transistor’[2]. These devices require both atomically precise positioning of single P atoms, and the patterning of much larger areas for leads and contact pads. Our vision is to


develop a specialised STM-based HDL tool to perform atomically precise lithography of arbitrary designs over multiple length scales, in an automated process, which would greatly increase the throughput and yield of Si-based QIP devices. Lithography on the atomic scale requires that we take account of the local positions of the atoms on the surface. Before writing, the STM tip images the surface to locate the dimer rows, and the positions of the dimers within them, locking the tip position to the centre of the dimer row. Writing is then performed along vectors aligned to the lattice, either along or across dimer rows. Key to achieving atomic precision in the lithography with this vector writing approach is minimising errors in position and movement. The two main sources of position error in an STM with a piezoelectric scanner are thermal drift, which is typically of the order of 1-2 pm/s, and piezo creep, in which the tip will initially undershoot any movement by around 10%, with this error decaying to zero over time (up to 12000 s). We correct for these errors in real time, enabling us to make large jumps (up to 500 nm) with high precision. Automation of the writing process is therefore an integral part of achieving atomic precision. By laying out grids of fiducial marks we can extend the writeable area beyond the range of our ability to make precise movements. Large patterns are made by stitching together sections, thus scaling up the process to µm-scale patterns while maintaining atomic precision. We have defined a writing pixel on the Si(001):H surface to be a pair of Si dimers on a single dimer row, giving a square 0.768 nm pixel, a shown below. Input patterns are defined in terms of an arbitrary bitmap of these pixels. At low biases, around 4.5 V, moving at 20 nm/s, the line width of depassivation is 1 pixel with zero edge roughness, which we term the Atomically Precise (AP) mode. To increase the writing speed, we can use multiple lithography modes. Above 7 V, field emission of electrons from the tip dominates over tunnelling, producing a wider line width, of around 8 pixels at 8V, and moving at 50 nm/s, translating into an overall 20x areal write speed increase. Even larger linewidths are achievable for biases above 10 V and higher currents. However, the Field Emission(FE) modes have considerable line edge roughness. When converting a bitmap pattern to a list of tip vectors suitable for writing, therefore, we first lay out as much of the pattern as possible using wide FE mode vectors, using the slower AP mode where atomically precise features, such as boundaries, are required. A pattern file is created, which contains a list of tip vectors arranged in write order, and includes any other movements, such as non-writing jumps between parts of the pattern. A simple scripting language is used to control the STM, scanning, moving around the surface, checking the position of the tip periodically, writing patterns, and imaging the result.

Figure 1. Patterns generated with our vector compiler. From left: 2 dimers == 1 px; four 5x5 px serpentines,

16 px apart; four concentric squares, with 3 px spacing; Hello Kitty!

[1] J. W. Lyding, T.-C. Shen, J. S. Hubacek, J. R. Tucker, and G. C. Abeln Applied Physics Letters 64 2010-2012 (1994) 10.1063/1.111722

[2] M. Fuechsle, J. A. Miwa, S. Mahapatra, H. Ryu, S. Lee, O. Warschkow, L. C. L. Hollenberg, G. Klimeck, and M. Y. Simmons Nat Nano 7 242-246 (2012) 10.1038/nnano.2012.21


Real time electrical detection of coherent spin oscillations in silicon

F Hoehne1, C Huck1, M S Brandt1 and H Huebl2 1Technische Universität München, Germany, 2Walther-Meißner-Institut, Germany

In this presentation we demonstrate that the bandwidth of pulsed electrically detected magnetic resonance (EDMR) can be increased to at least 80 MHz using a radio frequency-reflectometry scheme based on a tank circuit and homodyne detection. Using this technique, we measure Rabi oscillations of phosphorus donors and Si/SiO2 interface states in real time during a resonant microwave pulse. We find that the observed signal is in quantitative agreement with simulations based on rate equations modeling the recombination dynamics of the spin system under study. The increased bandwidth demonstrated opens the way to study faster spin-dependent transport processes and could therefore significantly broaden the range of spin systems studied by EDMR.

Silicon hybrid qubit: effective model and single qubit operations

E Ferraro1, M De Michielis1, G Mazzeo1, M Fanciulli1,2 and E Prati 1 1Laboratorio MDM, IMM-CNR, Italy, 2University of Milano Bicocca, Italy

Dynamics of the quantum dot hybrid qubit is obtained from the Schrieffer-Wolff transformed effective Hamiltonian in terms of effective exchange coupling interaction between pairs of electrons (see Ref.[1]). Spin dynamics in quantum dot have attracted wide attention in the scientific community both from experimental and theoretical point of view because of their long coherence times and potential scaling. Several architectures have been proposed based on single, double and triple quantum dot, later implemented in GaAs, Si and InSb nanostructures. Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single qubit and two qubits quantum logic ports. The interest raised by this architecture is due to the possibility to obtain gate operations entirely implemented with purely electrical manipulations. We derive the Schrieffer-Wolff effective Hamiltonian that describes in a simple and intuitive way the qubit by combining a Hubbard-like model with a projector operator method. As a result, the Hubbard-like Hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons. The effective Hamiltonian is exploited to derive the dynamical behaviour of the system and its eigenstates on the Bloch sphere to generate qubits operation for quantum logic ports. A realistic implementation in silicon and the coupling of the qubit with a detector described by a single electron transistor (SET) are discussed. Differently from bulk silicon which has a conduction band structure with three couples of energy degenerate valleys, in silicon quantum dots a sequence of energy levels is present with their valley degeneracy removed by interface delta-like potentials (see Ref.[2]). The SET was modeled as a silicon nanowire on the top of a silicon dioxide slab where a tri-sided metal gate, insulated from the nanowire with a silicon dioxide layer and from the source/drain contacts with two silicon nitride spacers, electrostatically forms a quantum dot, like in Ref.[3]. Focusing on the stationary solutions of the Hamiltonian, we study the eigenvalues and the probabilities of the eigenvectors to be found in |0> as a function of the tunneling couplings t13 and t23, as shown in Fig.1. Moreover a genetic algorithm is exploited to find the sequences of interactions between pairs of electrons that realize the single logical gates p/8 and Hadamard, shown in Fig.2. [1] E. Ferraro et al., ArXiv e-prints (2013), arXiv:1304.1800 . [2] M. De Michielis et al., Applied Physics Express 5, 124001 (2012).


[3] E. Prati et al., Nanotechnology 23, 215204 (2012).

Quantum dot spin cellular automata for realizing a quantum processor

A Bayat, C E Creffield, J H Jefferson, M Pepper and S Bose

University College London, UK

We exploit the non-dissipative dynamics of a pair of electrons in a large square quantum dot to perform singlet-triplet spin measurement through a single charge detection and show how this may be used for entanglement swapping and teleportation. The method is also used to generate the AKLT ground state, a further resource for quantum computation. We justify, and derive analytic results for, an effective charge-spin Hamiltonian which is valid over a wide range of parameters and agrees well with exact numerical results of a realistic effective-mass model. We show that our spin filter mechanism can serve as quantum cellular automata. To realize that we show how to implement single and two-qubit quantum gates through capacitive interaction between the square quantum dots. Such fully coherent quantum automata provide a rapid, deterministic, and stable way of performing universal quantum computation. Our analysis also indicates that the method is robust to choice of dot-size and initialization errors, as well as decoherence introduced by the hyperfine interaction.

Modeling and optimizing donor-dot exchange in a Si:Bi system for implementation of a surface code architecture

G Pica1,2, B W Lovett1, R N Bhatt2, and S A Lyon2 1Heriot Watt University, UK, 2Princeton University, USA We present and analyze a new scheme for quantum computation in silicon: we exploit the ex-change coupling between a bismuth donor electron located in the bulk of the Si layer and a quantum dot electron close to the Si/SiO2 interface. It is tuned to perform transfer of coherent quantum information from the Bi nuclear spin, which acts as a memory qubit, to the electron spin states of the surface dots: this gate will form the basic building block for implementing a surface code architecture. Our reasons for using Bi donors include: their nuclear spin is 9/2, so that there are many more states among which to choose the qubit logical |0〉 and |1〉; their hyperfine interaction is the strongest available among the V group subsitutional donors in Si, which makes it easier to transfer the information from the electron to the nuclear spin;


and the valley-orbit excited states of the donor electron are less likely to be populated, since their distance from the ground state is more than 40 meV. Additionally Bi donors exhibit so-called clock transitions [2], i.e. inter-spin transitions that are very insensitive to the actual magnetic field of the environment, which decreases spin decoherence due to the local uctuations in magnetic field: the electron spin T2 can be enhanced by a factor of 1000, up to 3 s [5]. The main advantage over one-electron tunnelling schemes is that efficient adiabatic and selective tuning of the exchange can be achieved thanks to the external gates (electric and magnetic fields) and this renders quantum operations robust to decoherence due to electron-phonon coupling or unwanted involvement of excited electronic states. This theoretical analysis is aimed at finding the optimal parameters for the scheme, such as external electric field and donor depth, and the required sweeping rates of the gates. This is done by numerically evaluating the Heitler-London exchange integrals between the two electrons involved, and includes the impact of the different nature and valley structure of their two single-particle states. We adopt an effective mass theory (EMT) approach, modified by using a pseudopotential improved from [3] by including anisotropy (important for exchange) and up-to-date experimental values. This allows us to consistently account for the valley-orbit energies of 1s donor states, with only two adjustable parameters. This theory should provide an accurate qualitative description of behaviour, and we further refine our estimates by including effects beyond EMT by hand, through extrapolation from [4], whose analysis we broaden to the regimes of interest. We point out some key aspects of the scheme that would be useful for experimental implementations.

[1] A. G. Fowler, M. Mariantoni, J.M.Martinis, A.N.Cleland, Phys. Rev. A 86, 032324 (2012) [2] G. Wolfowicz et al., Phys. Rev. B 86, 245301 (2012) [3] T.H. Ning, C.T. Sah, Phys. Rev. B 4 (1971) 3468 [4] C. Wellard, L. Hollenberg, Phys. Rev. B 72, 085202 [5] G. Wolfowicz et al., Nature Nanotechnology 117, (2013) Plenary: The unique optical properties of highly enriched 28Si from the perspective of Si-based quantum information

M Thewalt

Simon Fraser University, Canada

Highly enriched 28Si has been found to have unique optical properties as compared to other semiconductors, resulting from the near-elimination of inhomogeneous broadening mechanisms for a wide variety of optical transitions. It provides a “semiconductor vacuum” state in which the properties of well-known impurities and defects can be studied and manipulated with unprecedented precision. I will review the optical properties of highly enriched 28Si with emphasis on systems which are of interest for quantum information processing. These include the near-gap absorption and emission transitions of shallow donor bound excitons, emission transitions of deeper ‘isoelectronic’ bound excitons, and the mid-infrared absorption transitions involving the electronic excited states of both shallow and deep donors, and shallow acceptors. I will also describe how these optical methods can be used to measure remarkably long coherence times for the nuclear spin of the neutral phosphorus donor at cryogenic temperatures, and for the ionized phosphorus donor at both cryogenic and room temperature.


Poster abstracts

P.01 Modelling of coupled silicon hybrid qubits and synthesis of two qubit operations for quantum information processing and communication

M De Michielis1, E Ferraro1, M Fanciulli1,2 and E Prati1 1Laboratorio MDM, IMM-CNR, Italy, 2Università degli Studi di Milano-Bicocca, Italy

We report on the modelling and simulation of two coupled silicon double quantum dot hybrid qubits. Hybrid qubits represent a promising compromise between high speed and simple fabrication in solid state qubit implementations [1]. A hybrid qubit consists of a double quantum dot (QD) with three electrons in such a manner that two electrons are electrostatically confined in one QD and one electron in the other as pictured in Figure 1. The logical base {|0>,|1>} is defined as |0>=|S0>|↓> and |1>=(1/3)1/2|T0>|↓>-(2/3)1/2|T->|↑> where |S0> is the singlet state and |T0> and |T-> are the triplet states of the couple of electrons in one QD whereas the |↓> and |↑> are the spin down and up states of the single electron in the other QD [1]. Exchange interactions between pair of spins suffice for all qubit operations. When coupling two qubits, configurations A and B reported in Figure 2 are considered. By extending the results obtained in Ref. [2] to the two qubit case we find a Schrieffer-Wolff effective Hamiltonian model of the composite system which allows to express the evolution operator in a simple form in order to obtain sequences with appropriate interactions and times for the realization of CNOT [3] and SWAP gates. The CNOT operation is an important item of a universal set of quantum instructions and the SWAP sequence is necessary to control chains of hybrid qubits which can be exploited as communication channels between remote hybrid qubits. The search for sequences for the couple of hybrid qubit in the two different configurations A and B is performed numerically by using a versatile search algorithm similar to the one described in Ref. [4], which is a combination of simplex and genetic algorithms. Control sequences for CNOT and SWAP operations are obtained for both configurations A and B. The final transfer matrix, which couples input to output quantum states, of the CNOT and SWAP operations for the configuration A is shown in Figures 3 and 4, respectively. [1] Shi et al, PRL 108, 140503 (2012) [2] E. Ferraro et al, ArXiv e-prints (2013), arXiv:1304.1800 [3] M. De Michielis et al , to be submitted [4] Fong et al., Quantum Information and Computation Vol. 11 No. 11&12 (2011) 1003-1018


P.02 209Bi in 28Si for high-fidelity quantum storage of microwave photons

J J Pla1, C Grezes2, D Esteve2, J J L Morton1 and P Bertet2 1University College London, UK, 2Quantronics group, SPEC (CNRS URA 2464), France

The storage and retrieval of microwave photons in a spin ensemble is a research topic currently experiencing much interest. The attraction is in the potentially long coherence times offered by spin systems, which could serve as a memory element for a superconducting qubit mediated by their interaction with the microwave photons [1]. Various spin systems have been investigated, including NV centres in diamond [2], rare earth spins in Y2SiO5 [3] and Cr3+

spins in ruby [4]. However, so far only modest storage times have been achieved as a result of inhomogeneous broadening caused by magnetic impurities in the host crystal. Spin refocusing techniques can be employed, and the fidelity of such operations are limited by the coherence (T2) time of the spins, as well as the homogeneity of the spin-cavity coupling strength distribution [5].

Bismuth (209Bi) is a deep donor in Silicon, with a large hyperfine constant of 1.4754 GHz. This produces a correspondingly large zero-field splitting (7.377 GHz), enabling experiments to be performed at low magnetic fields – a useful trait when working with superconductors. In addition, Bismuth has a nuclear spin of I = 9/2, giving rise to so called “clock transitions” where (to first order) the spin resonance frequency becomes insensitive to magnetic field fluctuations. Silicon can be isotopically enriched to remove the nuclear spin-half 29Si atoms, further reducing magnetic noise and providing exceptionally long electron spin coherence times of up to 2.7 s [6].

Here we present efforts towards the implementation of a spin memory using 209Bi in highly enriched 28Si. A lumped LC superconducting resonator has been fabricated with a resonance frequency of 7.338 GHz, corresponding to the lowest magnetic field clock transition. We discuss coupling the resonator to a spin ensemble in an implanted 209Bi:28Si sample. The Bismuth implantation profile has been chosen to provide long spin coherence times and a high coupling strength uniformity – presenting the prospects of a high-fidelity microwave photon memory element.

[1] Y. Kubo, et al. Phys. Rev. Lett. 107, 220501 (2011). [2] Y. Kubo, et al. Phys. Rev. A 85, 012333 (2012). [3] P. Bushev, et al. Phys. Rev. B 84, 060501(R) (2011). [4] D. Schuster, et al. 105, 140501 (2010). [5] B. Julsgaard, C. Grezes, P. Bertet & K. Mølmer, arXiv preprint (2013). [6] G. Wolfowicz, et al. Nature Nano. A.O.P., DOI: 10.1038/NNANO.2013.117 (2013).


P.03 Laboratory evidence for extreme magnetic fields (105 T) on white dwarf stars

B N Murdin1, J Li1, M L Y Pang1, E T Bowyer1, K L Litvinenko1, S K Clowes1, H Engelkamp2, C R Pidgeon3, I Galbraith3, N V Abrosimo4, H Riemann4, S G Pavlov5, H-W Hübers5,6 and P G Murdin7 1University of Surrey, UK, 2Radboud University Nijmegen, Netherlands, 3Heriot-Watt University, UK, 4Leibniz Institute of Crystal Growth, Germany, 5Institute of Planetary Research, German Aerospace Center (DLR), Germany, 6Technische Universität Berlin, Germany,7University of Cambridge, UK

The response of atoms to high magnetic fields has been of interest for many decades [1] and flux densities up to 105 T have been inferred from the Hα spectroscopy of hydrogen-rich dwarfs and cataclysmic variables [2,3,4] in combination with theoretical models for the very complex high field Zeeman structure [5, 6, 7]. Although laboratory at 105 T is impossible because the practically available fields are about a thousand times less [8,9], hydrogen-like bound states commonly found in solids [10, 11] can experience equivalent fields because the cyclotron and binding energies are scaled by the effective mass and dielectric constant [1,12]. Here we demonstrate polarized Zeeman spectroscopy of phosphorus impurities in silicon (see Fig. 1) using very high purity samples and high fields up to values equivalent to the highest-field magnetic white dwarf observed [13]. We conclude that missing features and shifts in the astrophysical spectra do not arise from inadequacies in the theory, even at fields up to 105 T, and we point the way to experiments on analogues of He and H2 where electron-electron interactions make the theory is even more challenging.

[1] R.H. Garstang, Rep. Prog. Phys. 40, 105 (1977). [2] D.T. Wickramasinghe and L. Ferrario, Publ. Astron. Soc. Pacif. 112, 873 (2000). [3] S.Vennes et al., Ap J 593, 1040 (2003). [4] K.M. Vanlandingham et al., Astron. J. 130, 734 (2005). [5] L.I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939). [6] A. Holle et al., Phys. Rev. Lett., 56, 2594 (1986). [7] G. Droungas et al., Phys. Rev. A 51, 191 (1995). [8] M. Motokawa, Rep. Prog. Phys. 67, 1995 (2004). [9] G. Pettinari et al., Phys. Rev. B 83, 201201(R) (2011). [10] A.K. Ramdas and S. Rodriguez, Rep. Prog. Phys. 44, 1297 (1981). [11] M. Steger et al., Phys. Rev. B 79, 205210 (2009). [12] W. Zawadzki et al., Phys. Rev. B, 42, 5260 (1990). [13] B. Murdin et al., Nature Comms, 4, 1469 (2013).


P.04 Reversible logic gates using time-independent Hamiltonians

B Antonio and S Bose


In 1961, Rolf Landauer argued [1] that erasing a bit of information necessarily leads to heat dissipation; this leads to a fundamental limit in the energy efficiency of an irreversible computer (the Landauer limit). Reversible computation offers the possibility of devices with an energy efficiency beyond the Landauer limit, as there is no erasure of information, and therefore theoretically no heat dissipation. We investigate 3 different implementations of reversible logic gates, using atime independent Hamiltonian acting on three or more spin qubits, with uniform interactions. Using such a setup, we hope to provide new methods for performing gates which require less control or timed interactions, and so could be more robust against decoherence and timing errors. We also look into how these gates could be realistically implemented using dopants in silicon. [1] R. Landauer, IBM Journal of Research and Development, 5 (1961).

P.05 The magneto-optics of the donor bound exciton in silicon.

K L Litvinenko1, H Engelkamp2, N Stavrias3, C R Pidgeon4, J Li1, S K Clowes1, E T Bowyer1 and B N Murdin1

1University of Surrey, UK, 2High Field Magnet Laboratory, Radboud University Nijmegen, The Netherlands, 3FELIX Facility, Radboud University Nijmegen, The Netherlands, 4Heriot-Watt University, UK

Shallow donors in silicon produce bound states that are strongly analogous to the states of free hydrogen atoms and are very attractive for quantum information applications due to their very long spin and orbital coherence times. We are developing a scheme where the magnetic interaction between two neighbouring deep donor impurity atoms (Bi) can be controlled by a THz excitation of the third shallow donor impurity (P). In principle the information can be transferred then along chains of impurity atoms, manipulated and read out electrically. High magnetic fields have been shown to be a useful tool for the control of the wave-function of bound states that will lead to a control of the overlap of adjacent impurities. Production and relaxation of donor bound excitons may be utilized as a direct way to read-out the donor spin. It has been shown that auger recombination of the donor bound exciton (D0X) is much more likely than radiative emission, so that resonant laser excitation of specific D0X states can be efficiently followed by electrical readout of the conduction electron produced. In this work we report on the D0X energy levels at high magnetic field (up to 30T) and their electrical detection as a first and necessary step in electrical read out of the D0 spin.

P.06 Charge motion in a two isolated silicon double quantum dot structure

S Das, T-Y Yang, A Betz, F Gonzalez-Zalba, T Ferrus and D A Williams

Hitachi Cambridge Laboratory, UK

One of the most critical steps for realiang quantum information is the quantum measurements of entanglement. Two-level qubit states in double quantum dots are of special interest in this respect as they have shown possible coherent control [1] and read-out mechanism. However, on the industrial view point, a successful integration of such qubit devices on a large scale restricts in practice the selection for the material to be used, the device design and the type of qubit. These considerations have led us to implement charge qubit states in an isolated double quantum dot (IDQD) made of doped silicon. Detection is made by a single electron transistor in close proximity to the IDQD. Here, we present a preliminary study of a two-IDQD device with the aim of demonstrating scalability and the possibility to capacitively detect electron tunnelling in a complex structure (Fig. 1). Individual stability diagrams are produced for each IDQD and show clear Coulomb blockade shifts due electron tunnelling detection by the SET (Fig. 2 (a) and (b)). Other features similar to the one observed in triple dots are also present [2]. To demonstrate


the coupling between the two IDQDs we performed compensation techniques which aim as minimising the detector influence on the two-IDQD system. Reasonably good coupling is found by observing the detuning of one IDQD when charge is tunnelling between the two dots of the other IDQD (Fig. 3). Both sharp and smooth transitions are present, either involving a single electron process or multi-electrons via charge rearrangement.

This work has been partly supported by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. [1] J. Gorman et al, Phys. Rev. Lett. 95, 9, 090502 (2005) [2] L. Gaudreau, Nature Physics 8, 54 (2012); L. Gaudreau et al, Appl. Phys. Lett. 95,193101 (2009)

P.07 Doped silicon quantum dots in high magnetic fields

F Gonzalez-Zalba1, J Galibert2, F Iacovella2, D A Williams1 and T Ferrus1 1Hitachi Cambridge Laboratory, UK, 2Laboratoire National des Chams Magnétiques Intenses, France

Recent progress in single ion implantation [1] and in electron beam lithography below 10 nm have led to an increasing interest towards the development and the study of single atom devices, with the aim on implementing quantum computing [3] or realising high-frequency single electron pumps [4]. Such devices can also be realised by electrostatically reducing the size of quantum dots. Although easily achievable in III-V material, the method is more challenging in silicon due to interface effects. Here, we present a preliminary study on the electronic properties of highly doped quantum dots under very high magnetic fields. Devices were fabricated from a 40-nm SOI that was doped with phosphorous at a concentration of 3 1019 cm-3. The 80-nm dot, source and drain contacts as well as the planar gate were defined within a single etch


process step. Annealing was then performed by thermal oxidation, leading to a 15-nm oxide being created at the silicon interfaces. Experiments have been carried out with pulsed magnetic field up to 45 T applied perpendicularly to the SOI plane. In all devices, we observed a nearly quadratic increase in magnetoresistance, for a wide range of temperatures (Fig. 1) despite significant deviations below 4.2 K. At high source-drain biases ~ 40 mV, the magnetoresistance is seen to increase by more than 700 %. Such behaviour is expected for insulating material where magnetic field enhances localization. However, at zero field, the behaviour of conductivity clearly points out to a weakly metallic behaviour down to 4.2 K. This can be explained by field-induced localization in a quantum dot in series with metallic source and drain contacts. To further understand these effects, we have analysed the conductivity as it is varying with field at the edge of the blockade region. Three main regimes are visible (Fig. 2) : below Bc0 ~ 7 T, a positive magnetoconductivity is observed, probably due to interference effects. The second regime shows a linear variation with field up to 39 T. Early interpretations involve inhomogeneity in the material due to the presence localizing and extended regions inside the quantum dot [5]. Above 39 T, the conductivity remains linear with field but its slope increases abruptly indicating that the field has successfully quenched the quantum dot, leading to strong localisation around donors. Part of this work has been supported by EuroMagNET II under the EU contract number TSC29-112 and by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. [1] Jamieson et al., APL 86, 202101 (2005). Johnson et al., APL 96, 264102 (2010) [2] E. Dupont-Ferrier et al, arXiv:1207.1884 [3] J. J. Pla et al, Nature 489, 541 (2012) [4] B. Roche, Nature Communications 4, 1581 (2013) [5] N. A. Porter et al, Scientific reports 2, 565 (2012)

Figure 1: Variation of the magneto resistance at different temperatures in perpendicular magnetic field.


Figure 2: Variation of the source to drain conductivity at VSD = 10 mV, showing the three regimes and the linear magnetoconductivity.

P.08 Electrostatic definition of quantum dots in intrinsic silicon

M K Husain, V Krishnamurthi, Y P Lin, F M Alkhalil, S J Pearce Y Tsuchiya, H M H Chong, H Mizuta and S Saito

University of Southampton, UK

Silicon offers a promising platform for electron spin studies [1] for qubit applications. Their long spin relaxation time and compatibility with conventional CMOS fabrication methods make them an attractive alternative to GaAs devices. Realisation of silicon quantum dots for single electron studies, however, still remains a major challenge. Earlier in our project we realised Si dots on constricted nanowires formed on SOI substrates [2]. This method proved to be unreliable as the line edge roughness of the nanowires resulted in the formation of unintentional quantum dots. Moreover, the defects and charges on the deposited interlayer gate oxide resulted in unstable gate characteristics of the single electron transistors. To overcome these errors, we have recently adopted a different approach, where Al-gates define the Si quantum dots electrostatically on intrinsic Si as shown schematically in Fig 1. In order to improve the gate controllability, thin (10 nm) and high-quality oxide was grown by dry thermal oxidation of Si. The sidewall effect is minimised since any roughness observed (Fig 1b) on the gate sidewalls will be smeared out by the electric field. Therefore, by applying a positive gate bias (Vg) on the Al gate, a clean 1D channel is created on the bulk Si by inversion, as shown schematically in Fig 1c. Again, the depletion, which is required for quantum confinement, can be obtained by applying a negative bias (Vsg) to the Al side-gates (Fig. 1d). The Id-Vg and the Id-Vd characteristics as a function of Vsg of a transistor with channel length Lch = 4 μm and width Wch = 100 nm are shown in Fig 2a and 2b, respectively. We observe effective side gate control of the channel current, which is crucial for the electrostatic quantum dot definition in the channel. The samples will be studied at room temperature and also at cryogenic temperatures for SET operations and charge sensing in the low electron regime. We will report progress towards these measurements.


The author acknowledges support from EPSRC IAA (EP/K503770/1), EPSRC SISSQIT (EP/H016872/1) and the Hitachi Cambridge Laboratory.

Fig.1 a. A schematic representation of the Al gated transistor; b. a SEM image of a fabricated SET; c. the schematic cross-section (along line 1 Fig. 1a) of the transistor showing the formation of inverted channel on Si; d. the schematic cross-section (along line 2 Fig. 1a) of the transistor showing the formation of quantum confinement due to the depletion created by Al sidegate.

Fig.2 a. Id vs. Vg characteristics of a 1D channel transistor showing the suppression of Id with increasing side gate bias (Vsg); b. Id vs. Vd characteristics of the same transistor showing the suppression of Id with increasing Vsg. [1] Lai, N. S., Lim, W. H., Yang, C. H., Zwanenburg, F. A., Coish, W. A., Qassemi, F., Morello, A. and Dzurak,

A. S., Pauli Spin Blockade in a Highly Tunable Silicon Double Quantum Dot. Scientific Reports 1, 110 (2011).

[2] Y. P. Lin, M. K. Husain, F. M. Alkhalil, N. Lambert, J. Perez-Barraza, A. J. Ferguson, H. M. H. Chong, Y. Tsuchiya, and H. Mizuta, Microelectronics Engineering 98, 386 (2012).


P.09 Printed circuit board metal powder filters for low electron temperatures F Mueller1, R N Schouten2, M Brauns1, T Gang1, W Han Lim3, N Shyan Lai3, A S Dzurak3, W G van der Wiel1 and F A Zwanenburg1

1University of Twente, The Netherlands, 2Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands, 3ARC Centre of Excellence for Quantum Computation and Communication Technology, The University of New South Wales, Australia

We report the characterisation of printed circuit boards (PCB) metal powder filters and their influence on the effective electron temperature which is as low as 22 mK for a quantum dot in a silicon MOSFET structure in a dilution refrigerator. We investigate the attenuation behaviour (10 MHz- 20 GHz) of filter made of four metal powders with a grain size below 50 µm. The room-temperature attenuation of a stainless steel powder filter is more than 80 dB at frequencies above 1.5 GHz. In all metal powder filters the attenuation increases with temperature. Compared to classical powder filters, the design presented here is much less laborious to fabricate and specifically the copper powder PCB-filters deliver an equal or even better performance than their classical counterparts. Published in: Rev. Sci. Instrum. 84, 044706 (2013); DOI: 10.1063/1.4802875

P.10 Electrical detection of orbital donor states

E Bowyer

Advanced Technology Institute, University of Surrey, UK

The electrical detection of orbital states of donors in silicon is not a new concept as it has conducted using Fourier transform infrared Spectrometers for decades. Here we present work using Free Electron Lasers to study the dynamics of silicon-donor systems including the ionization from excited orbital states and the recapture of donor electrons using electrical detection.

P.11 Theoretical analysis of spin qubit decoherence in mixed electronic-nuclear systems

S J Balian, G Wolfowicz, J J L Morton and T S Monteiro


Recent theoretical and experimental studies have investigated regimes of strongly mixed electron-nuclear spin qubits, revealing a rich structure of forbidden transitions with potential for quantum computing applications [1]. In addition, they also reveal critical field values or ‘optimal working points’ (OWPs) - particular magnetic field values where theoretical simulations indicate suppression of spin energy splittings [2] and that T2 values can be greatly enhanced [3, 4]. Theoretical analysis of mixed spin systems to date is usually framed in terms of the qubit's reduced sensitivity to externally induced and uncorrelated magnetic field noise at df/dB = 0 points (i.e. where the frequency-field gradient vanishes); the T2 behavior is then related to the curvature of the f(B) function including higher order behavior such as d2f=dB2. However, such an approach is most appropriate for uncorrelated classical (Marko-vian) field fluctuations. Here, we examine the central spin decoherence problem for a mixed central spin system interacting with a quantum spin bath. We conclude that for important decoherence processes (spin diffusion, instantaneous diffusion and in- direct flip-flops) the spin bath environment has slowly decaying correlations. Hence, decoherence from the full dynamics including back-action effects and mutual entanglement can differ qualitatively from decoherence arising from a random Markovian process. We obtain analytical expressions for spin diffusion which give excellent agreement with full CCE numerics and recently obtained data, even in regimes near OWPs where T2 changes by


orders of magnitude. Surprisingly, they predict that T2(B) depends only weakly on the strength of the coupling between the central spin and the bath. Further details can be found in Ref. 5. [1] G. W. Morley, P. Lueders, M. Hamed Mohammady, S. J. Balian, G. Aeppli, C. W. M. Kay, W. M. Witzel,

G. Jeschke, and T. S. Monteiro, Nature Mater. 12, 103 (2013). [2] M. H. Mohammady, G. W. Morley, and T. S. Monteiro, Phys. Rev. Lett. 105, 067602 (2010). [3] S. J. Balian, M. B. A. Kunze, M. H. Mohammady, G. W. Morley, W. M. Witzel, C. W. M. Kay, and T. S.

Monteiro, Phys. Rev. B 86, 104428 (2012). [4] G. Wolfowicz, A. M. Tyryshkin, R. E. George, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, M. L. W.

Thewalt, S. A. Lyon, and J. J. L. Morton, Nat. Nanotechnol. 8, 561 (2013). [5] S. J. Balian, G. Wolfowicz, J. J. L. Morton and T. S. Monteiro, arXiv:1302.1709 (2013).

P12 Investigating individual arsenic dopant atoms in silicon using low-temperature scanning tunneling microscopy

K Sinthiptharakoon, S R Schofield, P Studer, V Brázdová, C F Hirjibehedin, D R Bowler and N J Curson


Keyword: subsurface dopant, semiconductor, STM

Semiconductor device features have reached the nanometre scale, so that it is now critical to develop an understanding of individual dopant atoms in semiconductor materials and the way in which they are affected by changes in their local environment such as the application of local bias voltages. Scanning tunneling microscopy is an ideal tool for the measurement of the electronic properties of individual dopants due to its ability to probe not only the surface, but also the near surface region, with atomic resolution. In this work, arsenic dopants in a bulk As-doped silicon substrate have been studied using scanning tunneling microscopy (STM) and spectroscopy (STS) at 77K. Measurements were performed using the technologically important Si(001) surface, which has been terminated with a single layer of hydrogen atoms. We observed a number of long-range features superimposed on the background Si(001):H lattice structure that we attribute to subsurface As donors. We categorise the observed features into two groups; As1 and As2, corresponding to two different contrast characteristics. When the sample bias is negative, the As1 features appear as protrusions of a few nanometers in size with different characteristic shapes superimposed on the background lattice structure. The appearance of the features is due to the different projections on the surface of the wavefunction of As dopants that are neutral (As0). We suggest that the difference of the wavefunction projections on the surface is due to the different dopant positions in the silicon crystal which is also supported by theoretical simulation. However, for the empty-state imaging, all of the As1 electronic features exhibit long-range isotropic circular protrusions. The appearance of these features is caused by the Coulomb potential created by positively charged As donors (As+) formed by tip-induced ionisation. The intensity of both anisotropic and isotropic protrusions is strongly dependent on magnitude of the sample bias with the intensity decreasing as the bias magnitude becomes larger. Our spectroscopic measurements of some As1 features also reveal additional tunneling current with a similar behaviour in the semiconductor band gap, providing evidence that the As1 features are induced by subsurface donors of the same energetic behaviour. Unlike the As1 features, As2 features appear as delocalised circular protrusions in filled-state but depressions with diameter of a few nanometers in empty-state images respectively. We attribute the contrast behaviour to the influence of Coulomb potentials of negatively-charged subsurface dopants (As-) that possibly occur because second electrons are bound to the donors close to the semiconductor surface due to the enhanced binding energy. The intensity of this class of subsurface As donor-induced features also shows the same dependence on the bias magnitude as Feature As1.


P13 Simulation of charge-based qubit dynamics in double quantum dots

J Mosakowski1, T Ferrus2, D A Williams2, A Andreev2 and C H W Barnes1 1Cavendish Laboratory, UK, 2Hitachi Cambridge Laboratory, UK Quantum computation offers ways of solving problems which are unreachable for conventional computers such as factorisation of large numbers or fast searching algorithms [1]. The basic unit of quantum computation is the quantum bit (qubit), which is an analogue of the classical bit. Double quantum dots (DQDs) are of great interest as candidates for implementing solid state qubits. One of their greatest advantages is long coherence time of the electrons confined in the dots. The use of geometrically isolated structures (with the detectors coupled capacitively) improves the electrical isolation of the dots from the rest of the system, however, it makes the detection process more challenging [2]. In our research, we have computationally modelled the dynamical behaviour of an electron in a 2D quantum dot using the time-dependent Schrödinger equation and the finite difference method. Starting with spatial and temporal discretisation of the system and using Taylor's theorem allows to convert the problem into a finite set of equations, which then can be solved iteratively over time to investigate the dynamics of the particle. As long as the stability criterion is met, this method proves to be highly convergent, stable and accurate. In particular, total electron probability is conserved and small errors arising due to finite computational accuracy do not accumulate with time [3]. Using this 2D solver, any arbitrary type of electron (qubit) manipulations in the dots can be modelled as well as any type of time-dependent potential to control it [Fig. 1]. If we define the |0> and |1> qubit states as the electron being in the right or left dot, respectively, then the σx and σz rotations (using the Bloch sphere representation) can be simulated [Fig. 2]. Furthermore, it is possible to investigate how finite raise (fall) times of the controlling pulses affect the quality of the oscillation, in particular its amplitude [Fig. 3]. In the near future, it is also planned to add second electron to the program and simulate the controlled phase shift gate. This work has been partly supported by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. [1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University

Press, Cambridge, 2000). [2] T. Ferrus, A. Rossi, M. Tanner, G. Podd, P. Chapman and D. A. Williams, Detection of charge motion in a

non-metallic silicon isolated double quantum dot, New Journal of Physics 13 (2011) 103012. [3] Jon J. V. Maestri, Rubin H. Landau and Manuel J. Páez, Two-particle Schrödinger equation animations of

wave packet–wave packet scattering, American Journal of Physics 68, 12 (2000).

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Programme and abstracts Silicon Quantum Information ......Spin qubits in silicon are excellent candidates for scalable quantum information processing (QIP) due to their long coherence