Magnetic resonance detection of individual proton spins using quantum reporters

Quantum Spin Probe of Single Charge Dynamics

Electronic defects in semiconductors form the basis for emerging quantum technologies, but many defect centers are difficult to access at the single-particle level. A method for probing optically inactive spin defects would reveal semiconductor physics at the atomic scale and advance the study of new quantum systems. We exploit the intrinsic correlation between the charge and spin states of defect centers to measure the charge populations and dynamics of single substitutional nitrogen spin defects in diamond. By probing their steady-state spin population, read out at the single-defect level with a nearby nitrogen vacancy center, we directly measure the defect ionization-corroborated by first-principles calculations-an effect we do not have access to with traditional coherence-based quantum sensing.

Understanding Central Spin Decoherence Due to Interacting Dissipative Spin Baths

We propose a new approach to simulate the decoherence of a central spin coupled to an interacting dissipative spin bath with cluster-correlation expansion techniques. We benchmark the approach on generic 1D and 2D spin baths and find excellent agreement with numerically exact simulations. Our calculations show a complex interplay between dissipation and coherent spin exchange, leading to increased central spin coherence in the presence of fast dissipation. Finally, we model near-surface nitrogen-vacancy centers in diamond and show that accounting for bath dissipation is crucial to understanding their decoherence. Our method can be applied to a variety of systems and provides a powerful tool to investigate spin dynamics in dissipative environments.

Four-Order Power Reduction in Nanoscale Electron-Nuclear Double Resonance with a Nitrogen-Vacancy Center in Diamonds

Detecting nuclear spins using single nitrogen-vacancy (NV) centers is of particular importance in nanoscale science and engineering but often suffers from the heating effect of microwave fields for spin manipulation, especially under high magnetic fields. Here, we realize an energy-efficient nanoscale nuclear-spin detection using a phase-modulation electron-nuclear double resonance scheme. The microwave field can be reduced to 1/250 of the previous requirements, and the corresponding power is over four orders lower. Meanwhile, the microwave-induced broadening to the line-width of the spectroscopy is significantly canceled, and we achieve a nuclear-spin spectrum with a resolution down to 2.1 kHz under a magnetic field at 1840 Gs. The spectral resolution can be further improved by upgrading the experimental control precision. This scheme can also be used in sensing microwave fields and can be extended to a wide range of applications in the future.

Prospects of single-cell nuclear magnetic resonance spectroscopy with quantum sensors

Single-cell analysis can unravel functional heterogeneity within cell populations otherwise obscured by ensemble measurements. However, noninvasive techniques that probe chemical entities and their dynamics are still lacking. This challenge could be overcome by novel sensors based on nitrogen-vacancy (NV) centers in diamond, which enable nuclear magnetic resonance (NMR) spectroscopy on unprecedented sample volumes. In this perspective, we briefly introduce NV-based quantum sensing and review the progress made in microscale NV-NMR spectroscopy. Last, we discuss approaches to enhance the sensitivity of NV ensemble magnetometers to detect biologically relevant concentrations and provide a roadmap toward their application in single-cell analysis.

Imaging local diffusion in microstructures using NV-based pulsed field gradient NMR

Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, medicine, or energy research. While magnetic resonance (MR) methods are the gold standard for diffusion measurements, spatial encoding in MR imaging has limitations. Here, we introduce nitrogen-vacancy (NV) center-based nuclear MR (NMR) spectroscopy as a powerful tool to probe diffusion within microscopic sample volumes. We have developed an experimental scheme that combines pulsed gradient spin echo (PGSE) with optically detected NV-NMR spectroscopy, allowing local quantification of molecular diffusion and flow. We demonstrate correlated optical imaging with spatially resolved PGSE NV-NMR experiments probing anisotropic water diffusion within an individual model microstructure. Our optically detected PGSE NV-NMR technique opens up prospects for extending the current capabilities of investigating diffusion processes with the future potential of probing single cells, tissue microstructures, or ion mobility in thin film materials for battery applications.

Advances in Stabilization and Enrichment of Shallow Nitrogen-Vacancy Centers in Diamond for Biosensing and Spin-Polarization Transfer

Negatively charged nitrogen-vacancy (NV^-) centers in diamond have unique magneto-optical properties, such as high fluorescence, single-photon generation, millisecond-long coherence times, and the ability to initialize and read the spin state using purely optical means. This makes NV^- centers a powerful sensing tool for a range of applications, including magnetometry, electrometry, and thermometry. Biocompatible NV-rich nanodiamonds find application in cellular microscopy, nanoscopy, and in vivo imaging. NV^- centers can also detect electron spins, paramagnetic agents, and nuclear spins. Techniques have been developed to hyperpolarize ¹⁴N, ¹⁵N, and ¹³C nuclear spins, which could open up new perspectives in NMR and MRI. However, defects on the diamond surface, such as hydrogen, vacancies, and trapping states, can reduce the stability of NV^- in favor of the neutral form (NV⁰), which lacks the same properties. Laser irradiation can also lead to charge-state switching and a reduction in the number of NV^- centers. Efforts have been made to improve stability through diamond substrate doping, proper annealing and surface termination, laser irradiation, and electric or electrochemical tuning of the surface potential. This article discusses advances in the stabilization and enrichment of shallow NV^- ensembles, describing strategies for improving the quality of diamond devices for sensing and spin-polarization transfer applications. Selected applications in the field of biosensing are discussed in more depth.

Magnetically Detected Protein Binding Using Spin-Labeled Slow Off-Rate Modified Aptamers

Recent developments in aptamer chemistry open up opportunities for new tools for protein biosensing. In this work, we present an approach to use immobilized slow off-rate modified aptamers (SOMAmers) site-specifically labeled with a nitroxide radical via azide-alkyne click chemistry as a means for detecting protein binding. Protein binding induces a change in rotational mobility of the spin label, which is detected via solution-state electron paramagnetic resonance (EPR) spectroscopy. We demonstrate the workflow and test the protocol using the SOMAmer SL5 and its protein target, platelet-derived growth factor B (PDGF-BB). In a complete site scan of the nitroxide over the SOMAmer, we determine the rotational mobility of the spin label in the absence and presence of target protein. Several sites with sufficiently tight affinity and large rotational mobility change upon protein binding are identified. We then model a system where the spin-labeled SOMAmer assay is combined with fluorescence detection via diamond nitrogen-vacancy (NV) center relaxometry. The NV center spin-lattice relaxation time is modulated by the rotational mobility of a proximal spin label and thus responsive to SOMAmer-protein binding. The spin label-mediated assay provides a general approach for transducing protein binding events into magnetically detectable signals.

Probing many-body dynamics in a two-dimensional dipolar spin ensemble

The most direct approach for characterizing the quantum dynamics of a strongly interacting system is to measure the time evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate approach is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Here we investigate what the decoherence dynamics of such a probe tells us about the many-body system. In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in nitrogen delta-doped diamond: nitrogen-vacancy colour centres, which we use as probe spins, and a many-body ensemble of substitutional nitrogen impurities. We demonstrate that the many-body system's dimensionality, dynamics and disorder are naturally encoded in the probe spins' decoherence profile. Furthermore, we obtain direct control over the spectral properties of the many-body system, with potential applications in quantum sensing and simulation.

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.

Single-Nitrogen-Vacancy NMR of Amine-Functionalized Diamond Surfaces

Nuclear magnetic resonance (NMR) imaging with shallow nitrogen-vacancy (NV) centers in diamond offers an exciting route toward sensitive and localized chemical characterization at the nanoscale. Remarkable progress has been made to combat the degradation in coherence time and stability suffered by near-surface NV centers using suitable chemical surface termination. However, approaches that also enable robust control over adsorbed molecule density, orientation, and binding configuration are needed. We demonstrate a diamond surface preparation for mixed nitrogen- and oxygen-termination that simultaneously improves NV center coherence times for <10 nm-deep emitters and enables direct and recyclable chemical functionalization via amine-reactive cross-linking. Using this approach, we probe single NV centers embedded in nanopillar waveguides to perform ¹⁹F NMR sensing of covalently bound fluorinated molecules with detection on the order of 100 molecules. This work signifies an important step toward nuclear spin localization and structure interrogation at the single-molecule level.

Decoherence of V[Formula: see text] spin defects in monoisotopic hexagonal boron nitride

Spin defects in hexagonal boron nitride (hBN) are promising quantum systems for the design of flexible two-dimensional quantum sensing platforms. Here we rely on hBN crystals isotopically enriched with either 10B or 11B to investigate the isotope-dependent properties of a spin defect featuring a broadband photoluminescence signal in the near infrared. By analyzing the hyperfine structure of the spin defect while changing the boron isotope, we first confirm that it corresponds to the negatively charged boron-vacancy center ([Formula: see text]). We then show that its spin coherence properties are slightly improved in 10B-enriched samples. This is supported by numerical simulations employing cluster correlation expansion methods, which reveal the importance of the hyperfine Fermi contact term for calculating the coherence time of point defects in hBN. Using cross-relaxation spectroscopy, we finally identify dark electron spin impurities as an additional source of decoherence. This work provides new insights into the properties of [Formula: see text] spin defects, which are valuable for the future development of hBN-based quantum sensing foils.

Advances in nano- and microscale NMR spectroscopy using diamond quantum sensors

Quantum technologies have seen a rapid developmental surge over the last couple of years. Though often overshadowed by quantum computation, quantum sensors show tremendous potential for widespread applications in chemistry and biology. One system stands out in particular: the nitrogen-vacancy (NV) center in diamond, an atomic-sized sensor allowing the detection of nuclear magnetic resonance (NMR) signals at unprecedented length scales down to a single proton. In this article, we review the fundamentals of NV center-based quantum sensing and its distinct impact on nano- and microscale NMR spectroscopy. Furthermore, we highlight possible future applications of this novel technology ranging from energy research, materials science, to single-cell biology, and discuss the associated challenges of these rapidly developing NMR sensors.

The effect of spin polarization on double electron-electron resonance (DEER) spectroscopy

Double electron-electron resonance (DEER) spectroscopy measures the distribution of distances between two electron spins in the nanometer range, often on doubly spin-labeled proteins, via the modulation of a refocused spin echo by the dipolar interaction between the spins. DEER is commonly conducted under conditions where the polarization of the spins is small. Here, we examine the DEER signal under conditions of high spin polarization, thermally obtainable at low temperatures and high magnetic fields, and show that the signal acquires a polarization-dependent out-of-phase component both for the intramolecular and intermolecular contributions. For the latter, this corresponds to a phase shift of the spin echo that is linear in the pump pulse position. We derive a compact analytical form of this phase shift and show experimental measurements using monoradical and biradical nitroxides at several fields and temperatures. The effect highlights a novel aspect of the fundamental spin physics underlying DEER spectroscopy.

Open quantum systems coupled to finite baths: A hierarchy of master equations

An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium but it induces a dynamical evolution of the bath state. In this paper, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy, we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which not only is more realistic but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular noninteracting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model.

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.

Surface NMR using quantum sensors in diamond

NMR is a noninvasive, molecular-level spectroscopic technique widely used for chemical characterization. However, it lacks the sensitivity to probe the small number of spins at surfaces and interfaces. Here, we use nitrogen vacancy (NV) centers in diamond as quantum sensors to optically detect NMR signals from chemically modified thin films. To demonstrate the method's capabilities, aluminum oxide layers, common supports in catalysis and materials science, are prepared by atomic layer deposition and are subsequently functionalized by phosphonate chemistry to form self-assembled monolayers. The surface NV-NMR technique detects spatially resolved NMR signals from the monolayer, indicates chemical binding, and quantifies molecular coverage. In addition, it can monitor in real time the formation kinetics at the solid-liquid interface. With our approach, we show that NV quantum sensors are a surface-sensitive NMR tool with femtomole sensitivity for in situ analysis in catalysis, materials, and biological research.

Tunable and Transferable Diamond Membranes for Integrated Quantum Technologies

Color centers in diamond are widely explored as qubits in quantum technologies. However, challenges remain in the effective and efficient integration of these diamond-hosted qubits in device heterostructures. Here, nanoscale-thick uniform diamond membranes are synthesized via "smart-cut" and isotopically (¹²C) purified overgrowth. These membranes have tunable thicknesses (demonstrated 50 to 250 nm), are deterministically transferable, have bilaterally atomically flat surfaces (R_q ≤ 0.3 nm), and bulk-diamond-like crystallinity. Color centers are synthesized via both implantation and in situ overgrowth incorporation. Within 110-nm-thick membranes, individual germanium-vacancy (GeV^-) centers exhibit stable photoluminescence at 5.4 K and average optical transition line widths as low as 125 MHz. The room temperature spin coherence of individual nitrogen-vacancy (NV^-) centers shows Ramsey spin dephasing times (T₂^*) and Hahn echo times (T₂) as long as 150 and 400 μs, respectively. This platform enables the straightforward integration of diamond membranes that host coherent color centers into quantum technologies.

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.

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.

Persistent dark states in anisotropic central spin models

Long-lived dark states, in which an experimentally accessible qubit is not in thermal equilibrium with a surrounding spin bath, are pervasive in solid-state systems. We explain the ubiquity of dark states in a large class of inhomogeneous central spin models using the proximity to integrable lines with exact dark eigenstates. At numerically accessible sizes, dark states persist as eigenstates at large deviations from integrability, and the qubit retains memory of its initial polarization at long times. Although the eigenstates of the system are chaotic, exhibiting exponential sensitivity to small perturbations, they do not satisfy the eigenstate thermalization hypothesis. Rather, we predict long relaxation times that increase exponentially with system size. We propose that this intermediate chaotic but non-ergodic regime characterizes mesoscopic quantum dot and diamond defect systems, as we see no numerical tendency towards conventional thermalization with a finite relaxation time.

Ultralong Spin-Coherence Times for Rubidium Atoms in Solid Parahydrogen via Dynamical Decoupling

Coherence time is an essential parameter for quantum sensing, quantum information, and quantum computation. In this work, we demonstrate electron spin coherence times as long as 0.1 s for an ensemble of rubidium atoms trapped in a solid parahydrogen matrix. We explore the underlying physics limiting the coherence time. The properties of these matrix isolated atoms are very promising for future applications, including quantum sensing of nuclear spins. If combined with efficient single-atom readout, this would enable NMR and magnetic resonance imaging of single molecules cotrapped with alkali-metal atom quantum sensors within a parahydrogen matrix.

Nanoscale Electrometry Based on a Magnetic-Field-Resistant Spin Sensor

The nitrogen-vacancy (NV) center is a potential atomic-scale spin sensor for electric field sensing. However, its natural susceptibility to the magnetic field hinders effective detection of the electric field. Here we propose a robust electrometric method utilizing continuous dynamic decoupling (CDD) technique. During the CDD period, the NV center evolves in a dressed frame, where the sensor is resistant to magnetic fields but remains sensitive to electric fields. As an example, we use this method to isolate the electric noise from a complex electromagnetic environment near diamond surface via measuring the dephasing rate between dressed states. By reducing the surface electric noise with different covered liquids, we observe an unambiguous relation between the dephasing rate and the relative dielectric permittivity of the liquid, which enables a quantitative investigation of electric noise model near the diamond surface.

Extending the Quantum Coherence of a Near-Surface Qubit by Coherently Driving the Paramagnetic Surface Environment

Surfaces enable useful functionalities for quantum systems, e.g., as interfaces to sensing targets, but often result in surface-induced decoherence where unpaired electron spins are common culprits. Here we show that the coherence time of a near-surface qubit is increased by coherent radio-frequency driving of surface electron spins, where we use a diamond nitrogen-vacancy (NV) center as a model qubit. This technique is complementary to other methods of suppressing decoherence and, importantly, requires no additional materials processing or control of the qubit. Further, by combining driving with the increased magnetic susceptibility of the double-quantum basis, we realize an overall fivefold sensitivity enhancement in NV magnetometry. Informed by our results, we discuss a path toward relaxation-limited coherence times for near-surface NV centers. The surface-spin driving technique presented here is broadly applicable to a wide variety of qubit platforms afflicted by surface-induced decoherence.

Extreme nuclear magnetic resonance: Zero field, single spins, dark matter…

An unusual regime for liquid-state nuclear magnetic resonance (NMR) where the magnetic field strength is so low that the J-coupling (intramolecular spin-spin) interactions dominate the spin Hamiltonian opens a new paradigm with applications in spectroscopy, quantum control, and in fundamental-physics experiments, including searches for well-motivated dark-matter candidates. An interesting possibility is to bring this kind of "extreme NMR" together with another one-single nuclear spin detected with a single-spin quantum sensor. This would enable single-molecule J-spectroscopy.

Understanding the Linewidth of the ESR Spectrum Detected by a Single NV Center in Diamond

Spectral analysis of electron spin resonance (ESR) is a powerful technique for various investigations including characterization of spin systems, measurements of spin concentration, and probing spin dynamics. The nitrogen-vacancy (NV) center in diamond is a promising magnetic sensor enabling improvement of ESR sensitivity to the level of a single spin. Therefore, understanding the nature of the NV-detected ESR (NV-ESR) spectrum is critical for applications to nanoscale ESR. Within this work, we investigate the linewidth of NV-ESR from single substitutional nitrogen centers (called P1 centers). NV-ESR is detected by a double electron-electron resonance (DEER) technique. By studying the dependence of the DEER excitation bandwidth on the NV-ESR linewidth, we find that the spectral resolution is improved significantly and eventually limited by inhomogeneous broadening of the detected P1 ESR. Moreover, we show that the NV-ESR linewidth can be as narrow as 0.3 MHz.

Spin Properties of Germanium-Vacancy Centers in Bulk and Near-Surface Regions of Diamond

Germanium-vacancy (GeV) centers are now studied extensively due to perspectives of their applications in quantum information processing, nanometrology and nanoscale magnetic resonance imaging. One of the important requirements for these applications is a detailed understanding of the hyperfine interactions in such systems. Quantum chemistry simulation of the negatively charged GeV− color center in diamond is the primary goal of this paper in which we present preliminary results of computer simulation of the bulk H-terminated cluster C[Formula: see text][GeV−]H[Formula: see text], as well as of the surface cluster C[Formula: see text][GeV−]H[Formula: see text]_(100)_H[Formula: see text] having one dangling bond at (1 0 0) surface using the DFT/PW91/RI/def2-SVP level of theory.

Engineering of Shallow Layers of Nitrogen Vacancy Colour Centres in Diamond Using Plasma Immersion Ion Implantation

Sensing nano-scale magnetic field sources is at the heart of many applications in nano-science and biology. Given its very small size and high magnetic sensitivity, the nitrogen vacancy (NV) colour centre in diamond is one of the leading candidates for such applications. However, issues regarding the stability and performance of the NV centre near the diamond’s surface are the major obstacle in the practical realization of theses sensors. So far, conventional implantation and growth techniques did not produce practical and/or repeatable solutions to this problem. In this report, we show first results of shallow layers of NVs created using plasma immersion ion implantation (PIII). We show, using Forster Resonance Energy Transfer (FRET), that most NVs are within 3.6 nm from the diamond’s surface. Despite the relatively low quality of the diamond substrates used and the simplicity of our PIII system, we have an estimated magnetic sensitivity of around 2.29 μT/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{Hz\cdot \mu {m}^{-2}}$$\end{document}Hz⋅μm−2.

Selective Decoupling and Hamiltonian Engineering in Dipolar Spin Networks

We present a protocol to selectively decouple, recouple, and engineer effective interactions in mesoscopic dipolar spin networks. In particular, we develop a versatile protocol that relies upon magic angle spinning to perform Hamiltonian engineering. By using global control fields in conjunction with a local actuator, such as a diamond nitrogen vacancy center located in the vicinity of a nuclear spin network, both global and local control over the effective couplings can be achieved. We show that the resulting effective Hamiltonian can be well understood within a simple, intuitive geometric picture, and corroborate its validity by performing exact numerical simulations in few-body systems. Applications of our method are in the emerging fields of two-dimensional room temperature quantum simulators in diamond platforms, as well as in molecular magnet systems.

Broadband loop gap resonator for nitrogen vacancy centers in diamond

We present an S-band tunable loop gap resonator (LGR), which provides strong, homogeneous, and directionally uniform broadband microwave (MW) drive for nitrogen-vacancy (NV) ensembles. With 42 dBm of input power, the composite device provides drive field amplitudes approaching 5 G over a circular area ≳50 mm² or cylindrical volume ≳250 mm³. The wide 80 MHz device bandwidth allows driving all NV Zeeman resonances for bias magnetic fields below 20 G. The device realizes percent-scale MW drive inhomogeneity; we measure a fractional root-mean-square inhomogeneity σ _rms = 1.6% and a peak-to-peak variation σ _pp = 3% over a circular area of 11 mm² and σ _rms = 3.2% and σ _pp = 10.5% over a larger 32 mm² circular area. We demonstrate incident MW power coupling to the LGR using two methodologies: a printed circuit board-fabricated exciter antenna for deployed compact bulk sensors and an inductive coupling coil suitable for microscope-style imaging. The inductive coupling coil allows for approximately 2π steradian combined optical access above and below the device, ideal for envisioned and existing NV imaging and bulk sensing applications.

Sensing Coherent Dynamics of Electronic Spin Clusters in Solids

We observe coherent spin exchange between identical electronic spins in the solid state, a key step towards full quantum control of electronic spin registers in room temperature solids. In a diamond substrate, a single nitrogen vacancy (NV) center coherently couples to two adjacent S=1/2 dark electron spins via the magnetic dipolar interaction. We quantify NV-electron and electron-electron couplings via detailed spectroscopy, with good agreement to a model of strongly interacting spins. The electron-electron coupling enables an observation of coherent flip-flop dynamics between electronic spins in the solid state, which occur conditionally on the state of the NV. Finally, as a demonstration of coherent control, we selectively couple and transfer polarization between the NV and the pair of electron spins. Our observations enable the realization of fast quantum gate operations and quantum state transfer in a scalable, room temperature, quantum processor.

Fast Preparation of Critical Ground States Using Superluminal Fronts

We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼L^{d} (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L^{2}) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.

Quantum measurement of a rapidly rotating spin qubit in diamond

A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realizing a single qubit that can be measured and controlled during physical rotation is experimentally challenging. We demonstrate quantum control of a single nitrogen-vacancy (NV) center within a diamond rotated at 200,000 rpm, a rotational period comparable to the NV spin coherence time T₂. We stroboscopically image individual NV centers that execute rapid circular motion in addition to rotation and demonstrate preparation, control, and readout of the qubit quantum state with lasers and microwaves. Using spin-echo interferometry of the rotating qubit, we are able to detect modulation of the NV Zeeman shift arising from the rotating NV axis and an external DC magnetic field. Our work establishes single NV qubits in diamond as quantum sensors in the physically rotating frame and paves the way for the realization of single-qubit diamond-based rotation sensors.

Nanoscale zero-field electron spin resonance spectroscopy

Electron spin resonance (ESR) spectroscopy has broad applications in physics, chemistry, and biology. As a complementary tool, zero-field ESR (ZF-ESR) spectroscopy has been proposed for decades and shown its own benefits for investigating the electron fine and hyperfine interaction. However, the ZF-ESR method has been rarely used due to the low sensitivity and the requirement of much larger samples than conventional ESR. In this work, we present a method for deploying ZF-ESR spectroscopy at the nanoscale by using a highly sensitive quantum sensor, the nitrogen vacancy center in diamond. We also measure the nanoscale ZF-ESR spectrum of a few P1 centers in diamond, and show that the hyperfine coupling constant can be directly extracted from the spectrum. This method opens the door to practical applications of ZF-ESR spectroscopy, such as investigation of the structure and polarity information in spin-modified organic and biological systems.

Demonstrations of sensing devices using nitrogen vacancy centres have shown significantly improved sensitivity compared to traditional methods. Here the authors demonstrate an approach for performing nanoscale electron spin resonance without magnetic fields in order to achieve better spectral resolution.

Submillihertz magnetic spectroscopy performed with a nanoscale quantum sensor

Precise timekeeping is critical to metrology, forming the basis by which standards of time, length, and fundamental constants are determined. Stable clocks are particularly valuable in spectroscopy because they define the ultimate frequency precision that can be reached. In quantum metrology, the qubit coherence time defines the clock stability, from which the spectral linewidth and frequency precision are determined. We demonstrate a quantum sensing protocol in which the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock. Using this technique, we observed a precision in frequency estimation scaling in time T as T^-3/2 for classical oscillating fields. The narrow linewidth magnetometer based on single spins in diamond is used to sense nanoscale magnetic fields with an intrinsic frequency resolution of 607 microhertz, which is eight orders of magnitude narrower than the qubit coherence time.

Achieving Optimal Quantum Acceleration of Frequency Estimation Using Adaptive Coherent Control

Precision measurements of frequency are critical to accurate time keeping and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians the uncertainty of any parameter scales at best as 1/T, where T is the duration of the experiment, recent theoretical works have predicted that explicitly time-dependent Hamiltonians can yield a 1/T^{2} scaling of the uncertainty for an oscillation frequency. This quantum acceleration in precision requires coherent control, which is generally adaptive. We experimentally realize this quantum improvement in frequency sensitivity with superconducting circuits, using a single transmon qubit. With optimal control pulses, the theoretically ideal frequency precision scaling is reached for times shorter than the decoherence time. This result demonstrates a fundamental quantum advantage for frequency estimation.

A molecular quantum spin network controlled by a single qubit

Scalable quantum technologies require an unprecedented combination of precision and complexity for designing stable structures of well-controllable quantum systems on the nanoscale. It is a challenging task to find a suitable elementary building block, of which a quantum network can be comprised in a scalable way. We present the working principle of such a basic unit, engineered using molecular chemistry, whose collective control and readout are executed using a nitrogen vacancy (NV) center in diamond. The basic unit we investigate is a synthetic polyproline with electron spins localized on attached molecular side groups separated by a few nanometers. We demonstrate the collective readout and coherent manipulation of very few (≤ 6) of these S = 1/2 electronic spin systems and access their direct dipolar coupling tensor. Our results show that it is feasible to use spin-labeled peptides as a resource for a molecular qubit-based network, while at the same time providing simple optical readout of single quantum states through NV magnetometry. This work lays the foundation for building arbitrary quantum networks using well-established chemistry methods, which has many applications ranging from mapping distances in single molecules to quantum information processing.

Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers

We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.

Dissipatively Stabilized Quantum Sensor Based on Indirect Nuclear-Nuclear Interactions

We propose to use a dissipatively stabilized nitrogen vacancy (NV) center as a mediator of interaction between two nuclear spins that are protected from decoherence and relaxation of the NV due to the periodical resets of the NV center. Under ambient conditions this scheme achieves highly selective high-fidelity quantum gates between nuclear spins in a quantum register even at large NV-nuclear distances. Importantly, this method allows for the use of nuclear spins as a sensor rather than a memory, while the NV spin acts as an ancillary system for the initialization and readout of the sensor. The immunity to the decoherence and relaxation of the NV center leads to a tunable sharp frequency filter while allowing at the same time the continuous collection of the signal to achieve simultaneously high spectral selectivity and high signal-to-noise ratio.

Superresolution optical magnetic imaging and spectroscopy using individual electronic spins in diamond

Nitrogen vacancy (NV) color centers in diamond are a leading modality for both superresolution optical imaging and nanoscale magnetic field sensing. In this work, we address the key challenge of performing optical magnetic imaging and spectroscopy selectively on multiple NV centers that are located within a diffraction-limited field-of-view. We use spin-RESOLFT microscopy to enable precision nanoscale mapping of magnetic field patterns with resolution down to ~20 nm, while employing a low power optical depletion beam. Moreover, we use a shallow NV to demonstrate the detection of proton nuclear magnetic resonance (NMR) signals exterior to the diamond, with 50 nm lateral imaging resolution and without degrading the proton NMR linewidth.

Double-Quantum Spin-Relaxation Limits to Coherence of Near-Surface Nitrogen-Vacancy Centers

We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a T_{1} relaxation time that sets the T_{2}≤2T_{1} coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates T_{1} of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate 1/f^{α} spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.

Environmentally Mediated Coherent Control of a Spin Qubit in Diamond

The coherent control of spin qubits forms the basis of many applications in quantum information processing and nanoscale sensing, imaging, and spectroscopy. Such control is conventionally achieved by direct driving of the qubit transition with a resonant global field, typically at microwave frequencies. Here we introduce an approach that relies on the resonant driving of nearby environment spins, whose localized magnetic field in turn drives the qubit when the environmental spin Rabi frequency matches the qubit resonance. This concept of environmentally mediated resonance (EMR) is explored experimentally using a qubit based on a single nitrogen-vacancy (NV) center in diamond, with nearby electronic spins serving as the environmental mediators. We demonstrate EMR driven coherent control of the NV spin state, including the observation of Rabi oscillations, free induction decay, and spin echo. This technique also provides a way to probe the nanoscale environment of spin qubits, which we illustrate by acquisition of electron spin resonance spectra from single NV centers in various settings.

Nitrogen-Terminated Diamond (111) Surface for Room-Temperature Quantum Sensing and Simulation

The nitrogen-vacancy (NV) center in diamond has shown great promise of nanoscale sensing applications, however, near-surface NV suffer from relatively short spin coherence time that limits its sensitivity. This is presumably caused by improper surface termination. Using first-principles calculations, we propose that nitrogen-terminated (111) diamond provides electrical inactivity and surface spin noise free properties. We anticipate that the nitrogen-terminated (111) surface can be fabricated by nitrogen plasma treatment. Our findings pave the way toward an improved NV-based quantum sensing and quantum simulation operating at room temperature.

Delayed entanglement echo for individual control of a large number of nuclear spins

Methods to selectively detect and manipulate nuclear spins by single electrons of solid-state defects play a central role for quantum information processing and nanoscale nuclear magnetic resonance (NMR). However, with standard techniques, no more than eight nuclear spins have been resolved by a single defect centre. Here we develop a method that improves significantly the ability to detect, address and manipulate nuclear spins unambiguously and individually in a broad frequency band by using a nitrogen-vacancy (NV) centre as model system. On the basis of delayed entanglement control, a technique combining microwave and radio frequency fields, our method allows to selectively perform robust high-fidelity entangling gates between hardly resolved nuclear spins and the NV electron. Long-lived qubit memories can be naturally incorporated to our method for improved performance. The application of our ideas will increase the number of useful register qubits accessible to a defect centre and improve the signal of nanoscale NMR.

Single electrons of solid-state defects can be used to detect nearby nuclear spins, but so far only a few at a time have been resolved. Here the authors propose an approach based on delayed entanglement echo that demonstrates improved detection and manipulation capabilities of nuclear spins by an NV centre.

Single-spin magnetic resonance in the nitrogen-vacancy center of diamond

Magnetic resonance of single spins has flourished mostly because of the unique properties of the NV center in diamond. This review covers the basic physics of this defect center, introduces the techniques for working with single spins and gives an overview of some applications like quantum information and sensing.

Nuclear quantum-assisted magnetometer

Magnetic sensing and imaging instruments are important tools in biological and material sciences. There is an increasing demand for attaining higher sensitivity and spatial resolution, with implementations using a single qubit offering potential improvements in both directions. In this article we describe a scanning magnetometer based on the nitrogen-vacancy center in diamond as the sensor. By means of a quantum-assisted readout scheme together with advances in photon collection efficiency, our device exhibits an enhancement in signal to noise ratio of close to an order of magnitude compared to the standard fluorescence readout of the nitrogen-vacancy center. This is demonstrated by comparing non-assisted and assisted methods in a T₁ relaxation time measurement.

A quantum spin-probe molecular microscope

Imaging the atomic structure of a single biomolecule is an important challenge in the physical biosciences. Whilst existing techniques all rely on averaging over large ensembles of molecules, the single-molecule realm remains unsolved. Here we present a protocol for 3D magnetic resonance imaging of a single molecule using a quantum spin probe acting simultaneously as the magnetic resonance sensor and source of magnetic field gradient. Signals corresponding to specific regions of the molecule's nuclear spin density are encoded on the quantum state of the probe, which is used to produce a 3D image of the molecular structure. Quantum simulations of the protocol applied to the rapamycin molecule (C₅₁H₇₉NO₁₃) show that the hydrogen and carbon substructure can be imaged at the angstrom level using current spin-probe technology. With prospects for scaling to large molecules and/or fast dynamic conformation mapping using spin labels, this method provides a realistic pathway for single-molecule microscopy.

Single spin defects can allow high-resolution sensing of molecules under an applied magnetic field. Here, the authors propose a protocol for three-dimensional magnetic resonance imaging with angstrom-level resolution exploiting the dipolar field of a spin qubit, such as a diamond nitrogen-vacancy.

Single spin magnetic resonance

Different approaches have improved the sensitivity of either electron or nuclear magnetic resonance to the single spin level. For optical detection it has essentially become routine to observe a single electron spin or nuclear spin. Typically, the systems in use are carefully designed to allow for single spin detection and manipulation, and of those systems, diamond spin defects rank very high, being so robust that they can be addressed, read out and coherently controlled even under ambient conditions and in a versatile set of nanostructures. This renders them as a new type of sensor, which has been shown to detect single electron and nuclear spins among other quantities like force, pressure and temperature. Adapting pulse sequences from classic NMR and EPR, and combined with high resolution optical microscopy, proximity to the target sample and nanoscale size, the diamond sensors have the potential to constitute a new class of magnetic resonance detectors with single spin sensitivity. As diamond sensors can be operated under ambient conditions, they offer potential application across a multitude of disciplines. Here we review the different existing techniques for magnetic resonance, with a focus on diamond defect spin sensors, showing their potential as versatile sensors for ultra-sensitive magnetic resonance with nanoscale spatial resolution.