Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor

Room Temperature Dynamics of an Optically Addressable Single Spin in Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) hosts pure single-photon emitters that have shown evidence of optically detected electronic spin dynamics. However, the electrical and chemical structures of these optically addressable spins are unknown, and the nature of their spin-optical interactions remains mysterious. Here, we use time-domain optical and microwave experiments to characterize a single emitter in h-BN exhibiting room temperature optically detected magnetic resonance. Using dynamical simulations, we constrain and quantify transition rates in the model, and we design optical control protocols that optimize the signal-to-noise ratio for spin readout. This constitutes a necessary step toward quantum control of spin states in h-BN.

Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits

High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition-metal complexes via optically detected magnetic resonance (ODMR) mechanisms analogous to the diamond-nitrogen-vacancy color center. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are π-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realize a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimize radical-radical interactions in the ground state, generating π-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarization. The molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular color centers.

Coherent electric field control of orbital state of a neutral nitrogen-vacancy center

The coherent control of the orbital state is crucial for realizing the extremely-low power manipulation of the color centers in diamonds. Herein, a neutrally-charged nitrogen-vacancy center, NV0, is proposed as an ideal system for orbital control using electric fields. The electric susceptibility in the ground state of NV0 is estimated, and found to be comparable to that in the excited state of NV-. Also, the coherent control of the orbital states of NV0 is demonstrated. The required power for orbital control is three orders of magnitude smaller than that for spin control, highlighting the potential for interfacing a superconducting qubit operated in a dilution refrigerator.

High-Fidelity Optical Readout of a Nuclear-Spin Qubit in Silicon Carbide

Quantum state readout is a key requirement for a successful qubit platform. In this work, we demonstrate a high-fidelity quantum state readout of a V2 center nuclear spin based on a repetitive readout technique. We demonstrate up to 99.5% readout fidelity and 99% for state preparation. Using this efficient readout, we initialize the nuclear spin by measurement and demonstrate its Rabi and Ramsey nutation. Finally, we use the nuclear spin as a long-lived memory for quantum sensing application of a weakly coupled diatomic nuclear-spin bath.

Multidimensional Spectroscopy of Nuclear Spin Clusters in Diamond

Optically active spin defects in solids offer promising platforms to investigate nuclear spin clusters with high sensitivity and atomic-site resolution. To leverage near-surface defects for molecular structure analysis in chemical and biological contexts using nuclear magnetic resonance (NMR), further advances in spectroscopic characterization of nuclear environments are essential. Here, we report Fourier spectroscopy techniques to improve localization and mapping of the test bed ^{13}C nuclear spin environment of individual, shallow nitrogen-vacancy centers at room temperature. We use multidimensional spectroscopy, well-known from classical NMR, in combination with weak measurements of single-nuclear-spin precession. We demonstrate two examples of multidimensional NMR: (i) improved nuclear spin localization by separate encoding of the two hyperfine components along spectral dimensions and (ii) spectral editing of nuclear-spin pairs, including measurement of internuclear coupling constants. Our work adds important tools for the spectroscopic analysis of molecular structures by single-spin probes.

Diamond surface functionalization via visible light-driven C-H activation for nanoscale quantum sensing

Nitrogen-vacancy (NV) centers in diamond are a promising platform for nanoscale NMR sensing. Despite significant progress toward using NV centers to detect and localize nuclear spins down to the single spin level, NV-based spectroscopy of individual, intact, arbitrary target molecules remains elusive. Such sensing requires that target molecules are immobilized within nanometers of NV centers with long spin coherence. The inert nature of diamond typically requires harsh functionalization techniques such as thermal annealing or plasma processing, limiting the scope of functional groups that can be attached to the surface. Solution-phase chemical methods can be readily generalized to install diverse functional groups, but they have not been widely explored for single-crystal diamond surfaces. Moreover, realizing shallow NV centers with long spin coherence times requires highly ordered single-crystal surfaces, and solution-phase functionalization has not yet been shown with such demanding conditions. In this work, we report a versatile strategy to directly functionalize C-H bonds on single-crystal diamond surfaces under ambient conditions using visible light, forming C-F, C-Cl, C-S, and C-N bonds at the surface. This method is compatible with NV centers within 10 nm of the surface with spin coherence times comparable to the state of the art. As a proof-of-principle demonstration, we use shallow ensembles of NV centers to detect nuclear spins from surface-bound functional groups. Our approach to surface functionalization opens the door to deploying NV centers as a tool for chemical sensing and single-molecule spectroscopy.

Suppression of Pulsed Dynamic Nuclear Polarization by Many-Body Spin Dynamics

We study a mechanism by which nuclear hyperpolarization due to the polarization transfer from a microwave-pulse-controlled electron spin is suppressed. From analytical and numerical calculations of the unitary dynamics of multiple nuclear spins, we uncover that, combined with the formation of the dark state within a cluster of nuclei, coherent higher-order nuclear spin dynamics impose limits on the efficiency of the polarization transfer even in the absence of mundane depolarization processes such as nuclear spin diffusion and relaxation. Furthermore, we show that the influence of the dark state can be partly mitigated by introducing a disentangling operation. Our analysis is applied to the nuclear polarizations observed in ^{13}C nuclei coupled with a single nitrogen-vacancy center in diamond [Randall et al., Science 374, 1474 (2021)SCIEAS0036-807510.1126/science.abk0603]. Our Letter sheds light on collective engineering of nuclear spins as well as future designs of pulsed dynamic nuclear polarization protocols.

Mapping a 50-spin-qubit network through correlated sensing

Spins associated to optically accessible solid-state defects have emerged as a versatile platform for exploring quantum simulation, quantum sensing and quantum communication. Pioneering experiments have shown the sensing, imaging, and control of multiple nuclear spins surrounding a single electron spin defect. However, the accessible size of these spin networks has been constrained by the spectral resolution of current methods. Here, we map a network of 50 coupled spins through high-resolution correlated sensing schemes, using a single nitrogen-vacancy center in diamond. We develop concatenated double-resonance sequences that identify spin-chains through the network. These chains reveal the characteristic spin frequencies and their interconnections with high spectral resolution, and can be fused together to map out the network. Our results provide new opportunities for quantum simulations by increasing the number of available spin qubits. Additionally, our methods might find applications in nano-scale imaging of complex spin systems external to the host crystal.

Sub-nanotesla sensitivity at the nanoscale with a single spin

High-sensitivity detection of the microscopic magnetic field is essential in many fields. Good sensitivity and high spatial resolution are mutually contradictory in measurement, which is quantified by the energy resolution limit. Here we report that a sensitivity of 0.5 nT/[Formula: see text] at the nanoscale is achieved experimentally by using nitrogen-vacancy defects in diamond with depths of tens of nanometers. The achieved sensitivity is substantially enhanced by integrating with multiple quantum techniques, including real-time-feedback initialization, dynamical decoupling with shaped pulses and repetitive readout via quantum logic. Our magnetic sensors will shed new light on searching new physics beyond the standard model, investigating microscopic magnetic phenomena in condensed matters, and detection of life activities at the sub-cellular scale.

T1 Anisotropy Elucidates Spin Relaxation Mechanisms in an S = 1 Cr(IV) Optically Addressable Molecular Qubit

Paramagnetic molecules offer unique advantages for quantum information science owing to their spatial compactness, synthetic tunability, room-temperature quantum coherence, and potential for optical state initialization and readout. However, current optically addressable molecular qubits are hampered by rapid spin-lattice relaxation (T1) even at sub-liquid nitrogen temperatures. Here, we use temperature- and orientation-dependent pulsed electron paramagnetic resonance (EPR) to elucidate the negative sign of the ground state zero-field splitting (ZFS) and assign T1 anisotropy to specific types of motion in an optically addressable S = 1 Cr(o-tolyl)4 molecular qubit. The anisotropy displays a distinct sin2(2θ) functional form that is not observed in S = 1/2 Cu(acac)2 or other Cu(II)/V(IV) microwave addressable molecular qubits. The Cr(o-tolyl)4 T1 anisotropy is ascribed to couplings between electron spins and rotational motion in low-energy acoustic or pseudoacoustic phonons. Our findings suggest that rotational degrees of freedom should be suppressed to maximize the coherence temperature of optically addressable qubits.

Electron Induced Nanoscale Nuclear Spin Relaxation Probed by Hyperpolarization Injection

We report on experiments that quantify the role of a central electronic spin as a relaxation source for nuclear spins in its nanoscale environment. Our strategy exploits hyperpolarization injection from the electron as a means to controllably probe an increasing number of nuclear spins in the bath and subsequently interrogate them with high fidelity. Our experiments are focused on a model system of a nitrogen vacancy center electronic spin surrounded by several hundred ^{13}C nuclear spins. We observe that the ^{13}C transverse spin relaxation times vary significantly with the extent of hyperpolarization injection, allowing the ability to measure the influence of electron-mediated relaxation extending over several nanometers. These results suggest interesting new means to spatially discriminate nuclear spins in a nanoscale environment and have direct relevance to dynamic nuclear polarization and quantum sensors and memories constructed from hyperpolarized nuclei.

Temperature-Dependent Spin-Lattice Relaxation of the Nitrogen-Vacancy Spin Triplet in Diamond

Spin-lattice relaxation within the nitrogen-vacancy (NV) center's electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center's |m_{s}=0⟩↔|m_{s}=±1⟩ and |m_{s}=-1⟩↔|m_{s}=+1⟩ transitions as a function of temperature from 9 to 474 K in high-purity samples. We show that the temperature dependencies of the rates are reproduced by an ab initio theory of Raman scattering due to second-order spin-phonon interactions, and we discuss the applicability of the theory to other spin systems. Using a novel analytical model based on these results, we suggest that the high-temperature behavior of NV spin-lattice relaxation is dominated by interactions with two groups of quasilocalized phonons centered at 68.2(17) and 167(12) meV.

Fresnel-type solid immersion lens for efficient light collection from quantum defects in diamond

Quantum defects in diamonds have been studied as a promising resource for quantum science. The subtractive fabrication process for improving photon collection efficiency often require excessive milling time that can adversely affect the fabrication accuracy. We designed and fabricated a Fresnel-type solid immersion lens using the focused ion beam. For a 5.8 µm-deep Nitrogen-vacancy (NV^-) center, the milling time was highly reduced (1/3 compared to a hemispherical structure), while retaining high photon collection efficiency (> 2.24 compared to a flat surface). In numerical simulation, this benefit of the proposed structure is expected for a wide range of milling depths.

First-Principles Calculation of the Temperature-Dependent Transition Energies in Spin Defects

Spin qubits associated with color centers are promising platforms for various quantum technologies. However, to be deployed in robust quantum devices, the variations of their intrinsic properties with the external conditions, in particular temperature and strain, should be known with high precision. Unfortunately, a predictive theory on the temperature dependence of the resonance frequency of electron and nuclear spin defects in solids remains lacking. In this work, we develop a first-principles method for the temperature dependence of the zero-field splitting, hyperfine interaction, and nuclear quadrupole interaction of color centers. As a testbed, we compare our ab initio calculations with experiments for the nitrogen-vacancy (NV^-) center in diamond, finding good agreements. We identify the major origin of the temperature dependence as a second-order effect of dynamic phonon vibrations, instead of the thermal-expansion strain. The method can be applied to different color centers and provides a theoretical tool for designing high-precision quantum sensors.

Detection of Quantum Signals Free of Classical Noise via Quantum Correlation

Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application, especially in quantum sensing. Here, we propose a signal-nature-based (not signal-pattern-based) approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. We design a novel protocol to extract the quantum correlation signal and use it to single out the signal of a remote nuclear spin from its overwhelming classical noise backgrounds, which is impossible to be accomplished by conventional filter methods. Our Letter demonstrates the quantum or classical nature as a new degree of freedom in quantum sensing. The further generalization of this quantum nature-based method opens a new direction in quantum research.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubit gates.

Quantum sensors for biomedical applications

Quantum sensors are finding their way from laboratories to the real world, as witnessed by the increasing number of start-ups in this field. The atomic length scale of quantum sensors and their coherence properties enable unprecedented spatial resolution and sensitivity. Biomedical applications could benefit from these quantum technologies, but it is often difficult to evaluate the potential impact of the techniques. This Review sheds light on these questions, presenting the status of quantum sensing applications and discussing their path towards commercialization. The focus is on two promising quantum sensing platforms: optically pumped atomic magnetometers, and nitrogen-vacancy centres in diamond. The broad spectrum of biomedical applications is highlighted by four case studies ranging from brain imaging to single-cell spectroscopy.

Anisotropic Hyperfine Interaction of Surface-Adsorbed Single Atoms

Hyperfine interactions have been widely used in material science, organic chemistry, and structural biology as a sensitive probe to local chemical environments. However, traditional ensemble measurements of hyperfine interactions average over a macroscopic number of spins with different geometrical locations and nuclear isotopes. Here, we use a scanning tunneling microscope (STM) combined with electron spin resonance (ESR) to measure hyperfine spectra of hydrogenated-Ti on MgO/Ag(100) at low-symmetry binding sites and thereby determine the isotropic and anisotropic hyperfine interactions at the single-atom level. Combining vector-field ESR spectroscopy with STM-based atom manipulation, we characterize the full hyperfine tensors of ⁴⁷Ti and ⁴⁹Ti and identify significant spatial anisotropy of the hyperfine interactions for both isotopes. Density functional theory calculations reveal that the large hyperfine anisotropy arises from highly anisotropic distributions of the ground-state electron spin density. Our work highlights the power of ESR-STM-enabled single-atom hyperfine spectroscopy in revealing electronic ground states and atomic-scale chemical environments.

Anti-Zeno purification of spin baths by quantum probe measurements

The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state purity and yield a low-entropy steady state of the bath. The purified bath state persists long after the measurements are completed. Such purification enables the exploitation of spin baths as long-lived quantum memories or as quantum-enhanced sensors. The experiment involved a repeatedly probed defect center dephased by a nuclear spin bath in a diamond at low-temperature.

Room-Temperature Quantitative Quantum Sensing of Lithium Ions with a Radical-Embedded Metal-Organic Framework

Recent advancements in quantum sensing have sparked transformative detection technologies with high sensitivity, precision, and spatial resolution. Owing to their atomic-level tunability, molecular qubits and ensembles thereof are promising candidates for sensing chemical analytes. Here, we show quantum sensing of lithium ions in solution at room temperature with an ensemble of organic radicals integrated in a microporous metal-organic framework (MOF). The organic radicals exhibit electron spin coherence and microwave addressability at room temperature, thus behaving as qubits. The high surface area of the MOF promotes accessibility of the guest analytes to the organic qubits, enabling unambiguous identification of lithium ions and quantitative measurement of their concentration through relaxometric and hyperfine spectroscopic methods based on electron paramagnetic resonance (EPR) spectroscopy. The sensing principle presented in this work is applicable to other metal ions with nonzero nuclear spin.

Diamond surface engineering for molecular sensing with nitrogen-vacancy centers

Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.

Divergent Effects of Laser Irradiation on Ensembles of Nitrogen-Vacancy Centers in Bulk and Nanodiamonds: Implications for Biosensing

Ensembles of negatively charged nitrogen-vacancy centers (NV^-) in diamond have been proposed for sensing of magnetic fields and paramagnetic agents, and as a source of spin-order for the hyperpolarization of nuclei in magnetic resonance applications. To this end, strongly fluorescent nanodiamonds (NDs) represent promising materials, with large surface areas and dense ensembles of NV^-. However, surface effects tend to favor the less useful neutral form, the NV⁰ centers, and strategies to increase the density of shallow NV^- centers have been proposed, including irradiation with strong laser power (Gorrini in ACS Appl Mater Interfaces. 13:43221-43232, 2021). Here, we study the fluorescence properties and optically detected magnetic resonance (ODMR) of NV^- centers as a function of laser power in strongly fluorescent bulk diamond and in nanodiamonds obtained by nanomilling of the native material. In bulk diamond, we find that increasing laser power increases ODMR contrast, consistent with a power-dependent increase in spin-polarization. Conversely, in nanodiamonds we observe a non-monotonic behavior, with a decrease in ODMR contrast at higher laser power. We hypothesize that this phenomenon may be ascribed to more efficient NV^-→NV⁰ photoconversion in nanodiamonds compared to bulk diamond, resulting in depletion of the NV^- pool. A similar behavior is shown for NDs internalized in macrophage cells under the typical experimental conditions of imaging bioassays. Our results suggest strong laser irradiation is not an effective strategy in NDs, where the interplay between surface effects and local microenvironment determine the optimal experimental conditions.

Atomic-Scale Quantum Sensing of Ensembles of Guest Molecules in a Metal-Organic Framework with Intrinsic Electron Spin Centers

One of the exciting applications of electron-spin-based quantum sensing is the detection of distant nuclear spins of external molecular species. Here, we explore the application of a metal-organic framework (MOF) material as a host matrix for sensing spin centers. As a sensor, we employ inherent Cu²⁺ ions in the structure of a Zn-doped HKUST-1 framework. As a target molecular species, we use butane gas that exhibits no specific chemical reactivity toward the inner surface of HKUST-1 and is thus randomly distributed inside the MOF pore network. By employing a conventional double-resonance pulse sequence, we can effectively detect the coupling of the distant ¹H nuclear spins of butane to the electron spin of the sensor and gain atomic-scale insight into their spatial distribution. Thus, our proof-of-the-concept experiment demonstrates that MOFs, the materials featuring extremely large surface area and great tunability, are perfectly suited as a key element for emerging magnetic quantum sensing solutions.

Optically induced static magnetic field in the ensemble of nitrogen-vacancy centers in diamond

Generation of a local magnetic field at the nanoscale is desirable for many applications such as spin-qubit-based quantum memories. However, this is a challenge due to the slow decay of static magnetic fields. Here, we demonstrate a photonic spin density (PSD)-induced effective static magnetic field for an ensemble of nitrogen-vacancy (NV) centers in bulk diamond. This locally induced magnetic field is a result of coherent interaction between the optical excitation and the NV centers. We demonstrate an optically induced spin rotation on the Bloch sphere exceeding 10 degrees which has potential applications in all-optical coherent control of spin qubits.

One decade of quantum optimal control in the chopped random basis

The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

Fault-tolerant operation of a logical qubit in a diamond quantum processor

Solid-state spin qubits is a promising platform for quantum computation and quantum networks^1,2. Recent experiments have demonstrated high-quality control over multi-qubit systems^3–8, elementary quantum algorithms^8–11 and non-fault-tolerant error correction^12–14. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations^15–18. Overcoming imperfections in this way remains an important outstanding challenge for quantum science^15,19–27. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits^28–30. We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. Although future improvements in fidelity and the number of qubits will be required to suppress logical error rates below the physical error rates, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards quantum information processing based on solid-state spins.

By using a five-qubit error-correcting code with a recently discovered flag protocol, a logical qubit that is operated fault-tolerantly is realized based on solid-state spin qubits in diamond.

Robust Quantum State Tomography Method for Quantum Sensing

Reliable and efficient reconstruction of pure quantum states under the processing of noisy measurement data is a vital tool in fundamental and applied quantum information sciences owing to communication, sensing, and computing. Specifically, the purity of such reconstructed quantum systems is crucial in surpassing the classical shot-noise limit and achieving the Heisenberg limit, regarding the achievable precision in quantum sensing. However, the noisy reconstruction of such resourceful sensing probes limits the quantum advantage in precise quantum sensing. For this, we formulate a pure quantum state reconstruction method through eigenvalue decomposition. We show that the proposed method is robust against the depolarizing noise; it remains unaffected under high strength white noise and achieves quantum state reconstruction accuracy similar to the noiseless case.

Parallel detection and spatial mapping of large nuclear spin clusters

Nuclear magnetic resonance imaging (MRI) at the atomic scale offers exciting prospects for determining the structure and function of individual molecules and proteins. Quantum defects in diamond have recently emerged as a promising platform towards reaching this goal, and allowed for the detection and localization of single nuclear spins under ambient conditions. Here, we present an efficient strategy for extending imaging to large nuclear spin clusters, fulfilling an important requirement towards a single-molecule MRI technique. Our method combines the concepts of weak quantum measurements, phase encoding and simulated annealing to detect three-dimensional positions from many nuclei in parallel. Detection is spatially selective, allowing us to probe nuclei at a chosen target radius while avoiding interference from strongly-coupled proximal nuclei. We demonstrate our strategy by imaging clusters containing more than 20 carbon-13 nuclear spins within a radius of 2.4 nm from single, near-surface nitrogen-vacancy centers at room temperature. The radius extrapolates to 5-6 nm for ¹H. Beside taking an important step in nanoscale MRI, our experiment also provides an efficient tool for the characterization of large nuclear spin registers in the context of quantum simulators and quantum network nodes.

Biocompatible surface functionalization architecture for a diamond quantum sensor

Diamond-based quantum sensing enables nanoscale measurements of biological systems with unprecedented sensitivity. Potential applications of this emerging technology range from the investigation of fundamental biological processes to the development of next-generation medical diagnostics devices. One of the main challenges faced by bioquantum sensing is the need to interface quantum sensors with biological target systems. Specifically, such an interface needs to maintain the highly fragile quantum states of our sensor and at the same time be able to fish intact biomolecules out of solution and immobilize them on our quantum sensor surface. Our work overcomes these challenges by combining tools from quantum engineering, single-molecule biophysics, and material processing.

Quantum metrology enables some of the most precise measurements. In the life sciences, diamond-based quantum sensing has led to a new class of biophysical sensors and diagnostic devices that are being investigated as a platform for cancer screening and ultrasensitive immunoassays. However, a broader application in the life sciences based on nanoscale NMR spectroscopy has been hampered by the need to interface highly sensitive quantum bit (qubit) sensors with their biological targets. Here, we demonstrate an approach that combines quantum engineering with single-molecule biophysics to immobilize individual proteins and DNA molecules on the surface of a bulk diamond crystal that hosts coherent nitrogen vacancy qubit sensors. Our thin (sub–5 nm) functionalization architecture provides precise control over the biomolecule adsorption density and results in near-surface qubit coherence approaching 100 μs. The developed architecture remains chemically stable under physiological conditions for over 5 d, making our technique compatible with most biophysical and biomedical applications.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Fabrication and nanophotonic waveguide integration of silicon carbide colour centres with preserved spin-optical coherence

Optically addressable spin defects in silicon carbide (SiC) are an emerging platform for quantum information processing compatible with nanofabrication processes and device control used by the semiconductor industry. System scalability towards large-scale quantum networks demands integration into nanophotonic structures with efficient spin-photon interfaces. However, degradation of the spin-optical coherence after integration in nanophotonic structures has hindered the potential of most colour centre platforms. Here, we demonstrate the implantation of silicon vacancy centres (V_Si) in SiC without deterioration of their intrinsic spin-optical properties. In particular, we show nearly lifetime-limited photon emission and high spin-coherence times for single defects implanted in bulk as well as in nanophotonic waveguides created by reactive ion etching. Furthermore, we take advantage of the high spin-optical coherences of V_Si centres in waveguides to demonstrate controlled operations on nearby nuclear spin qubits, which is a crucial step towards fault-tolerant quantum information distribution based on cavity quantum electrodynamics.

Many-body-localized discrete time crystal with a programmable spin-based quantum simulator

[Figure: see text].

Long-Lived Solid-State Optical Memory for High-Rate Quantum Repeaters

We argue that long optical storage times are required to establish entanglement at high rates over large distances using memory-based quantum repeaters. Triggered by this conclusion, we investigate the 795.325  nm^{3} H_{6}↔^{3}H_{4} transition of Tm:Y_{3}Ga_{5}O_{12} (Tm:YGG). Most importantly, we find that the optical coherence time can reach 1.1 ms, and, using laser pulses, we demonstrate optical storage based on the atomic frequency comb protocol during up to 100  μs as well as a memory decay time T_{m} of 13.1  μs. Possibilities of how to narrow the gap between the measured value of T_{m} and its maximum of 275  μs are discussed. In addition, we demonstrate multiplexed storage, including with feed-forward selection, shifting and filtering of spectral modes, as well as quantum state storage using members of nonclassical photon pairs. Our results show the potential of Tm:YGG for creating multiplexed quantum memories with long optical storage times, and open the path to repeater-based quantum networks with high entanglement distribution rates.

Floquet Prethermalization with Lifetime Exceeding 90 s in a Bulk Hyperpolarized Solid

We report the observation of long-lived Floquet prethermal states in a bulk solid composed of dipolar-coupled ^{13}C nuclei in diamond at room temperature. For precessing nuclear spins prepared in an initial transverse state, we demonstrate pulsed spin-lock Floquet control that prevents their decay over multiple-minute-long periods. We observe Floquet prethermal lifetimes T_{2}^{'}≈90.9  s, extended >60 000-fold over the nuclear free induction decay times. The spins themselves are continuously interrogated for ∼10  min, corresponding to the application of ≈5.8×10^{6} control pulses. The ^{13}C nuclei are optically hyperpolarized by lattice nitrogen vacancy centers; the combination of hyperpolarization and continuous spin readout yields significant signal-to-noise ratio in the measurements. This allows probing the Floquet thermalization dynamics with unprecedented clarity. We identify four characteristic regimes of the thermalization process, discerning short-time transient processes leading to the prethermal plateau and long-time system heating toward infinite temperature. This Letter points to new opportunities possible via Floquet control in networks of dilute, randomly distributed, low-sensitivity nuclei. In particular, the combination of minutes-long prethermal lifetimes and continuous spin interrogation opens avenues for quantum sensors constructed from hyperpolarized Floquet prethermal nuclei.

Diamond quantum thermometry: from foundations to applications

Diamond quantum thermometry exploits the optical and electrical spin properties of colour defect centres in diamonds and, acts as a quantum sensing method exhibiting ultrahigh precision and robustness. Compared to the existing luminescent nanothermometry techniques, a diamond quantum thermometer can be operated over a wide temperature range and a sensor spatial scale ranging from nanometres to micrometres. Further, diamond quantum thermometry is employed in several applications, including electronics and biology, to explore these fields with nanoscale temperature measurements. This review covers the operational principles of diamond quantum thermometry for spin-based and all-optical methods, material development of diamonds with a focus on thermometry, and examples of applications in electrical and biological systems with demand-based technological requirements.

Star-topology registers: NMR and quantum information perspectives

Quantum control of large spin registers is crucial for many applications ranging from spectroscopy to quantum information. A key factor that determines the efficiency of a register for implementing a given information processing task is its network topology. One particular type, called star-topology, involves a central qubit uniformly interacting with a set of ancillary qubits. A particular advantage of the star-topology quantum registers is in the efficient preparation of large entangled states, called NOON states, and their generalized variants. Thanks to the robust generation of such correlated states, spectral simplicity, ease of polarization transfer from ancillary qubits to the central qubit, as well as the availability of large spin-clusters, the star-topology registers have been utilized for several interesting applications over the last few years. Here we review some recent progress with the star-topology registers, particularly via nuclear magnetic resonance methods.

Room-temperature control and electrical readout of individual nitrogen-vacancy nuclear spins

Nuclear spins in semiconductors are leading candidates for future quantum technologies, including quantum computation, communication, and sensing. Nuclear spins in diamond are particularly attractive due to their long coherence time. With the nitrogen-vacancy (NV) centre, such nuclear qubits benefit from an auxiliary electronic qubit, which, at cryogenic temperatures, enables probabilistic entanglement mediated optically by photonic links. Here, we demonstrate a concept of a microelectronic quantum device at ambient conditions using diamond as wide bandgap semiconductor. The basic quantum processor unit – a single ¹⁴N nuclear spin coupled to the NV electron – is read photoelectrically and thus operates in a manner compatible with nanoscale electronics. The underlying theory provides the key ingredients for photoelectric quantum gate operations and readout of nuclear qubit registers. This demonstration is, therefore, a step towards diamond quantum devices with a readout area limited by inter-electrode distance rather than by the diffraction limit. Such scalability could enable the development of electronic quantum processors based on the dipolar interaction of spin-qubits placed at nanoscopic proximity.

Nuclear spins in diamond are promising for applications in quantum technologies due to their long coherence times. Here, the authors demonstrate a scalable electrical readout of individual intrinsic ¹⁴N nuclear spins in diamond, mediated by hyperfine coupling to electron spin of the NV center, as a step towards room-temperature nanoscale diamond quantum devices.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Toward Quantitative Bio-sensing with Nitrogen-Vacancy Center in Diamond

The long-dreamed-of capability of monitoring the molecular machinery in living systems has not been realized yet, mainly due to the technical limitations of current sensing technologies. However, recently emerging quantum sensors are showing great promise for molecular detection and imaging. One of such sensing qubits is the nitrogen-vacancy (NV) center, a photoluminescent impurity in a diamond lattice with unique room-temperature optical and spin properties. This atomic-sized quantum emitter has the ability to quantitatively measure nanoscale electromagnetic fields via optical means at ambient conditions. Moreover, the unlimited photostability of NV centers, combined with the excellent diamond biocompatibility and the possibility of diamond nanoparticles internalization into the living cells, makes NV-based sensors one of the most promising and versatile platforms for various life-science applications. In this review, we will summarize the latest developments of NV-based quantum sensing with a focus on biomedical applications, including measurements of magnetic biomaterials, intracellular temperature, localized physiological species, action potentials, and electronic and nuclear spins. We will also outline the main unresolved challenges and provide future perspectives of many promising aspects of NV-based bio-sensing.

Quantum Interfaces to the Nanoscale

Scalable quantum information systems would store, manipulate, and transmit quantum information locally and across a quantum network, but no single qubit technology is currently robust enough to perform all necessary tasks. Defect centers in solid-state materials have emerged as potential intermediaries between other physical manifestations of qubits, such as superconducting qubits and photonic qubits, to leverage their complementary advantages. It remains an open question, however, how to design and to control quantum interfaces to defect centers. Such interfaces would enable quantum information to be moved seamlessly between different physical systems. Understanding and constructing the required interfaces would, therefore, unlock the next big steps in quantum computing, sensing, and communications. In this Perspective, we highlight promising coupling mechanisms, including dipole-, phonon-, and magnon-mediated interactions, and discuss how contributions from nanotechnologists will be paramount in realizing quantum information processors in the near-term.

Hyperfine Interactions in the NV-13C Quantum Registers in Diamond Grown from the Azaadamantane Seed

Nanostructured diamonds hosting optically active paramagnetic color centers (NV, SiV, GeV, etc.) and hyperfine-coupled with them quantum memory 13C nuclear spins situated in diamond lattice are currently of great interest to implement emerging quantum technologies (quantum information processing, quantum sensing and metrology). Current methods of creation such as electronic-nuclear spin systems are inherently probabilistic with respect to mutual location of color center electronic spin and 13C nuclear spins. A new bottom-up approach to fabricate such systems is to synthesize first chemically appropriate diamond-like organic molecules containing desired isotopic constituents in definite positions and then use them as a seed for diamond growth to produce macroscopic diamonds, subsequently creating vacancy-related color centers in them. In particular, diamonds incorporating coupled NV-13C spin systems (quantum registers) with specific mutual arrangements of NV and 13C can be obtained from anisotopic azaadamantane molecule. Here we predict the characteristics of hyperfine interactions (hfi) for the NV-13C systems in diamonds grown from various isotopically substituted azaadamantane molecules differing in 13C position in the seed, as well as the orientation of the NV center in the post-obtained diamond. We used the spatial and hfi data simulated earlier for the H-terminated cluster C510[NV]-H252. The data obtained can be used to identify (and correlate with the seed used) the specific NV-13C spin system by measuring, e.g., the hfi-induced splitting of the mS = ±1 sublevels of the NV center in optically detected magnetic resonance (ODMR) spectra being characteristic for various NV-13C systems.

High-fidelity single-shot readout of single electron spin in diamond with spin-to-charge conversion

High fidelity single-shot readout of qubits is a crucial component for fault-tolerant quantum computing and scalable quantum networks. In recent years, the nitrogen-vacancy (NV) center in diamond has risen as a leading platform for the above applications. The current single-shot readout of the NV electron spin relies on resonance fluorescence method at cryogenic temperature. However, the spin-flip process interrupts the optical cycling transition, therefore, limits the readout fidelity. Here, we introduce a spin-to-charge conversion method assisted by near-infrared (NIR) light to suppress the spin-flip error. This method leverages high spin-selectivity of cryogenic resonance excitation and flexibility of photoionization. We achieve an overall fidelity > 95% for the single-shot readout of an NV center electron spin in the presence of high strain and fast spin-flip process. With further improvements, this technique has the potential to achieve spin readout fidelity exceeding the fault-tolerant threshold, and may also find applications on integrated optoelectronic devices.

The NV centre in diamond has been used extensively in quantum information processing; however fault-tolerant readout of its spin remains challenging. Here, Zhang et al demonstrate a robust scheme that achieves high-fidelity readout via spin to charge conversion.

Lower than low: Perspectives on zero- to ultralow-field nuclear magnetic resonance

The less-traveled low road in nuclear magnetic resonance is discussed, honoring the contributions of Prof. Bernhard Blümich, aspiring towards reaching 'a new low.' A history of the subject and its current status are briefly reviewed, followed by an effort to prophesy possible directions for future developments.

NV center pumped and enhanced by nanowire ring resonator laser to integrate a 10 μm-scale spin-based sensor structure

In this work, we propose a 10 μm-scale spin-based sensor structure, which mainly consists of a nanowire (NW) ring resonator laser, nitrogen-vacancy (NV) defects in a nanodiamond (ND) and a microwave (MW) antenna. The NW laser was bent into a ring with a gap to pump the NV defects in the ND which was assembled in the gap with the diameter of ∼8 μm. And the fluorescent light of NV defects was enhanced by the NW ring resonator about 8 times. Furthermore, the NW laser pulse was produced by the optical switch and a simple plus-sequences was designed to get the Rabi oscillation signal. Based on the Rabi oscillation, a Ramsey-type sequence was used to detect the magnetic field with the sensitivity of 83 nT √Hz^-1 for our 10 μm-scale spin-based sensor structure. It proves the spin state in our structure allows for coherent spin manipulation for more complex quantum control schemes. And our structure fulfills the fundamental requirements to develop chip-scale spin-based sensors.

Entanglement and control of single nuclear spins in isotopically engineered silicon carbide

Nuclear spins in the solid state are both a cause of decoherence and a valuable resource for spin qubits. In this work, we demonstrate control of isolated ²⁹Si nuclear spins in silicon carbide (SiC) to create an entangled state between an optically active divacancy spin and a strongly coupled nuclear register. We then show how isotopic engineering of SiC unlocks control of single weakly coupled nuclear spins and present an ab initio method to predict the optimal isotopic fraction that maximizes the number of usable nuclear memories. We bolster these results by reporting high-fidelity electron spin control (F = 99.984(1)%), alongside extended coherence times (Hahn-echo T₂ = 2.3 ms, dynamical decoupling T₂^DD > 14.5 ms), and a >40-fold increase in Ramsey spin dephasing time (T₂*) from isotopic purification. Overall, this work underlines the importance of controlling the nuclear environment in solid-state systems and links single photon emitters with nuclear registers in an industrially scalable material.

Trigonal Bipyramidal V3+ Complex as an Optically Addressable Molecular Qubit Candidate

Synthetic chemistry enables a bottom-up approach to quantum information science, where atoms can be deterministically positioned in a quantum bit or qubit. Two key requirements to realize quantum technologies are qubit initialization and read-out. By imbuing molecular spins with optical initialization and readout mechanisms, analogous to solid-state defects, molecules could be integrated into existing quantum infrastructure. To mimic the electronic structure of optically addressable defect sites, we designed the spin-triplet, V3+ complex, (C6F5)3trenVCNtBu (1). We measured the static spin properties as well as the spin coherence time of 1 demonstrating coherent control of this spin qubit with a 240 GHz electron paramagnetic resonance spectrometer powered by a free electron laser. We found that 1 exhibited narrow, near-infrared photoluminescence (PL) from a spin-singlet excited state. Using variable magnetic field PL spectroscopy, we resolved emission into each of the ground-state spin sublevels, a crucial component for spin-selective optical initialization and readout. This work demonstrates that trigonally symmetric, heteroleptic V3+ complexes are candidates for optical spin addressability.

Optically addressable molecular spins for quantum information processing

Spin-bearing molecules are promising building blocks for quantum technologies as they can be chemically tuned, assembled into scalable arrays, and readily incorporated into diverse device architectures. In molecular systems, optically addressing ground-state spins would enable a wide range of applications in quantum information science, as has been demonstrated for solid-state defects. However, this important functionality has remained elusive for molecules. Here, we demonstrate such optical addressability in a series of synthesized organometallic, chromium(IV) molecules. These compounds display a ground-state spin that can be initialized and read out using light and coherently manipulated with microwaves. In addition, through atomistic modification of the molecular structure, we vary the spin and optical properties of these compounds, indicating promise for designer quantum systems synthesized from the bottom-up.

Calibration-Free Vector Magnetometry Using Nitrogen-Vacancy Center in Diamond Integrated with Optical Vortex Beam

We report a new method to determine the orientation of individual nitrogen-vacancy (NV) centers in a bulk diamond and use them to realize a calibration-free vector magnetometer with nanoscale resolution. Optical vortex beam is used for optical excitation and scanning the NV center in a [111]-oriented diamond. The scanning fluorescence patterns of NV center with different orientations are completely different. Thus, the orientation information on each NV center in the lattice can be known directly without any calibration process. Further, we use three differently oriented NV centers to form a magnetometer and reconstruct the complete vector information on the magnetic field based on the optically detected magnetic resonance(ODMR) technique. Compared with previous schemes to realize vector magnetometry using an NV center, our method is much more efficient and is easily applied in other NV-based quantum sensing applications.