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We report on low-frequency measurements of few electrons floating on superfluid helium using a bespoke cryogenic cascode amplifier circuit built with off-the-shelf GaAs High-Electron-Mobility Transistors (HEMTs). We integrate this circuit with a Charge-Coupled Device (CCD) to transport the electrons on helium and characterize its performance. We show that this circuit has a Signal-to-Noise ratio (SNR) of $\thicksim$ 2$\frac{e}{\sqrt{Hz}}$ at 102 kHz, an order of magnitude improvement from previous implementations and provides a compelling alternative to few electron sensing with high frequency resonators.

Superconducting qubits are a leading system for realizing large scale quantum processors, but overall gate fidelities suffer from coherence times limited by microwave dielectric loss. Recently discovered tantalum-based qubits exhibit record lifetimes exceeding 0.3 ms. Here we perform systematic, detailed measurements of superconducting tantalum resonators in order to disentangle sources of loss that limit state-of-the-art tantalum devices. By studying the dependence of loss on temperature, microwave photon number, and device geometry, we quantify materials-related losses and observe that the losses are dominated by several types of saturable two level systems (TLSs), with evidence that both surface and bulk related TLSs contribute to loss. Moreover, we show that surface TLSs can be altered with chemical processing. With four different surface conditions, we quantitatively extract the linear absorption associated with different surface TLS sources. Finally, we quantify the impact of the chemical processing at single photon powers, the relevant conditions for qubit device performance. In this regime we measure resonators with internal quality factors ranging from 5 to 15 x 10^6, comparable to the best qubits reported. In these devices the surface and bulk TLS contributions to loss are comparable, showing that systematic improvements in materials on both fronts will be necessary to improve qubit coherence further.

Over the past decades, superconducting qubits have emerged as one of the leading hardware platforms for realizing a quantum processor. Consequently, researchers have made significant effort to understand the loss channels that limit the coherence times of superconducting qubits. A major source of loss has been attributed to two level systems that are present at the material interfaces. We recently showed that replacing the metal in the capacitor of a transmon with tantalum yields record relaxation and coherence times for superconducting qubits, motivating a detailed study of the tantalum surface. In this work, we study the chemical profile of the surface of tantalum films grown on c-plane sapphire using variable energy X-ray photoelectron spectroscopy (VEXPS). We identify the different oxidation states of tantalum that are present in the native oxide resulting from exposure to air, and we measure their distribution through the depth of the film. Furthermore, we show how the volume and depth distribution of these tantalum oxidation states can be altered by various chemical treatments. By correlating these measurements with detailed measurements of quantum devices, we can improve our understanding of the microscopic device losses.

Neutral silicon vacancy (SiV0) centers in diamond are promising candidates for quantum networks because of their excellent optical properties and long spin coherence times. However, spin-dependent fluorescence in such defects has been elusive due to poor understanding of the excited state fine structure and limited off-resonant spin polarization. Here we report the realization of optically detected magnetic resonance and coherent control of SiV0 centers at cryogenic temperatures, enabled by efficient optical spin polarization via previously unreported higher-lying excited states. We assign these states as bound exciton states using group theory and density functional theory. These bound exciton states enable new control schemes for SiV0 as well as other emerging defect systems.

Atomic and atom-like defects in the solid-state are widely explored for quantum computers, networks and sensors. Rare earth ions are an attractive class of atomic defects that feature narrow spin and optical transitions that are isolated from the host crystal, allowing incorporation into a wide range of materials. However, the realization of long electronic spin coherence times is hampered by magnetic noise from abundant nuclear spins in the most widely studied host crystals. Here, we demonstrate that Er$^{3+}$ ions can be introduced via ion implantation into TiO$_2$, a host crystal that has not been studied extensively for rare earth ions and has a low natural abundance of nuclear spins. We observe efficient incorporation of the implanted Er$^{3+}$ into the Ti$^{4+}$ site (40% yield), and measure narrow inhomogeneous spin and optical linewidths (20 and 460 MHz, respectively) that are comparable to bulk-doped crystalline hosts for Er$^{3+}$. This work demonstrates that ion implantation is a viable path to studying rare earth ions in new hosts, and is a significant step towards realizing individually addressed rare earth ions with long spin coherence times for quantum technologies.

Coherence times of electron spins bound to phosphorus donors have been measured, using a standard Hahn echo technique, to be up to 20 ms in isotopically pure silicon with [P]$ = 10^{14}$ cm$^{-3}$ and at temperatures $\leq 4 $K. Although such times are exceptionally long for electron spins in the solid state, they are nevertheless limited by donor electron spin-spin interactions. Suppressing such interactions requires even lower donor concentrations, which lie below the detection limit for typical electron spin resonance (ESR) spectrometers. Here we describe an alternative method for phosphorus donor ESR detection, exploiting the spin-to-charge conversion provided by the optical donor bound exciton transition. We characterise the method and its dependence on laser power and use it to measure a coherence time of $T_2 = 130 $ms for one of the purest silicon samples grown to-date ([P]$ = 5\times 10^{11} $cm$^{-3}$). We then benchmark this result using an alternative application of the donor bound exciton transition: optically polarising the donor spins before using conventional ESR detection at 1.7~K for a sample with [P]$ = 4\times10^{12} $cm$^{-3}$, and measuring in this case a $T_2$ of 350 ms.

One of the biggest challenges impeding the progress of Metal-Oxide-Silicon (MOS) quantum dot devices is the presence of disorder at the Si/SiO$_2$ interface which interferes with controllably confining single and few electrons. In this work we have engineered a low-disorder MOS quantum double-dot device with critical electron densities, i.e. the lowest electron density required to support a conducting pathway, approaching critical electron densities reported in high quality Si/SiGe devices and commensurate with the lowest critical densities reported in any MOS device. Utilizing a nearby charge sensor, we show that the device can be tuned to the single-electron regime where charging energies of $\approx$8 meV are measured in both dots, consistent with the lithographic size of the dot. Probing a wide voltage range with our quantum dots and charge sensor, we detect three distinct electron traps, corresponding to a defect density consistent with the ensemble measured critical density. Low frequency charge noise measurements at 300 mK indicate a 1/$f$ noise spectrum of 3.4 $\mu$eV/Hz$^{1/2}$ at 1 Hz and magnetospectroscopy measurements yield a valley splitting of 110$\pm$26 $\mu$eV. This work demonstrates that reproducible MOS spin qubits are feasible and represents a platform for scaling to larger qubit systems in MOS., Comment: 16 pages, 5 figures

We have developed a method to probe the temperature of surface state electrons (SSE) above a superfluid Helium-4 surface using the Seebeck effect. In contrast to previously used SSE thermometry, this technique does not require detailed knowledge of the non-linear mobility. We demonstrate the use of this method by measuring energy relaxation of SSE at 1.6 K in a microchannel device with $0.6\:\mu\mbox{m}$ deep helium. In this regime, both vapor atom scattering and 2-ripplon scattering contribute to energy relaxation to which we compare our measurements. We conclude that this technique provides a reliable measure of electron temperature while requiring a less detailed understanding of the electron interactions with the environment than previously utilized thermometry techniques.

Color centers in diamond are a promising platform for quantum technologies, and understanding their interactions with the environment is crucial for these applications. We report a study of spin- lattice relaxation (T1) of the neutral charge state of the silicon vacancy center in diamond. Above 20 K, T1 decreases rapidly with a temperature dependence characteristic of an Orbach process, and is strongly anisotropic with respect to magnetic field orientation. As the angle of the magnetic field is rotated relative to the symmetry axis of the defect, T1 is reduced by over three orders of magnitude. The electron spin coherence time (T2) follows the same temperature dependence but is drastically shorter than T1. We propose that these observations result from phonon-mediated transitions to a low lying excited state that are spin conserving when the magnetic field is aligned with the defect axis, and we discuss likely candidates for this excited state.

We use the nuclear spin coherence of $^{31}$P donors in $^{28}$Si to determine flip-flop rates of donor electron spins. Isotopically purified $^{28}$Si crystals minimize the number of $^{29}$Si flip-flops, and measurements at 1.7 K suppress electron spin relaxation. The crystals have donor concentrations ranging from $1.2\times10^{14}$ to $3.3\times10^{15}~\text{P/cm}^3$, allowing us to detect how electron flip-flop rates change with donor density. We also simulate how electron spin flip-flops can cause nuclear spin decoherence. We find that when these flip-flops are the primary cause of decoherence, Hahn echo decays have a stretched exponential form. For our two higher donor density crystals ($> 10^{15}~\text{P/cm}^3$), there is excellent agreement between simulations and experiments. In lower density crystals ($< 10^{15}~\text{P/cm}^3$), there is no longer agreement between simulations and experiments, suggesting a different, unknown mechanism is limiting nuclear spin coherence. The nuclear spin coherence in the lowest density crystal ($1.2 \times 10^{14}~\text{P/cm}^3$) allows us to place upper bounds on the magnitude of noise sources in bulk crystals such as electric field fluctuations that may degrade silicon quantum devices., Comment: 13 pages, 4 figures

Engineering coherent systems is a central goal of quantum science. Color centers in diamond are a promising approach, with the potential to combine the coherence of atoms with the scalability of a solid state platform. However, the solid environment can adversely impact coherence. For example, phonon- mediated spin relaxation can induce spin decoherence, and electric field noise can change the optical transition frequency over time. We report a novel color center with insensitivity to both of these sources of environmental decoherence: the neutral charge state of silicon vacancy (SiV0). Through careful material engineering, we achieve over 80% conversion of implanted silicon to SiV0. SiV0 exhibits excellent spin properties, with spin-lattice relaxation times (T1) approaching one minute and coherence times (T2) approaching one second, as well as excellent optical properties, with approximately 90% of its emission into the zero-phonon line and near-transform limited optical linewidths. These combined properties make SiV0 a promising defect for quantum networks.

Electron-beam (e-beam) lithography is commonly used in fabricating metal-oxide-silicon (MOS) quantum devices but creates defects at the Si/SiO$_2$ interface. Here we show that a forming gas anneal is effective at removing shallow defects ($\leq$ 4 meV below the conduction band edge) created by an e-beam exposure by measuring the density of shallow electron traps in two sets of high-mobility MOS field-effect transistors (MOSFETs). One set was irradiated with an electron-beam (10 keV, 40 $\mu$C/cm$^2$) and was subsequently annealed in forming gas while the other set remained unexposed. Low temperature (335 mK) transport measurements indicate that the forming gas anneal recovers the e-beam exposed sample's peak mobility (14,000 cm$^2$/Vs) to within a factor of two of the unexposed sample's mobility (23,000 cm$^2$/Vs). Using electron spin resonance (ESR) to measure the density of shallow traps, we find that the two sets of devices are nearly identical, indicating the forming gas anneal is sufficient to anneal out shallow defects generated by the e-beam exposure. Fitting the two sets of devices' transport data to a percolation transition model, we extract a T=0 percolation threshold density in quantitative agreement with our lowest temperature ESR-measured trap densities.

Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as a function of $^{29}$Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that decoherence is controlled by $^{29}$Si flip-flops resulting in both fast (exponential) and slow (non-exponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50% $^{29}$Si to 3 s in crystals containing 1% $^{29}$Si. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors `protects' the donor nuclear spins by suppressing $^{29}$Si flip-flops within a `frozen core', as a result of the detuning of the $^{29}$Si spins caused by their hyperfine coupling to the electron spin.

Selenium impurities in silicon are deep double donors and their optical and electronic properties have been recently investigated due to their application for infrared detection. However, a singly-ionised selenium donor (Se$^{+}$) possesses an electron spin which makes it a potential candidate as a silicon-based spin qubit, with significant potential advantages compared to the more commonly studied group V donors. Here we study the electron spin relaxation ($T_1$) and coherence ($T_2$) times of Se$^{+}$ in isotopically purified 28-silicon, and find them to be up to two orders of magnitude longer than shallow group V donors at temperatures above $\sim 15$ K. We further study the dynamics of donor-acceptor recombination between selenium and boron, demonstrating that it is possible to control the donor charge state through optical excitation of neutral Se$^0$.

A major challenge in using spins in the solid state for quantum technologies is protecting them from sources of decoherence. This can be addressed, to varying degrees, by improving material purity or isotopic composition for example, or active error correction methods such as dynamic decoupling, or even combinations of the two. However, a powerful method applied to trapped ions in the context of frequency standards and atomic clocks, is the use of particular spin transitions which are inherently robust to external perturbations. Here we show that such `clock transitions' (CTs) can be observed for electron spins in the solid state, in particular using bismuth donors in silicon. This leads to dramatic enhancements in the electron spin coherence time, exceeding seconds. We find that electron spin qubits based on CTs become less sensitive to the local magnetic environment, including the presence of 29Si nuclear spins as found in natural silicon. We expect the use of such CTs will be of additional importance for donor spins in future devices, mitigating the effects of magnetic or electric field noise arising from nearby interfaces., Comment: 11 pages, 6 figures

Bismuth (209Bi) is the deepest Group V donor in silicon and possesses the most extreme characteristics such as a 9/2 nuclear spin and a 1.5 GHz hyperfine coupling. These lead to several potential advantages for a Si:Bi donor electron spin qubit compared to the more common phosphorus donor. Previous studies on Si:Bi have been performed using natural silicon where linewidths and electron spin coherence times are limited by the presence of 29Si impurities. Here we describe electron spin resonance (ESR) and electron nuclear double resonance (ENDOR) studies on 209Bi in isotopically pure 28Si. ESR and ENDOR linewidths, transition probabilities and coherence times are understood in terms of the spin Hamiltonian parameters showing a dependence on field and mI of the 209Bi nuclear spin. We explore various decoherence mechanisms applicable to the donor electron spin, measuring coherence times up to 700 ms at 1.7 K at X-band, comparable with 28Si:P. The coherence times we measure follow closely the calculated field-sensitivity of the transition frequency, providing a strong motivation to explore 'clock' transitions where coherence lifetimes could be further enhanced., Comment: 5 pages, 4 figures

Quantum computers (QCs) must implement quantum error correcting codes (QECCs) to protect their logical qubits from errors, and modeling the effectiveness of QECCs on QCs is an important problem for evaluating the QC architecture. The previously developed Monte Carlo (MC) error models may take days or weeks of execution to produce an accurate result due to their random sampling approach. We present an alternative analytical error model that generates, over the course of executing the quantum program, a probability tree of the QC's error states. By calculating the fidelity of the quantum program directly, this error model has the potential for enormous speedups over the MC model when applied to small yet useful problem sizes. We observe a speedup on the order of 1,000X when accuracy is required, and we evaluate the scaling properties of this new analytical error model.

We report Stark shift measurements for 121Sb donor electron spins in silicon using pulsed electron spin resonance. Interdigitated metal gates on top of a Sb-implanted 28Si epi-layer are used to apply electric fields. Two Stark effects are resolved: a decrease of the hyperfine coupling between electron and nuclear spins of the donor and a decrease in electron Zeeman g-factor. The hyperfine term prevails at X-band magnetic fields of 0.35T, while the g-factor term is expected to dominate at higher magnetic fields. A significant linear Stark effect is also resolved presumably arising from strain., Comment: 10 pages, 4 figures, to be submitted to PRL

Electron spin echo envelope modulation (ESEEM) has been observed for the first time from a coupled hetero-spin pair of electron and nucleus in liquid solution. Previously, modulation effects in spin echo experiments have only been described in liquid solutions for a coupled pair of homonuclear spins in NMR or a pair of resonant electron spins in EPR. We observe low-frequency ESEEM (26 and 52 kHz) due to a new mechanism present for any electron spin with S>1/2 that is hyperfine coupled to a nuclear spin. In our case these are electron spin (S=3/2) and nuclear spin (I=1) in the endohedral fullerene N@C60. The modulation is shown to arise from second order effects in the isotropic hyperfine coupling of an electron and 14N nucleus., Comment: 15 pages, 4 figures