arXiv subjects

S. A. Lyon

Publications and source records attributed to S. A. Lyon.

At least 37 records · Page 2Linked to original sources

arXiv2017

Electrically driving nuclear spin qubits with microwave photonic bangap resonators

The electronic and nuclear spin degrees of freedom for donor impurities in semiconductors form ultra coherent two-level systems that are useful for quantum information applications. Spins naturally have magnetic dipoles, so alternating current (AC) magnetic fields are frequently used to drive spin transitions and perform quantum gates. These fields can be difficult to spatially confine to single donor qubits so alternative methods of control such as AC electric field driven spin resonance are desirable. However, donor spin qubits do not have electric dipole moments so that they can not normally be driven by electric fields. In this work we challenge that notion by demonstrating a new, all-electric-field method for controlling neutral $^{31}$P and $^{75}$As donor nuclear spins in silicon through modulation of their donor-bound electrons. This method has major advantages over magnetic field control since electric fields are easy to confine at the nanoscale. This leads to lower power requirements, higher qubit densities, and faster gate times. We also show that this form of control allows for driving nuclear spin qubits at either their resonance frequency or the first subharmonic of that frequency, thus reducing device bandwidth requirements. Interestingly, as we relax the bandwidth requirements, we demonstrate that the computational Hilbert space is expanded to include double quantum transitions, making it feasible to use all four nuclear spin states to implement nuclear-spin-based qudits in Si:As. Based on these results, one can envision novel high-density, low-power quantum computing architectures using nuclear spins in silicon.

quant-ph↗

arXiv2016

Large Stark tuning of donor electron spin quantum bits in germanium

Donor electron spins in semiconductors make exceptional quantum bits because of their long coherence times and compatibility with industrial fabrication techniques. Despite many advances in donor-based qubit technology, it remains difficult to selectively manipulate single donor electron spins. Here, we show that by replacing the prevailing semiconductor host material (silicon) with germanium, donor electron spin qubits can be electrically tuned by more than an ensemble linewidth, making them compatible with gate addressable quantum computing architectures. Using X-band pulsed electron spin resonance, we measured the Stark effect for donor electron spins in germanium. We resolved both spin-orbit and hyperfine Stark shifts and found that at 0.4 T, the spin-orbit Stark shift dominates. The spin-orbit Stark shift is highly anisotropic, depending on the electric field orientation relative to the crystal axes and external magnetic field. When the Stark shift is maximized, the spin-orbit Stark parameter is four orders of magnitude larger than in silicon. At select orientations a hyperfine Stark effect was also resolved and is an order of magnitude larger than in silicon. We report the Stark parameters for $^{75}$As and $^{31}$P donor electrons and compare them to the available theory. Our data reveal that $^{31}$P donors in germanium can be tuned by at least four times the ensemble linewidth making germanium an appealing new host material for spin qubits that offers major advantages over silicon.

quant-ph↗

arXiv2016

Spin Coherence and $^{14}$N ESEEM Effects of Nitrogen-Vacancy Centers in Diamond with X-band Pulsed ESR

Pulsed ESR experiments are reported for ensembles of negatively-charged nitrogen-vacancy centers (NV$^-$) in diamonds at X-band magnetic fields (280-400 mT) and low temperatures (2-70 K). The NV$^-$ centers in synthetic type IIb diamonds (nitrogen impurity concentration $<1$~ppm) are prepared with bulk concentrations of $2\cdot 10^{13}$ cm$^{-3}$ to $4\cdot 10^{14}$ cm$^{-3}$ by high-energy electron irradiation and subsequent annealing. We find that a proper post-radiation anneal (1000$^\circ$C for 60 mins) is critically important to repair the radiation damage and to recover long electron spin coherence times for NV$^-$s. After the annealing, spin coherence times of T$_2 = 0.74$~ms at 5~K are achieved, being only limited by $^{13}$C nuclear spectral diffusion in natural abundance diamonds. At X-band magnetic fields, strong electron spin echo envelope modulation (ESEEM) is observed originating from the central $^{14}$N nucleus. The ESEEM spectral analysis allows for accurate determination of the $^{14}$N nuclear hypefine and quadrupole tensors. In addition, the ESEEM effects from two proximal $^{13}$C sites (second-nearest neighbor and fourth-nearest neighbor) are resolved and the respective $^{13}$C hyperfine coupling constants are extracted.

quant-ph↗

arXiv2016

Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings

A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighbouring spins via the natural exchange interaction according to current designs requires gate control structures with extremely small length scales. We present a silicon architecture where bismuth donors with long coherence times are coupled to electrons that can shuttle between adjacent quantum dots, thus relaxing the pitch requirements and allowing space between donors for classical control devices. An adiabatic SWAP operation within each donor/dot pair solves the scalability issues intrinsic to exchange-based two-qubit gates, as it does not rely on sub-nanometer precision in donor placement and is robust against noise in the control fields. We use this SWAP together with well established global microwave Rabi pulses and parallel electron shuttling to construct a surface code that needs minimal, feasible local control.

cond-mat.mes-hall↗

arXiv2016

Addressing spin transitions on 209Bi donors in silicon using circularly-polarized microwaves

Over the past decade donor spin qubits in isotopically enriched $^{28}$Si have been intensely studied due to their exceptionally long coherence times. More recently bismuth donor electron spins have become popular because Bi has a large nuclear spin which gives rise to clock transitions (first-order insensitive to magnetic field noise). At every clock transition there are two nearly degenerate transitions between four distinct states which can be used as a pair of qubits. Here it is experimentally demonstrated that these transitions are excited by microwaves of opposite helicity such that they can be selectively driven by varying microwave polarization. This work uses a combination of a superconducting coplanar waveguide (CPW) microresonator and a dielectric resonator to flexibly generate arbitrary elliptical polarizations while retaining the high sensitivity of the CPW.

quant-ph↗

arXiv2015

Electron spin coherence of shallow donors in natural and isotopically enriched germanium

Germanium is a widely used material for electronic and optoelectronic devices and recently it has become an important material for spintronics and quantum computing applications. Donor spins in silicon have been shown to support very long coherence times ($T_{2}$) when the host material is isotopically enriched to remove any magnetic nuclei. Germanium also has non-magnetic isotopes so it is expected to support long $T_{2}$s while offering some new properties. Compared to Si, Ge has a strong spin-orbit coupling, large electron wavefunction, high mobility, and highly anisotropic conduction band valleys which will all give rise to new physics. In this Letter, the first pulsed electron spin resonance (ESR) measurements of $T_{2}$ and the spin-lattice relaxation ($T_1$) times for $^{75}$As and $^{31}$P donors in natural and isotopically enriched germanium are presented. We compare samples with various levels of isotopic enrichment and find that spectral diffusion due to $^{73}$Ge nuclear spins limits the coherence in samples with significant amounts of $^{73}$Ge. For the most highly enriched samples, we find that $T_1$ limits $T_2$ to $T_2 = 2T_1$. We report an anisotropy in $T_1$ and the ensemble linewidths for magnetic fields oriented along different crystal axes but do not resolve any angular dependence to the spectral-diffusion-limited $T_2$ in samples with $^{73}$Ge.

cond-mat.mes-hall↗

arXiv2015

ESR measurements of phosphorus dimers in isotopically enriched 28Si silicon

Dopants in silicon have been studied for many decades using optical and electron spin resonance (ESR) spectroscopy. Recently, new features have been observed in the spectra of dopants in isotopically enriched 28Si since the reduced inhomogeneous linewidth in this material improves spectral resolution. With this in mind, we measured ESR on exchange coupled phosphorus dimers in 28Si and report two results. First, a new fine structure is observed in the ESR spectrum arising from state mixing by the hyperfine coupling to the 31P nuclei, which is enhanced when the exchange energy is comparable to the Zeeman energy. This fine structure enables us to spectroscopically address two separate dimer sub-ensembles, the first with exchange (J) coupling ranging from 2 to 7 GHz and the second with J ranging from 6 to 60 GHz. Next, the average spin relaxation times, T1 and T2 of both dimer sub-ensembles were measured using pulsed ESR at 0.35 T. Both T1 and T2 for transitions between triplet states of the dimers were found to be identical to the relaxation times of isolated phosphorus donors in 28Si, with T2 = 4 ms at 1.7 K limited by spectral diffusion due to dipolar interactions with neighboring donor electron spins. This result, consistent with theoretical predictions, implies that an exchange coupling of 2 - 60 GHz does not limit the dimer T1 and T2 in bulk Si at the 10 ms timescale.

cond-mat.mtrl-sci↗

arXiv2015

Anisotropic Stark Effect and Electric-Field Noise Suppression for Phosphorus Donor Qubits in Silicon

We report the use of novel, capacitively terminated coplanar waveguide (CPW) resonators to measure the quadratic Stark shift of phosphorus donor qubits in Si. We confirm that valley repopulation leads to an anisotropic spin-orbit Stark shift depending on electric and magnetic field orientations relative to the Si crystal. By measuring the linear Stark effect, we estimate the effective electric field due to strain in our samples. We show that in the presence of this strain, electric-field sources of decoherence can be non-negligible. Using our measured values for the Stark shift, we predict magnetic fields for which the spin-orbit Stark effect cancels the hyperfine Stark effect, suppressing decoherence from electric-field noise. We discuss the limitations of these noise-suppression points due to random distributions of strain and propose a method for overcoming them.

cond-mat.mes-hall↗

arXiv2014

Hybrid optical-electrical detection of donor electron spins with bound excitons in silicon

Electrical detection of spins is an essential tool in understanding the dynamics of spins in semiconductor devices, providing valuable insights for applications ranging from optoelectronics and spintronics to quantum information processing. For electron spins bound to shallow donors in silicon, bulk electrically-detected magnetic resonance has relied on coupling to spin readout partners such as paramagnetic defects or conduction electrons which fundamentally limits spin coherence times. Here we demonstrate electrical detection of phosphorus donor electron spin resonance by transport through a silicon device, using optically-driven donor-bound exciton transitions. We use this method to measure electron spin Rabi oscillations, and, by avoiding use of an ancillary spin for readout, we are able to obtain long intrinsic electron spin coherence times, limited only by the donor concentration. We go on to experimentally address critical issues for adopting this scheme for single spin measurement in silicon nanodevices, including the effects of strain, electric fields, and non-resonant excitation. This lays the foundations for realising a versatile readout method for single spin readout with relaxed magnetic field and temperature requirements compared with spin-dependent tunneling.

cond-mat.mes-hall↗

arXiv2014

Isolating electrons on superfluid helium

Electrons floating on the surface of superfluid helium have been suggested as promising mobile spin quantum bits (qubits). Transferring electrons extremely efficiently in a narrow channel structure with underlying gates has been demonstrated, showing no transfer error while clocking $10^9$ pixels in a 3-phase charge coupled device (CCD). While on average, one electron per channel was clocked, it is desirable to reliably obtain a single electron per channel. We have designed an electron turnstile consisting of a narrow (0.8$μ$m) channel and narrow underlying gates (0.5$μ$m) operating across seventy-eight parallel channels. Initially, we find that more than one electron can be held above the small gates. Underlying gates in the turnstile region allow us to repeatedly split these electron packets. Results show a plateau in the electron signal as a function of the applied gate voltages, indicating quantization of the number of electrons per pixel, simultaneously across the seventy-eight parallel channels.

cond-mat.mes-hall↗

arXiv2014

Hyperfine Stark effect of shallow donors in silicon

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.

cond-mat.mes-hall↗

arXiv2014

Host isotope mass effects on the hyperfine interaction of group-V donors in silicon

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.

cond-mat.mtrl-sci↗

arXiv2014

Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy

Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the inter donor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrinsic in the Si conduction band. We are able to accurately describe the single donor properties of valley-orbit coupling and the spatial extent of donor wave functions, highlighting the importance of fitting measured values of hyperfine coupling and the orbital energy of the $1s$ levels. Ours is a simple framework that can be applied flexibly to a range of experimental scenarios, but it is nonetheless able to provide fast and reliable predictions. We use it to estimate the exchange coupling between two donor electrons and we find a smoothing of its expected oscillations, and predict a monotonic dependence on separation if two donors are spaced precisely along the [100] direction.

cond-mat.mes-hall↗

arXiv2014

Fast, low-power manipulation of spin ensembles in superconducting microresonators

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.

cond-mat.mes-hall↗

arXiv2014

Stark shift and field ionization of arsenic donors in $^{28}$Si-SOI structures

We develop an efficient back gate for silicon-on-insulator (SOI) devices operating at cryogenic temperatures, and measure the quadratic hyperfine Stark shift parameter of arsenic donors in isotopically purified $^{28}$Si-SOI layers using such structures. The back gate is implemented using MeV ion implantation through the SOI layer forming a metallic electrode in the handle wafer, enabling large and uniform electric fields up to $\sim$ 2 V/$μ$m to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters of arsenic donors embedded in the $^{28}$Si SOI layer and find a contact hyperfine Stark parameter of $η_a=-1.9\pm0.2\times10^{-3} μ$m$^2$/V$^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.

cond-mat.mes-hall↗

arXiv2012

Superconducting coplanar waveguide resonators for low temperature pulsed electron spin resonance spectroscopy

We discuss the design and implementation of thin film superconducting coplanar waveguide micro- resonators for pulsed ESR experiments. The performance of the resonators with P doped Si epilayer samples is compared to waveguide resonators under equivalent conditions. The high achievable filling factor even for small sized samples and the relatively high Q-factor result in a sensitivity that is superior to that of conventional waveguide resonators, in particular to spins close to the sample surface. The peak microwave power is on the order of a few microwatts, which is compatible with measurements at ultra low temperatures. We also discuss the effect of the nonuniform microwave magnetic field on the Hahn echo power dependence.

cond-mat.mes-hall↗

arXiv2012

Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

We have performed continuous wave and pulsed electron spin resonance measurements of implanted bismuth donors in isotopically enriched silicon-28. Donors are electrically activated via thermal annealing with minimal diffusion. Damage from bismuth ion implantation is repaired during thermal annealing as evidenced by narrow spin resonance linewidths (B_pp=12uT and long spin coherence times T_2=0.7ms, at temperature T=8K). The results qualify ion implanted bismuth as a promising candidate for spin qubit integration in silicon.

cond-mat.mtrl-sci↗

arXiv2012

Effect of pulse error accumulation on dynamical decoupling of the electron spins of phosphorus donors in silicon

Dynamical decoupling (DD) is an efficient tool for preserving quantum coherence in solid-state spin systems. However, the imperfections of real pulses can ruin the performance of long DD sequences. We investigate the accumulation and compensation of different pulse errors in DD using the electron spins of phosphorus donors in silicon as a test system. We study periodic DD sequences (PDD) based on spin rotations about two perpendicular axes, and their concatenated and symmetrized versions. We show that pulse errors may quickly destroy some spin states, but maintain other states with high fidelity over long times. Pulse sequences based on spin rotations about $x$ and $y$ axes outperform those based on $x$ and $z$ axes due to the accumulation of pulse errors. Concatenation provides an efficient way to suppress the impact of pulse errors, and can maintain high fidelity for all spin components: pulse errors do not accumulate (to first order) as the concatenation level increases, despite the exponential increase in the number of pulses. Our theoretical model gives a clear qualitative picture of the error accumulation, and produces results in quantitative agreement with the experiments.

quant-ph↗