Search

Electrons trapped on the surface of cryogenic substrates (liquid helium, solid neon or hydrogen) are an emerging platform for quantum information processing made attractive by the inherent purity of the electron environment, the scalability of trapping devices and the predicted long lifetime of electron spin states. Here we demonstrate the spatial control and detection of single electrons above the surface of liquid helium at temperatures above 1 K. A superconducting coplanar waveguide resonator is used to read out the charge state of an electron trap defined by gate electrodes beneath the helium surface. Dispersive frequency shifts are observed as the trap is loaded with electrons, from several tens down to single electrons. These frequency shifts are in good agreement with our theoretical model that treats each electron as a classical oscillator coupled to the cavity field. This sensitive charge readout scheme can aid efforts to develop large-scale quantum processors that require the high cooling powers available in cryostats operating above 1 K., Comment: 12 pages, 6 figures

The in-plane motion of an electron on helium can couple to superconducting microwave resonators via electrical dipole coupling, offering a robust and rapid readout scheme. In previous efforts, microwave resonator designs for electrons on helium have lacked the coupling strength to reach the strong coupling regime, where coherent quantum effects outlast both electron and resonator decoherence rates. High-impedance superconducting microwave resonators offer a path to strong coupling, but integrating such resonators with electrons on helium remains an outstanding challenge. Here, we introduce a high-impedance resonator design compatible with strong coupling to electrons on helium. We fabricate and measure titanium nitride resonators with median internal quality factors of $3.9\times 10^5$ and average impedance of 2.5 k$\Omega$, promising a seven-fold increase in coupling strength compared with standard 50$\Omega$ resonators. Additionally, we develop a simplified resonator model from the capacitance matrix and sheet inductance that accurately predicts the mode frequencies, significantly simplifying the design process of future resonators for investigating quantum effects with electrons on helium., Comment: 15 pages, 7 figures, 2 tables

While there is much indirect evidence for the existence of dark matter (DM), to date it has evaded detection. Current efforts focus on DM masses over $\sim$GeV -- to push the sensitivity of DM searches to lower masses, new DM targets and detection schemes are needed. In this work, we focus on the latter - a novel detection scheme recently proposed to detect ~10-100 meV phonons in polar target materials. Previous work showed that well-motivated models of DM can interact with polar semiconductors to produce an athermal population of phonons. This new sensing scheme proposes that these phonons then facilitate quantum evaporation of $^3$He from a van der Waals film deposited on the target material. However, a fundamental understanding of the underlying process is still unclear, with several uncertainties related to the precise rate of evaporation and how it can be controlled. In this work, we use \textit{ab initio} density functional theory (DFT) calculations to compare the adsorption energies of helium atoms on a polar target material, sodium iodide (NaI), to understand the underlying evaporation physics. We explore the role of surface termination, monolayer coverage and elemental species on the rate of He evaporation from the target material. Using this, we discuss the optimal target features for He-evaporation experiments and their range of tunability through chemical and physical modifications such as applied field and surface termination.

We describe a helium source cell for use in cryogenic experiments that is hermetically sealed $in$ $situ$ on the cold plate of a cryostat. The source cell is filled with helium gas at room temperature and subsequently sealed using a cold weld crimping tool before the cryostat is closed and cooled down. At low temperature the helium condenses and collects in a connected experimental volume, as monitored via the frequency response of a planar superconducting resonator device sensitive to small amounts of liquid helium. This on-cryostat helium source negates the use of a filling tube between the cryogenic volumes and room temperature, thereby preventing unwanted effects such as such as temperature instabilities that arise from the thermomechanical motion of helium within the system. This helium source can be used in experiments investigating the properties of quantum fluids or to better thermalize quantum devices., Comment: 5 pages, 3 figures

Liquid He-4 is free from magnetic defects, making it an ideal substrate for electrons with long-lived spin states. Such states can serve as qubit states. Here we consider the spin states of electrons electrostatically localized in quantum dots on a helium surface. Efficient gate operations in this system require spin-orbit coupling. It can be created by a nonuniform magnetic field from a current-carrying wire, can be turned on and off, and allows one to obtain large electro-dipole moment and comparatively fast coupling of spins in neighboring dots. Of central importance is to understand the spin decay due to the spin-orbit coupling. We establish the leading mechanism of such decay and show that the decay is sufficiently slow to enable high-fidelity single- and two-qubit gate operations, Comment: The paper is a contribution to the PRB Collection in honor of Emmanuel Rashba

We have measured two-dimensional electron systems bound to a thin helium film supported by a metallic substrate. We report on our measurement of electron density obtained via a Kelvin probe technique. The underlying metallic substrate is an amorphous metallic alloy (TaWSi), which can support large uniform densities due to its low surface roughness and homogeneous work function. We find that this substrate is able to support high enough densities that the electrons are expected to be Fermi-degenerate., Comment: 13 Pages, 4 Figures

The search for particle-like dark matter with meV-to-GeV masses has developed rapidly in the past few years. We summarize the science case for these searches, the recent progress, and the exciting upcoming opportunities. Funding for Research and Development and a portfolio of small dark matter projects will allow the community to capitalize on the substantial recent advances in theory and experiment and probe vast regions of unexplored dark-matter parameter space in the coming decade., Comment: Contribution to Snowmass 2021. v2: includes endorsers and minor changes

Dark matter is five times more abundant than ordinary visible matter in our Universe. While laboratory searches hunting for dark matter have traditionally focused on the electroweak scale, theories of low mass hidden sectors motivate new detection techniques. Extending these searches to lower mass ranges, well below 1 GeV/c$^2$, poses new challenges as rare interactions with standard model matter transfer progressively less energy to electrons and nuclei in detectors. Here, we propose an approach based on phonon-assisted quantum evaporation combined with quantum sensors for detection of desorption events via tracking of spin coherence. The intent of our proposed dark matter sensors is to extend the parameter space to energy transfers in rare interactions to as low as a few meV for detection of dark matter particles in the keV/c$^2$ mass range., Comment: 8 pages, 3 figures. Updated various parts

Recent experiments on the coupling of the in-plane motional state of electrons floating on the surface of liquid helium to a microwave resonator have revealed the importance of helium surface fluctuations to the coherence of this motion. Here we investigate these surface fluctuations by studying the resonance properties of a superconducting coplanar waveguide (CPW) resonator filled with superfluid helium, where a significant fraction of the resonator's electromagnetic mode volume is coupled to the surface dynamics of the liquid. We present preliminary results on real-time CPW resonator frequency shifts driven by helium fluctuations, which are quantified via their power spectral density and compared with measurements using a commercial accelerometer. We find that a considerable contribution to the CPW resonator noise originates from the mechanical vibrations of the helium surface generated by the pulse tube (PT) cryocooler on the cryostat on which the experiments were performed., Comment: 10 pages, 3 figures. J. Low Temp. Phys. (2022)

We describe sensitive magnetometry using lumped-element resonators fabricated from a superconducting thin film of NbTiN. Taking advantage of the large kinetic inductance of the superconductor, we demonstrate a continuous resonance frequency shift of $27$ MHz for a change in magnetic field of $1.8~\mu$T within a perpendicular background field of 60 mT. By using phase-sensitive readout of microwaves transmitted through the sensors, we measure phase shifts in real time with a sensitivity of $1$ degree/nT. We present measurements of the noise spectral density of the sensors, and find their field sensitivity is at least within one to two orders of magnitude of superconducting quantum interference devices operating with zero background field. Our superconducting kinetic inductance field-frequency sensors enable real-time magnetometry in the presence of moderate perpendicular background fields up to at least 0.2 T. Applications for our sensors include the stabilization of magnetic fields in long coherence electron spin resonance measurements and quantum computation., Comment: 5 pages, 4 figures with 2-page supplementary material

We demonstrate that CPMG and XYXY decoupling sequences with non-ideal $\pi$ pulses can reduce dipolar interactions between spins of the same species in solids. Our simulations of pulsed electron spin resonance (ESR) experiments show that $\pi$ rotations with small ($<$~10\%) imperfections refocus instantaneous diffusion. Here, the intractable N-body problem of interacting dipoles is approximated by the average evolution of a single spin in a changing mean field. These calculations agree well with experiments and do not require powerful hardware. Our results add to past attempts to explain similar phenomena in solid state nuclear magnetic resonance (NMR). Although the fundamental physics of NMR are similar to ESR, the larger linewidths in ESR and stronger dipolar interactions between electron spins compared to nuclear spins preclude drawing conclusions from NMR studies alone. For bulk spins, we also find that using XYXY results in less inflation of the deduced echo decay times as compared to decays obtained with CPMG., Comment: 10 pages, 5 figures

We report transport measurements of electrons on helium in a microchannel device where the channels are 200 nm deep and 3 $\mu$m wide. The channels are fabricated above amorphous metallic Ta$_{40}$W$_{40}$Si$_{20}$, which has surface roughness below 1 nm and minimal variations in work function across the surface due to the absence of polycrystalline grains. We are able to set the electron density in the channels using a ground plane. We estimate a mobility of 300 cm$^2$/V$\cdot$s and electron densities as high as 2.56$\times$10$^9$ cm$^{-2}$. We demonstrate control of the transport using a barrier which enables pinchoff at a central microchannel connecting two reservoirs. The conductance through the central microchannel is measured to be 10 nS for an electron density of 1.58$\times$10$^9$ cm$^{-2}$. Our work extends transport measurements of surface electrons to thin helium films in microchannel devices above metallic substrates., Comment: 4 pages, 4 figures

We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multiple fluxonium transitions, observe multilevel Autler-Townes splitting and measure an excited state lifetime of $T_\mathrm{1}=20$ $\mu$s. By measuring $T_1$ at different magnetic flux values, we find a crossover in the lifetime limiting mechanism from capacitive to inductive losses.

In this work, we demonstrate the use of frequency-tunable superconducting NbTiN coplanar waveguide microresonators for multi-frequency pulsed electron spin resonance (ESR) experiments. By applying a bias current to the center pin, the resonance frequency ($\sim$7.6 GHz) can be continuously tuned by as much as 95 MHz in 270 ns without a change in the quality factor of 3000 at 2K. We demonstrate the ESR performance of our resonators by measuring donor spin ensembles in silicon and show that adiabatic pulses can be used to overcome magnetic field inhomogeneities and microwave power limitations due to the applied bias current. We take advantage of the rapid tunability of these resonators to manipulate both phosphorus and arsenic spins in a single pulse sequence, demonstrating pulsed double electron-electron resonance (DEER). Our NbTiN resonator design is useful for multi-frequency pulsed ESR and should also have applications in experiments where spin ensembles are used as quantum memories., Comment: 5 pages, 4 figures

We achieve the strong coupling regime between an ensemble of phosphorus donor spins in a highly enriched $^{28}$Si crystal and a 3D dielectric resonator. Spins were polarized beyond Boltzmann equilibrium using spin selective optical excitation of the no-phonon bound exciton transition resulting in $N$ = $3.6\cdot10^{13}$ unpaired spins in the ensemble. We observed a normal mode splitting of the spin ensemble-cavity polariton resonances of 2$g\sqrt{N}$ = 580 kHz (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75,000 ($\gamma \ll \kappa \approx$ 60 kHz where $\gamma$ and $\kappa$ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time (T$_2^*$ = 9 $\mu$s) providing a wide window for viewing the dynamics of the coupled spin ensemble-cavity system. The free induction decay shows up to a dozen collapses and revivals revealing a coherent exchange of excitations between the superradiant state of the spin ensemble and the cavity at the rate $g\sqrt{N}$. The ensemble is found to evolve as a single large pseudospin according to the Tavis-Cummings model due to minimal inhomogeneous broadening and uniform spin-cavity coupling. We demonstrate independent control of the total spin and the initial Z-projection of the psuedospin using optical excitation and microwave manipulation respectively. We vary the microwave excitation power to rotate the pseudospin on the Bloch sphere and observe a long delay in the onset of the superradiant emission as the pseudospin approaches full inversion. This delay is accompanied by an abrupt $\pi$ phase shift in the peusdospin microwave emission. The scaling of this delay with the initial angle and the sudden phase shift are explained by the Tavis-Cummings model., Comment: 9 pages, 7 figures

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.

We report on electron spin resonance (ESR) measurements of phosphorus donors localized in a 200 square micron area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design we are able to detect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1 - 10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Due to the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.

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.

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., Comment: 10 pages, 5 figures

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.

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.

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., Comment: Published version - more detailed discussions, robustness to dephasing pointed out additionally

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., Comment: 13 pages, 4 figures

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$\mu$m) channel and narrow underlying gates (0.5$\mu$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.

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., Comment: 24 pages, 9 figures

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.

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., Comment: 11 pages, 6 figures

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., Comment: 5 pages, 4 figures, 1 table

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., Comment: 5 pages, 4 figures

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/$\mu$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 $\eta_a=-1.9\pm0.2\times10^{-3} \mu$m$^2$/V$^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance., Comment: 5 pages, 3 figures

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., Comment: Published version. Corrected b and B values from previous version

The ESR response from highly metal-semiconductor(M-SC) separated SWCNTs for temperatures T between 0.39 and 200 K is characteristically different for the two systems. The signal originates from defect spins but interaction with free electrons leads to a larger line width for M tubes. The latter decreases with increasing T whereas it increases with T for SC tubes. The spins undergo a ferromagnetic phase transition below around 10 K. Indirect exchange is suggested to be responsible for the spin-spin interaction, supported by RKKY interaction in the case of M tubes. For SC tubes spin-lattice relaxation via an Orbach process is suggested to determine the line width.

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.

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., Comment: 4 pages, 4 figures

Spins of donor electrons and nuclei in silicon are promising quantum bit (qubit) candidates which combine long coherence times with the fabrication finesse of the silicon nanotechnology industry. We outline a potentially scalable spin qubit architecture where donor nuclear and electron spins are coupled to spins of electrons in quantum dots and discuss requirements for donor placement aligned to quantum dots by single ion implantation.

We present an electron spin resonance (ESR) approach to characterize shallow electron trapping in band-tail states at Si/SiO2 interfaces in metal-oxide-semiconductor (MOS) devices and demonstrate it on two MOS devices fabricated at different laboratories. Despite displaying similar low temperature (4.2 K) peak mobilities, our ESR data reveal a significant difference in the Si/SiO2 interface quality of these two devices, specifically an order of magnitude difference in the number of shallow trapped charges at the Si/SiO2 interfaces. Thus, our ESR method allows a quantitative evaluation of the Si/SiO2 interface quality at low electron densities, where conventional mobility measurements are not possible., Comment: 6 pages, 3 figures

Electrons floating on the surface of superfluid helium have been suggested as promising mobile spin qubits. Three micron wide channels fabricated with standard silicon processing are filled with superfluid helium by capillary action. Photoemitted electrons are held by voltages applied to underlying gates. The gates are connected as a 3-phase charge-coupled device (CCD). Starting with approximately one electron per channel, no detectable transfer errors occur while clocking $10^9$ pixels. One channel with its associated gates is perpendicular to the other 120, providing a CCD which can transfer electrons between the others. This perpendicular channel has not only shown efficient electron transport but also serves as a way to measure the uniformity of the electron occupancy in the 120 parallel channels.

Unprecedented transport efficiency is demonstrated for electrons on the surface of micron-scale superfluid helium filled channels by co-opting silicon processing technology to construct the equivalent of a charge-coupled device (CCD). Strong fringing fields lead to undetectably rare transfer failures after over a billion cycles in two dimensions. This extremely efficient transport is measured in 120 channels simultaneously with packets of up to 20 electrons, and down to singly occupied pixels. These results point the way towards the large scale transport of either computational qubits or electron spin qubits used for communications in a hybrid qubit system.

Silicon is undoubtedly one of the most promising semiconductor materials for spin-based information processing devices. Its highly advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of an isotopically-purified $^{28}$Si form with no magnetic nuclei overcomes what is a main 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 what can be achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in very pure $^{28}$Si material, with a residual $^{29}$Si concentration of less than 50 ppm and donor densities of $10^{14-15}$ per cm$^3$. We elucidate three separate mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime $T_2$ up to 2 seconds. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. We apply a magnetic field gradient in order to suppress such interactions and obtain an extrapolated electron spin $T_2$ of 10 seconds at 1.8 K. These coherence lifetimes are without peer in the solid state by several orders of magnitude and comparable with high-vacuum qubits, making electron spins of donors in silicon ideal components of a quantum computer, or quantum memories for systems such as superconducting qubits., Comment: 18 pages, 4 figures, supplementary information

We have measured the electrically detected magnetic resonance of channel-implanted donors in silicon field-effect transistors in resonant X- ($9.7\:$GHz) and W-band ($94\:$GHz) microwave cavities, with corresponding Zeeman fields of $0.35\:$T and $3.36\:$T, respectively. It is found that the conduction electron resonance signal increases by two orders of magnitude from X- to W-band, while the hyperfine-split donor resonance signals are enhanced by over one order of magnitude. We rule out a bolometric origin of the resonance signals, and find that direct spin-dependent scattering between the two-dimensional electron gas and neutral donors is inconsistent with the experimental observations. We propose a new polarization transfer model from the donor to the conduction electrons as the main contributer to the spin resonance signals observed., Comment: 5 pages, 3 figures

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., Comment: 13 pages, 5 figures

Electron spin qubits in molecular systems offer high reproducibility and the ability to self assemble into larger architectures. However, interactions between neighbouring qubits are 'always-on' and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both controllably turn on/off dipolar interactions between neighbouring spins and benefit from the long nuclear spin decoherence times (T2n). We transfer qubit states between the electron and 15N nuclear spin in 15N@C60 with a two-way process fidelity of 88%, using a series of tuned microwave and radiofrequency pulses and measure a nuclear spin coherence lifetime of over 100 ms., Comment: 5 pages, 3 figures with supplementary material (8 pages)

One of the most significant hurdles to be overcome on the path to practical quantum information processors is dealing with quantum errors. Dynamical decoupling is a particularly promising approach that complements conventional quantum error correction by eliminating some correlated errors without the overhead of additional qubits. In practice, the control pulses used for decoupling are imperfect and thus introduce errors which can accumulate after many pulses. These instrumental errors can destroy the quantum state. Here we examine several dynamical decoupling sequences, and their concatenated variants, using electron spin resonance of donor electron spins in a $^{28}$Si crystal. All of the sequences cancel phase noise arising from slowly fluctuating magnetic fields in our spectrometer, but only those sequences based upon alternating $\pi$-rotations about the X- and Y-axes in the rotating frame (XYXY sequences) demonstrate the ability to store an arbitrary quantum state. By comparing the experimental results with a detailed theoretical analysis we demonstrate that the superior performance of XYXY sequences arises from the fact that they are self-correcting for the dominant instrumental pulse errors in magnetic resonance experiments. We further find that concatenated sequences perform better than the periodic variants, maintaining near 100% fidelities for spin states even after several hundred control pulses. Intuitively, one would expect the instrumental error to increase with the number of pulses in the sequence but we show that the dominant first-order error does not increase when concatenating the XYXY sequence., Comment: 15 pages, 3 figures

Electrons on the surface of liquid helium are a widely studied system that may also provide a promising method to implement a quantum computer. One experimental challenge in these studies is to generate electrons on the helium surface in a reliable manner without heating the cryo-system. An electron source relying on photoemission from a zinc film has been previously described using a high power continuous light source that heated the low temperature system. This work has been reproduced more compactly by using a low power pulsed lamp that avoids any heating. About 5e3 electrons are collected on 1 cm^2 of helium surface for every pulse of light. A time-resolved experiment suggests that electrons are either emitted over or tunnel through the 1eV barrier formed by the thin superfluid helium film on the zinc surface. No evidence of trapping or bubble formation is seen., Comment: 9 pages, 3 figures, submitted to J. Low Temp. Phys

The electron paramagnetic resonance (EPR) linewidths of B acceptors in Si are found to reduce dramatically in isotopically purified 28Si single crystals. Moreover, extremely narrow substructures in the EPR spectra are visible corresponding to either an enhancement or a reduction of the absorbed microwave on resonance. The origin of the substructures is attributed to a combination of simultaneous double excitation and spin relaxation in the four level spin system of the acceptors. A spin population model is developed which qualitatively describes the experimental results., Comment: 4 pages, 3 figures

While electron spins in silicon heterostructures make attractive qubits, little is known about the coherence of electrons at the Si/SiO2 interface. We report spin relaxation (T1) and coherence (T2) times for mobile electrons and natural quantum dots at a 28Si/SiO2 interface. Mobile electrons have short T1 and T2 of 0.3 us at 5 K. In line with predictions, confining electrons and cooling increases T1 to 0.8 ms at 350 mK. In contrast, T2 for quantum dots is around 10 us at 350 mK, increasing to 30 us when the dot density is reduced by a factor of two. The quantum dot T2 is shorter than T1, indicating that T2 is not controlled by T1 at 350 mK but is instead limited by an extrinsic mechanism. The evidence suggests that this extrinsic mechanism is an exchange interaction between electrons in neighboring dots., Comment: Extended with more experiments and rewritten. 6 pages, 5 figures, to be submitted to Phys. Rev. B

We propose to couple an on-chip high finesse superconducting cavity to the lateral-motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 microseconds, while energy will be coherently exchanged with the cavity photons in less than 10 nanoseconds for charge states and faster than 1 microsecond for spin states, making the system attractive for quantum information processing and cavity quantum electrodynamics experiments. Strong interaction with cavity photons will provide the means for both nondestructive readout and coupling of distant electrons., Comment: 4 pages, 3 figures, supplemental materials

We report theoretical and experimental studies of the longitudinal electron spin and orbital relaxation time of interstitial Li donors in $^{28}$Si. We predict that despite the near-degeneracy of the ground-state manifold the spin relaxation times are extremely long for the temperatures below 0.3 K. This prediction is based on a new finding of the chiral symmetry of the donor states, which presists in the presence of random strains and magnetic fields parallel to one of the cubic axes. Experimentally observed kinetics of magnetization reversal at 2.1 K and 4.5 K are in a very close agreement with the theory. To explain these kinetics we introduced a new mechanism of spin decoherence based on a combination of a small off-site displacement of the Li atom and an umklapp phonon process. Both these factors weakly break chiral symmetry and enable the long-term spin relaxation.

The transfer of information between different physical forms is a central theme in communication and computation, for example between processing entities and memory. Nowhere is this more crucial than in quantum computation, where great effort must be taken to protect the integrity of a fragile quantum bit. Nuclear spins are known to benefit from long coherence times compared to electron spins, but are slow to manipulate and suffer from weak thermal polarisation. A powerful model for quantum computation is thus one in which electron spins are used for processing and readout while nuclear spins are used for storage. Here we demonstrate the coherent transfer of a superposition state in an electron spin 'processing' qubit to a nuclear spin 'memory' qubit, using a combination of microwave and radiofrequency pulses applied to 31P donors in an isotopically pure 28Si crystal. The electron spin state can be stored in the nuclear spin on a timescale that is long compared with the electron decoherence time and then coherently transferred back to the electron spin, thus demonstrating the 31P nuclear spin as a solid-state quantum memory. The overall store/readout fidelity is about 90%, attributed to systematic imperfections in radiofrequency pulses which can be improved through the use of composite pulses. We apply dynamic decoupling to protect the nuclear spin quantum memory element from sources of decoherence. The coherence lifetime of the quantum memory element is found to exceed one second at 5.5K., Comment: v2: Tomography added and storage of general initial states

We report measurements of spin-dependent scattering of conduction electrons by neutral donors in an accumulation-mode field-effect transistor formed in isotopically enriched silicon. Spin-dependent scattering was detected using electrically detected magnetic resonance where the spectra show resonant changes in the source-drain voltage for conduction electrons and electrons bound to donors. We discuss the utilization of spin-dependent scattering as a mechanism for the readout of donor spin-states in silicon based quantum computers., Comment: 14 pages, 3 figures. Correction made to figure3(b)