Electron Spin Resonance at the Level of 10^{4} Spins Using Low Impedance Superconducting Resonators

X-Band Single Chip Integrated Pulsed Electron Spin Resonance Microsystem

We report on the design and characterization of a single chip integrated pulsed electron spin resonance detector operating at 9.1 GHz. The microsystem consists of an excitation microcoil, a detection microcoil, a low noise microwave preamplifier, a mixer, and an intermediate frequency (IF) amplifier. The chip area is about 0.7 mm2. To exemplify its possible applications, we report the results of single pulse, Rabi nutation, Hahn echo, two echoes, Carr-Purcell, and inversion recovery echo experiments performed on 0.02 and 0.05 nL samples of α, γ-bisdiphenylene-β-phenylallyl (BDPA) and 1% BDPA in polystyrene (BDPA:PS) at room temperature. The measured spin sensitivity is about 8 × 107 spins/Hz1/2 on a sensitive volume of about 0.1 nL. The microsystem power consumption is less than 100 mW, the radio frequency (RF) input bandwidth is 8.8 to 9.8 GHz, the IF output bandwidth is DC to 350 MHz, and the deadtime is less than 30 ns.

Roadmap on nanoscale magnetic resonance imaging

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Strong microwave squeezing above 1 Tesla and 1 Kelvin

Squeezed states of light have been used extensively to increase the precision of measurements, from the detection of gravitational waves to the search for dark matter. In the optical domain, high levels of vacuum noise squeezing are possible due to the availability of low loss optical components and high-performance squeezers. At microwave frequencies, however, limitations of the squeezing devices and the high insertion loss of microwave components make squeezing vacuum noise an exceptionally difficult task. Here we demonstrate direct measurements of high levels of microwave squeezing. We use an ultra-low loss setup and weakly-nonlinear kinetic inductance parametric amplifiers to squeeze microwave noise 7.8(2) dB below the vacuum level. The amplifiers exhibit a resilience to magnetic fields and permit the demonstration of large squeezing levels inside fields of up to 2 T. Finally, we exploit the high critical temperature of our amplifiers to squeeze a warm thermal environment, achieving vacuum level noise at a temperature of 1.8 K. These results enable experiments that combine squeezing with magnetic fields and permit quantum-limited microwave measurements at elevated temperatures, significantly reducing the complexity and cost of the cryogenic systems required for such experiments.

Latched detection of zeptojoule spin echoes with a kinetic inductance parametric oscillator

When strongly pumped at twice their resonant frequency, nonlinear resonators develop a high-amplitude intracavity field, a phenomenon known as parametric self-oscillations. The boundary over which this instability occurs can be extremely sharp and thereby presents an opportunity for realizing a detector. Here, we operate such a device based on a superconducting microwave resonator whose nonlinearity is engineered from kinetic inductance. The device indicates the absorption of low-power microwave wavepackets by transitioning to a self-oscillating state. Using calibrated pulses, we measure the detection efficiency to zeptojoule energy wavepackets. We then apply it to measurements of electron spin resonance, using an ensemble of 209Bi donors in silicon that are inductively coupled to the resonator. We achieve a latched readout of the spin signal with an amplitude that is five hundred times greater than the underlying spin echoes.

Nanoscale Magnets Embedded in a Microstrip

Nanoscale magnetic resonance imaging (NanoMRI) is an active area of applied research with potential applications in structural biology and quantum engineering. The success of this technological vision hinges on improving the instrument's sensitivity and functionality. A particular challenge is the optimization of the magnetic field gradient required for spatial encoding and of the radio frequency field used for spin control, in analogy to the components used in clinical MRI. In this work, we present the fabrication and characterization of a magnet-in-microstrip device that yields a compact form factor for both elements. We find that our design leads to a number of advantages, among them a 4-fold increase of the magnetic field gradient compared to those achieved with traditional fabrication methods. Our results can be useful for boosting the efficiency of a variety of different experimental arrangements and detection principles in the field of NanoMRI.

Scanning Spin Probe Based on Magnonic Vortex Quantum Cavities

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients: First, a static magnetic field together with field gradients to Zeeman split the electronic energy levels with spatial resolution; second, a radio frequency (rf) magnetic field capable of inducing spin transitions; finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects, or scanning probes. Here, we theoretically propose the realization of an EPR scanning sensor merging all three characteristics into a single device: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, suggesting a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our numerical simulations show that, by using low damping magnets, it is theoretically possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

Microwave Fluorescence Detection of Spin Echoes

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.

Single-electron spin resonance detection by microwave photon counting

Electron spin resonance spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing^1,2, but it gives access only to ensemble-averaged quantities owing to its limited signal-to-noise ratio. Single-electron spin sensitivity has, however, been reached using spin-dependent photoluminescence^3-5, transport measurements^6-9 and scanning-probe techniques^10-12. These methods are system-specific or sensitive only in a small detection volume^13,14, so that practical single-spin detection remains an open challenge. Here, we demonstrate single-electron magnetic resonance by spin fluorescence detection¹⁵, using a microwave photon counter at millikelvin temperatures¹⁶. We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality-factor planar superconducting resonator to enhance their radiative decay rate¹⁷, with a signal-to-noise ratio of 1.9 in one second integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the spin radiative lifetime. The method has the potential to be applied to arbitrary paramagnetic species with long enough non-radiative relaxation times, and allows single-spin detection in a volume as large as the resonator magnetic mode volume (approximately 10 μm³ in the present experiment), orders of magnitude larger than other single-spin detection techniques. As such, it may find applications in magnetic resonance and quantum computing.

Probing spin dynamics of ultra-thin van der Waals magnets via photon-magnon coupling

Layered van der Waals (vdW) magnets can maintain a magnetic order even down to the single-layer regime and hold promise for integrated spintronic devices. While the magnetic ground state of vdW magnets was extensively studied, key parameters of spin dynamics, like the Gilbert damping, crucial for designing ultra-fast spintronic devices, remains largely unexplored. Despite recent studies by optical excitation and detection, achieving spin wave control with microwaves is highly desirable, as modern integrated information technologies predominantly are operated with these. The intrinsically small numbers of spins, however, poses a major challenge to this. Here, we present a hybrid approach to detect spin dynamics mediated by photon-magnon coupling between high-Q superconducting resonators and ultra-thin flakes of Cr₂Ge₂Te₆ (CGT) as thin as 11 nm. We test and benchmark our technique with 23 individual CGT flakes and extract an upper limit for the Gilbert damping parameter. These results are crucial in designing on-chip integrated circuits using vdW magnets and offer prospects for probing spin dynamics of monolayer vdW magnets.

In situ amplification of spin echoes within a kinetic inductance parametric amplifier

The use of superconducting microresonators together with quantum-limited Josephson parametric amplifiers has enhanced the sensitivity of pulsed electron spin resonance (ESR) measurements by more than four orders of magnitude. So far, the microwave resonators and amplifiers have been designed as separate components due to the incompatibility of Josephson junction-based devices with magnetic fields. This has produced complex spectrometers and raised technical barriers toward adoption of the technique. Here, we circumvent this issue by coupling an ensemble of spins directly to a weakly nonlinear and magnetic field-resilient superconducting microwave resonator. We perform pulsed ESR measurements with a 1-pL mode volume containing 6 × 107 spins and amplify the resulting signals within the device. When considering only those spins that contribute to the detected signals, we find a sensitivity of [Formula: see text] for a Hahn echo sequence at a temperature of 400 mK. In situ amplification is demonstrated at fields up to 254 mT, highlighting the technique's potential for application under conventional ESR operating conditions.

Spin-Echo Silencing Using a Current-Biased Frequency-Tunable Resonator

The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth ions and suppress on demand the echo emission ("echo silencing") by two methods: (1) detuning the resonator during the spin rephasing, and (2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.

Recent advances in microresonators and supporting instrumentation for electron paramagnetic resonance spectroscopy

Electron paramagnetic resonance (EPR) spectroscopy characterizes the magnetic properties of paramagnetic materials at the atomic and molecular levels. Resonators are an enabling technology of EPR spectroscopy. Microresonators, which are miniaturized versions of resonators, have advanced inductive-detection EPR spectroscopy of mass-limited samples. Here, we provide our perspective of the benefits and challenges associated with microresonator use for EPR spectroscopy. To begin, we classify the application space for microresonators and present the conceptual foundation for analysis of resonator sensitivity. We summarize previous work and provide insight into the design and fabrication of microresonators as well as detail the requirements and challenges that arise in incorporating microresonators into EPR spectrometer systems. Finally, we provide our perspective on current challenges and prospective fruitful directions.

Superconducting micro-resonators for electron spin resonance - the good, the bad, and the future

The field of electron spin resonance (ESR) is in constant need of improving its capabilities. Among other things, this means having better resonators to reach improved spin sensitivity and enable larger microwave-power-to-microwave-magnetic-field conversion factors. Surface micro-resonators, made of small metallic patches on a dielectric substrate, provide very good absolute spin sensitivity and high conversion factors due to their very small mode volume. However, such resonators suffer from relatively low spin concentration sensitivity and a low-quality factor, a fact that offsets some of their significant potential advantages. The use of superconducting patches to replace the metallic layer seems a reasonable and straightforward solution to the quality factor issue, at least for measurements carried out at cryogenic temperatures. Nevertheless, superconducting materials, especially those that can operate at moderate cryogenic temperatures, are not easily incorporated into setups requiring high magnetic fields due to the electric current vortices generated in the latter's surface. This makes the transition from normal conducting materials to superconductors highly nontrivial. Here we present the design, fabrication, and testing results of surface micro-resonators made of yttrium barium copper oxide (YBCO), a superconducting material that operates also at high magnetic fields and makes it possible to pursue ESR at moderate cryogenic temperatures (up to ∼ 80 K). We show that with a unique experimental setup, these resonators can be made to operate well even at high fields of ∼ 1.2 T. Furthermore, we analyze the effect of current vortices on the ESR signal and the spins' coherence times. Finally, we provide a head-to-head comparison of YBCO vs copper resonators of the same dimensions, which clearly shows their pros and cons and directs us to future potential developments and improvements in this field.

Detecting spins by their fluorescence with a microwave photon counter

Quantum emitters respond to resonant illumination by radiating part of the absorbed energy. A component of this radiation field is phase coherent with the driving tone, whereas another component is incoherent and consists of spontaneously emitted photons, forming the fluorescence signal¹. Atoms, molecules and colour centres are routinely detected by their fluorescence at optical frequencies, with important applications in quantum technology^2,3 and microscopy^4-7. By contrast, electron spins are usually detected by the phase-coherent echoes that they emit in response to microwave driving pulses⁸. The incoherent part of their radiation-a stream of microwave photons spontaneously emitted upon individual spin relaxation events-has not been observed so far because of the low spin radiative decay rate and of the lack of single microwave photon detectors (SMPDs). Here using superconducting quantum devices, we demonstrate the detection of a small ensemble of donor spins in silicon by their fluorescence at microwave frequencies and millikelvin temperatures. We enhance their radiative decay rate by coupling them to a high-quality-factor and small-mode-volume superconducting resonator⁹, and we connect the device output to a newly developed SMPD¹⁰ based on a superconducting qubit. In addition, we show that the SMPD can be used to detect spin echoes and that standard spin characterization measurements (Rabi nutation and spectroscopy) can be achieved with both echo and fluorescence detection. We discuss the potential of SMPD detection as a method for magnetic resonance spectroscopy of small numbers of spins.

Room-Temperature Quantum Memories Based on Molecular Electron Spin Ensembles

Whilst quantum computing has recently taken great leaps ahead, the development of quantum memories has decidedly lagged behind. Quantum memories are essential devices in the quantum technology palette and are needed for intermediate storage of quantum bit states and as quantum repeaters in long-distance quantum communication. Current quantum memories operate at cryogenic, mostly sub-Kelvin temperatures and require extensive and costly peripheral hardware. It is demonstrated that ensembles of weakly coupled molecular spins show long coherence times and can be used to store microwave pulses of arbitrary phase. These studies exploit strong coupling of the spin ensemble to special 3D microwave resonators. Most importantly, these systems operate at room temperature.

Ultrastrong photon-to-magnon coupling in multilayered heterostructures involving superconducting coherence via ferromagnetic layers

The critical step for future quantum industry demands realization of efficient information exchange between different-platform hybrid systems that can harvest advantages of distinct platforms. The major restraining factor for the progress in certain hybrids is weak coupling strength between the elemental particles. In particular, this restriction impedes a promising field of hybrid magnonics. In this work, we propose an approach for realization of on-chip hybrid magnonic systems with unprecedentedly strong coupling parameters. The approach is based on multilayered microstructures containing superconducting, insulating, and ferromagnetic layers with modified photon phase velocities and magnon eigenfrequencies. The enhanced coupling strength is provided by the radically reduced photon mode volume. Study of the microscopic mechanism of the photon-to-magnon coupling evidences formation of the long-range superconducting coherence via thick strong ferromagnetic layers in superconductor/ferromagnet/superconductor trilayer in the presence of magnetization precession. This discovery offers new opportunities in microwave superconducting spintronics for quantum technologies.

A sensitivity leap for X-band EPR using a probehead with a cryogenic preamplifier

Inspired by the considerable success of cryogenically cooled NMR cryoprobes, we present an upgraded X-band EPR probehead, equipped with a cryogenic low-noise preamplifier. Our setup suppresses source noise, can handle the high microwave powers typical in X-band pulsed EPR, and is compatible with the convenient resonator coupling and sample access found on commercially available spectrometers. Our approach allows standard pulsed and continuous-wave EPR experiments to be performed at X-band frequency with significantly increased sensitivity compared to the unmodified setup. The probehead demonstrates a voltage signal-to-noise ratio (SNR) enhancement by a factor close to 8× at a temperature of 6 K, and remains close to 2× at room temperature. By further suppressing room-temperature noise at the expense of reduced microwave power (and thus minimum π-pulse length), the factor of SNR improvement approaches 15 at 6 K, corresponding to an impressive 200-fold reduction in EPR measurement time. We reveal the full potential of this probehead by demonstrating such SNR improvements using a suite of typical hyperfine and dipolar spectroscopy experiments on exemplary samples.

Hyperfine spectroscopy in a quantum-limited spectrometer

We report measurements of electron-spin-echo envelope modulation (ESEEM) performed at millikelvin temperatures in a custom-built high-sensitivity spectrometer based on superconducting micro-resonators. The high quality factor and small mode volume (down to 0.2 pL) of the resonator allow us to probe a small number of spins, down to 5 × 10 2 . We measure two-pulse ESEEM on two systems: erbium ions coupled to 183 W nuclei in a natural-abundance CaWO 4 crystal and bismuth donors coupled to residual 29 Si nuclei in a silicon substrate that was isotopically enriched in the 28 Si isotope. We also measure three- and five-pulse ESEEM for the bismuth donors in silicon. Quantitative agreement is obtained for both the hyperfine coupling strength of proximal nuclei and the nuclear-spin concentration.

Pulsed electron spin resonance of an organic microcrystal by dispersive readout

We establish a testbed system for the development of high-sensitivity Electron Spin Resonance (ESR) techniques for small samples at cryogenic temperatures. Our system consists of a NbN thin-film planar superconducting microresonator designed to have a concentrated mode volume to couple to a small amount of paramagnetic material, and to be resilient to magnetic fields of up to 400mT. At 65mK we measure high-cooperativity coupling (C≈19) to an organic radical microcrystal containing 10¹² spins in a pico-litre volume. We detect the spin-lattice decoherence rate via the dispersive frequency shift of the resonator. Techniques such as these could be suitable for applications in quantum information as well as for pulsed ESR interrogation of very few spins to provide insights into the surface chemistry of, for example, the material defects in superconducting quantum processors.

A dissymmetric [Gd2] coordination molecular dimer hosting six addressable spin qubits

Artificial magnetic molecules can host several spin qubits, which could then implement small-scale algorithms. In order to become of practical use, such molecular spin processors need to increase the available computational space and warrant universal operations. Here, we design, synthesize and fully characterize dissymetric molecular dimers hosting either one or two Gadolinium(III) ions. The strong sensitivity of Gadolinium magnetic anisotropy to its local coordination gives rise to different zero-field splittings at each metal site. As a result, the [LaGd] and [GdLu] complexes provide realizations of distinct spin qudits with eight unequally spaced levels. In the [Gd₂] dimer, these properties are combined with a Gd-Gd magnetic interaction, sufficiently strong to lift all level degeneracies, yet sufficiently weak to keep all levels within an experimentally accessible energy window. The spin Hamiltonian of this dimer allows a complete set of operations to act as a 64-dimensional all-electron spin qudit, or, equivalently, as six addressable qubits. Electron paramagnetic resonance experiments show that resonant transitions between different spin states can be coherently controlled, with coherence times T_M of the order of 1 µs limited by hyperfine interactions. Coordination complexes with embedded quantum functionalities are promising building blocks for quantum computation and simulation hybrid platforms.

Multimode Storage of Quantum Microwave Fields in Electron Spins over 100 ms

We report long coherence times (up to 300 ms) for near-surface bismuth donor electron spins in silicon coupled to a superconducting microresonator, biased at a clock transition. This enables us to demonstrate the partial absorption of a train of weak microwave fields in the spin ensemble, their storage for 100 ms, and their retrieval, using a Hahn-echo-like protocol. Phase coherence and quantum statistics are preserved in the storage.

Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

We show experimentally and describe theoretically how a conventional magnetic resonance Hahn echo sequence can lead to a self-stimulated pulse echo train when an inhomogeneously broadened spin ensemble is coupled to a resonator. Effective strong coupling between the subsystems assures that the first Hahn echo can act as a refocusing pulse on the spins, leading to self-stimulated secondary echoes. Within the framework of mean field theory, we show that this process can continue multiple times leading to a train of echoes. We introduce an analytical model that explains the shape of the first echo and numerical results that account well for the experimentally observed shape and strength of the echo train and provides insights into the collective effects involved.

Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.

Enhanced Molecular Spin-Photon Coupling at Superconducting Nanoconstrictions

We combine top-down and bottom-up nanolithography to optimize the coupling of small molecular spin ensembles to 1.4 GHz on-chip superconducting resonators. Nanoscopic constrictions, fabricated with a focused ion beam at the central transmission line, locally concentrate the microwave magnetic field. Drops of free-radical molecules have been deposited from solution onto the circuits. For the smallest ones, the molecules were delivered at the relevant circuit areas by means of an atomic force microscope. The number of spins N_eff effectively coupled to each device was accurately determined combining Scanning Electron and Atomic Force Microscopies. The collective spin-photon coupling constant has been determined for samples with N_eff ranging between 2 × 10⁶ and 10¹² spins, and for temperatures down to 44 mK. The results show the well-known collective enhancement of the coupling proportional to the square root of N_eff. The average coupling of individual spins is enhanced by more than 4 orders of magnitude (from 4 mHz up to above 180 Hz), when the transmission line width is reduced from 400 μm down to 42 nm, and reaches maximum values near 1 kHz for molecules located on the smallest nanoconstrictions.

Pulsed electron spin resonance spectroscopy in the Purcell regime

In EPR, spin relaxation is typically governed by interactions with the lattice or other spins. However, it has recently been shown that given a sufficiently strong spin-resonator coupling and high resonator quality factor, the spontaneous emission of microwave photons from the spins into the resonator can become the main relaxation mechanism, as predicted by Purcell. With increasing attention on the use of microresonators for EPR to achieve high spin-number sensitivity it is important to understand how this novel regime influences measured EPR signals, for example the amplitude and temporal shape of the spin-echo. We study this regime theoretically and experimentally, using donor spins in silicon, under different conditions of spin-linewidth and coupling homogeneity. When the spin-resonator coupling is distributed inhomogeneously, we find that the effective spin-echo relaxation time measured in a saturation recovery sequence strongly depends on the parameters for the detection echo. When the spin linewidth is larger than the resonator bandwidth, the different Fourier components of the spin echo relax with different characteristic times - due to the role of the resonator in driving relaxation - which results in the temporal shape of the echo becoming dependent on the repetition time of the experiment.

Enhancing the dipolar coupling of a S-T0 qubit with a transverse sweet spot

A fundamental challenge for quantum dot spin qubits is to extend the strength and range of qubit interactions while suppressing their coupling to the environment, since both effects have electrical origins. Key tools include the ability to take advantage of physical resources in different regimes, and to access optimal working points, sweet spots, where dephasing is minimized. Here, we explore an important resource for singlet-triplet qubits: a transverse sweet spot (TSS) that enables transitions between qubit states, a strong dipolar coupling, and leading-order protection from electrical fluctuations. Of particular interest is the possibility of transitioning between the TSS and symmetric operating points while remaining continuously protected. This arrangement is ideal for coupling qubits to a microwave cavity, because it combines tunability of the coupling with noise insensitivity. We perform simulations with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/f$$\end{document}1∕f-type electrical noise, demonstrating that two-qubit gates mediated by a resonator can achieve fidelities >99% under realistic conditions.

Semiconductor quantum dots are controlled by external fields that are tuned in order to optimise for information storage or inter-qubit interaction. Here the authors identify a working point for long-range interactions that can be reached with continuous protection from environmental noise.

Exchange-Enhanced Ultrastrong Magnon-Magnon Coupling in a Compensated Ferrimagnet

We experimentally study the spin dynamics in a gadolinium iron garnet single crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic compensation temperature, we observe ultrastrong coupling of clockwise and counterclockwise magnon modes. The magnon-magnon coupling strength reaches almost 40% of the mode frequency and can be tuned by varying the direction of the external magnetic field. We theoretically explain the observed mode coupling as arising from the broken rotational symmetry due to a weak magnetocrystalline anisotropy. The effect of this anisotropy is exchange enhanced around the ferrimagnetic compensation point.

Strong Coupling between Magnons and Microwave Photons in On-Chip Ferromagnet-Superconductor Thin-Film Devices

We demonstrate strong magnon-photon coupling of a thin-film Permalloy device fabricated on a coplanar superconducting resonator. A coupling strength of 0.152 GHz and a cooperativity of 68 are found for a 30-nm-thick Permalloy stripe. The coupling strength is tunable by rotating the biasing magnetic field or changing the volume of Permalloy. We also observe an enhancement of magnon-photon coupling in the nonlinear regime of the superconducting resonator, which is attributed to the nucleation of dynamic flux vortices. Our results demonstrate a critical step towards future integrated hybrid systems for quantum magnonics and on-chip coherent information transfer.

Strong Coupling between Microwave Photons and Nanomagnet Magnons

Coupled microwave photon-magnon hybrid systems offer promising applications by harnessing various magnon physics. At present, in order to realize high coupling strength between the two subsystems, bulky ferromagnets with large spin numbers are utilized, which limits their potential applications for scalable quantum information processing. By enhancing single spin coupling strength using lithographically defined superconducting resonators, we report high cooperativities between a resonator mode and a Kittel mode in nanometer thick Permalloy wires. The on-chip, lithographically scalable, and superconducting quantum circuit compatible design provides a direct route towards realizing hybrid quantum systems with nanomagnets, whose coupling strength can be precisely engineered and dynamic properties can be controlled by various mechanisms derived from spintronic studies.

Nonresonant Transmission Line Probe for Sensitive Interferometric Electron Spin Resonance Detection

Electron spin resonance (ESR) spectroscopy measures paramagnetic free radicals, or electron spins, in a variety of biological, chemical, and physical systems. Detection of diverse paramagnetic species is important in applications ranging from quantum computation to biomedical research. Countless efforts have been made to improve the sensitivity of ESR detection. However, the improvement comes at the cost of experimental accessibility. Thus, most ESR spectrometers are limited to specific sample geometries and compositions. Here, we present a nonresonant transmission line ESR probe (microstrip geometry) that effectively couples high frequency microwave magnetic field into a wide range of sample geometries and compositions. The nonresonant transmission line probe maintains detection sensitivity while increasing availability to a wider range of applications. The high frequency magnetic field homogeneity is greatly increased by positioning the sample between the microstrip signal line and the ground plane. Sample interfacing occurs via a universal sample holder which is compatible with both solid and liquid samples. The unavoidable loss in sensitivity due to the nonresonant nature of the transmission line probe (low Q) is recuperated by using a highly sensitive microwave interferometer-based detection circuit. The combination of our sensitive interferometer and nonresonant transmission line provides similar sensitivity to a commercially available ESR spectrometer equipped with a high-Q resonator. The nonresonant probe allows for transmission, reflection, or dual-mode detection (transmission and reflection), where the dual-mode results in a √2 signal enhancement.

Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy

In high sensitivity inductive electron spin resonance spectroscopy, superconducting microwave resonators with large quality factors are employed. While they enhance the sensitivity, they also distort considerably the shape of the applied rectangular microwave control pulses, which limits the degree of control over the spin ensemble. Here, we employ shaped microwave pulses compensating the signal distortion to drive the spins faster than the resonator bandwidth. This translates into a shorter echo, with enhanced signal-to-noise ratio. The shaped pulses are also useful to minimize the dead-time of our spectrometer, which allows to reduce the wait time between successive drive pulses.

Possible Hundredfold Enhancement in the Direct Magnetic Coupling of a Single-Atom Electron Spin to a Circuit Resonator

We report on the challenges and limitations of direct coupling of the magnetic field from a circuit resonator to an electron spin bound to a donor potential. We propose a device consisting of a trilayer lumped-element superconducting resonator and a single donor implanted in enriched 28Si. The resonator impedance is significantly smaller than the practically achievable limit obtained with prevalent coplanar resonators. Furthermore, the resonator includes a nanoscale spiral inductor to spatially focus the magnetic field from the photons at the location of the implanted donor. The design promises an increase of approximately 2 orders of magnitude in the local magnetic field, and thus the spin-to-photon coupling rate g , compared with the estimated rate of coupling to the magnetic field of coplanar transmission line resonators. We show that by use of niobium (aluminum) as the resonator's superconductor and a single phosphorous (bismuth) atom as the donor, a coupling rate of g / 2 π = 0.24 MHz ( 0.39 MHz ) can be achieved in the single-photon regime. For this hybrid cavity-quantum-electrodynamic system, such enhancement in g is sufficient to enter the strong-coupling regime.

Advanced surface resonators for electron spin resonance of single microcrystals

Electron spin resonance (ESR) spectroscopy of paramagnetic species in single crystals is a powerful tool for characterizing the latter's magnetic interaction parameters in detail. Conventional ESR systems are optimized for millimeter-size samples and make use of cavities and resonators that accommodate tubes and capillaries in the range 1-5 mm. Unfortunately, in the case of many interesting materials such as enzymes and inorganic catalytic materials (e.g., zeolites), single crystals can only be obtained in micron-scale sizes (1-200 µm). To boost ESR sensitivity and to enable experiments on microcrystals, the ESR resonator needs to be adapted to the size and shape of these specific samples. Here, we present a unique family of miniature surface resonators, known as "ParPar" resonators, whose mode volume and shape are optimized for such micron-scale single crystals. This approach significantly improves upon the samples' filling factor and thus enables the measurement of much smaller crystals than was previously possible. We present here the design of such resonators with a typical mode dimension of 20-50 µm, as well as details about their fabrication and testing methods. The devices' resonant mode(s) are characterized by ESR microimaging and compared to the theoretical calculations. Moreover, experimental ESR spectra of single microcrystals with typical sizes of ∼25-50 µm are presented. The measured spin sensitivity for the 50-µm resonator at cryogenic temperatures of 50 K is found to be ∼1.8 × 10⁶ spins/G √Hz for a Cu-doped single crystal sample that is representative of many biological samples of relevance.

A single chip electron spin resonance detector based on a single high electron mobility transistor

Single-chip microwave oscillators are promising devices for inductive electron spin resonance spectroscopy (ESR) experiments on nanoliter and subnanoliter samples. Two major problems of the previously reported designs were the large minimum microwave magnetic field (0.1-0.7 mT) and large power consumption (0.5-200 mW), severely limiting their use for the investigation of samples having long relaxation times and for operation at low temperatures. Here we report on the design and characterization of a single-chip ESR detector operating with a microwave magnetic field and a power consumption orders of magnitude lower compared with previous designs. These significant improvements are mainly due to the use of a high electron mobility transistor (HEMT) technology instead of a complementary metal-oxide semiconductor (CMOS) technology. The realized single-chip ESR detector, which operates at 11.2 GHz, consists of an LC Colpitts oscillator realized with a single high-electron mobility transistor and a co-integrated single turn planar coil having a diameter of 440 μm. The realized detector operates from 300 K down to 1.4 K, at least. Its minimum microwave magnetic field is 0.4 μT at 300 K and 0.06 μT at 1.4 K, whereas its power consumption is 90 μW at 300 K and 4 μW at 1.4 K, respectively. The experimental spin sensitivity on a sensitive volume of about 30 nL, as measured with a single crystal of α,γ-bisdiphenylene-β-phenylallyl (BDPA)/benzene complex, is of 8 × 10¹⁰ spins/Hz^1/2 at 300 K and 2 × 10⁹ spins/Hz^1/2 at 10 K, respectively. In a volume of about 100 pL, located in proximity to the coil wire, the spin sensitivity improves by two orders of magnitude.

Realizing a Circuit Analog of an Optomechanical System with Longitudinally Coupled Superconducting Resonators

We realize a superconducting circuit analog of the generic cavity-optomechanical Hamiltonian by longitudinally coupling two superconducting resonators, which are an order of magnitude different in frequency. We achieve longitudinal coupling by embedding a superconducting quantum interference device into a high frequency resonator, making its resonance frequency depend on the zero point current fluctuations of a nearby low frequency LC resonator. By applying sideband drive fields we enhance the intrinsic coupling strength of about 15 kHz up to 280 kHz by controlling the amplitude of the drive field. Our results pave the way towards the exploration of optomechanical effects in a fully superconducting platform and could enable quantum optics experiments with photons in the yet unexplored radio frequency band.

Linear Hyperfine Tuning of Donor Spins in Silicon Using Hydrostatic Strain

We experimentally study the coupling of group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts that are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains |ϵ|<10^{-5}. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semiquantitative agreement with the experimental values. Our results provide a framework for making quantitative predictions of donor spins in silicon nanostructures, such as those being used to develop silicon-based quantum processors and memories. The strong spin-strain coupling we measure (up to 150 GHz per strain, for Bi donors in Si) offers a method for donor spin tuning-shifting Bi donor electron spins by over a linewidth with a hydrostatic strain of order 10^{-6}-as well as opportunities for coupling to mechanical resonators.

A coherent spin-photon interface in silicon

Electron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin-spin coupling and connections between arbitrary pairs of qubits ('all-to-all' connectivity) in a spin-based quantum processor. Realizing coherent spin-photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin-photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin-photon interactions is based on spin-charge hybridization in the presence of a magnetic-field gradient. In addition to spin-photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

Storing quantum information in spins and high-sensitivity ESR

Quantum information, encoded within the states of quantum systems, represents a novel and rich form of information which has inspired new types of computers and communications systems. Many diverse electron spin systems have been studied with a view to storing quantum information, including molecular radicals, point defects and impurities in inorganic systems, and quantum dots in semiconductor devices. In these systems, spin coherence times can exceed seconds, single spins can be addressed through electrical and optical methods, and new spin systems with advantageous properties continue to be identified. Spin ensembles strongly coupled to microwave resonators can, in principle, be used to store the coherent states of single microwave photons, enabling so-called microwave quantum memories. We discuss key requirements in realising such memories, including considerations for superconducting resonators whose frequency can be tuned onto resonance with the spins. Finally, progress towards microwave quantum memories and other developments in the field of superconducting quantum devices are being used to push the limits of sensitivity of inductively-detected electron spin resonance. The state-of-the-art currently stands at around 65 spins per Hz, with prospects to scale down to even fewer spins.

Surface loop-gap resonators for electron spin resonance at W-band

Electron spin resonance (ESR) is a spectroscopic method used to detect paramagnetic materials, reveal their structure, and also image their position in a sample. ESR makes use of a large static magnetic field to split the energy levels of the electron magnetic moment of the paramagnetic species. A strong microwave magnetic field is applied to excite the spins, and subsequently the ESR system detects their faint microwave signal response. The sensitivity of an ESR system is greatly influenced by the magnitude of the static field and the properties of the microwave resonator used to detect the spin signal. In general terms, the higher the static field (microwave frequency) and the smaller the resonator, the more sensitive the system will be. Previous work aimed at high-sensitivity ESR was focused on the development and testing of very small resonators operating at moderate magnetic fields in the range of ∼0.1-1.2 T (maximum frequency of ∼35 GHz). Here, we describe the design, construction, and testing of recently developed miniature surface loop-gap resonators used in ESR and operating at a much higher frequency of ∼95 GHz (W-band, corresponding to a field of ∼3.4 T). Such resonators can greatly enhance the sensitivity of ESR and also improve the resulting spectral resolution due to the higher static field employed. A detailed description of the resonator's design and coupling mechanism, as well as the supporting probe head, is provided. We also discuss the production method of the resonators and probe head and, in the end, provide preliminary experimental results that show the setup's high spin sensitivity and compare it to theoretical predictions.

All-electric control of donor nuclear spin qubits in silicon

The electronic and nuclear spin degrees of freedom of donor impurities in silicon form ultra-coherent two-level systems that are potentially useful for applications in quantum information and are intrinsically compatible with industrial semiconductor processing. However, because of their smaller gyromagnetic ratios, nuclear spins are more difficult to manipulate than electron spins and are often considered too slow for quantum information processing. Moreover, although alternating current magnetic fields are the most natural choice to drive spin transitions and implement quantum gates, they are difficult to confine spatially to the level of a single donor, thus requiring alternative approaches. In recent years, schemes for all-electrical control of donor spin qubits have been proposed but no experimental demonstrations have been reported yet. Here, we demonstrate a scalable all-electric method for controlling neutral ³¹P and ⁷⁵As donor nuclear spins in silicon. Using coplanar photonic bandgap resonators, we drive Rabi oscillations on nuclear spins exclusively using electric fields by employing the donor-bound electron as a quantum transducer, much in the spirit of recent works with single-molecule magnets. The electric field confinement leads to major advantages such as low power requirements, higher qubit densities and faster gate times. Additionally, this approach makes it possible to drive nuclear spin qubits either at their resonance frequency or at its first subharmonic, thus reducing device bandwidth requirements. Double quantum transitions can be driven as well, providing easy access to the full computational manifold of our system and making it convenient to implement nuclear spin-based qudits using ⁷⁵As donors.

Single-chip electron spin resonance detectors operating at 50GHz, 92GHz, and 146GHz

We report on the design and characterization of single-chip electron spin resonance (ESR) detectors operating at 50GHz, 92GHz, and 146GHz. The core of the single-chip ESR detectors is an integrated LC-oscillator, formed by a single turn aluminum planar coil, a metal-oxide-metal capacitor, and two metal-oxide semiconductor field effect transistors used as negative resistance network. On the same chip, a second, nominally identical, LC-oscillator together with a mixer and an output buffer are also integrated. Thanks to the slightly asymmetric capacitance of the mixer inputs, a signal at a few hundreds of MHz is obtained at the output of the mixer. The mixer is used for frequency down-conversion, with the aim to obtain an output signal at a frequency easily manageable off-chip. The coil diameters are 120μm, 70μm, and 45μm for the U-band, W-band, and the D-band oscillators, respectively. The experimental frequency noises at 100kHz offset from the carrier are 90Hz/Hz^1/2, 300Hz/Hz^1/2, and 700Hz/Hz^1/2 at 300K, respectively. The ESR spectra are obtained by measuring the frequency variations of the single-chip oscillators as a function of the applied magnetic field. The experimental spin sensitivities, as measured with a sample of α,γ-bisdiphenylene-β-phenylallyl (BDPA)/benzene complex, are 1×10⁸spins/Hz^1/2, 4×10⁷spins/Hz^1/2, 2×10⁷spins/Hz^1/2 at 300K, respectively. We also show the possibility to perform experiments up to 360GHz by means of the higher harmonics in the microwave field produced by the integrated single-chip LC-oscillators.