Roadmap on nanoscale magnetic resonance imaging.

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

Background-free dual-mode optical and 13C magnetic resonance imaging in diamond particles.

Multimodal imaging-the ability to acquire images of an object through more than one imaging mode simultaneously-has opened additional perspectives in areas ranging from astronomy to medicine. In this paper, we report progress toward combining optical and magnetic resonance (MR) imaging in such a "dual" imaging mode. They are attractive in combination because they offer complementary advantages of resolution and speed, especially in the context of imaging in scattering environments. Our approach relies on a specific material platform, microdiamond particles hosting nitrogen vacancy (NV) defect centers that fluoresce brightly under optical excitation and simultaneously "hyperpolarize" lattice [Formula: see text] nuclei, making them bright under MR imaging. We highlight advantages of dual-mode optical and MR imaging in allowing background-free particle imaging and describe regimes in which either mode can enhance the other. Leveraging the fact that the two imaging modes proceed in Fourier-reciprocal domains (real and k-space), we propose a sampling protocol that accelerates image reconstruction in sparse-imaging scenarios. Our work suggests interesting possibilities for the simultaneous optical and low-field MR imaging of targeted diamond nanoparticles.

Complex Three-Dimensional Microscale Structures for Quantum Sensing Applications.

We present a novel method for fabricating highly customizable three-dimensional structures hosting quantum sensors based on nitrogen vacancy (NV) centers using two-photon polymerization. This approach overcomes challenges associated with structuring traditional single-crystal quantum sensing platforms and enables the creation of complex, fully three-dimensional, sensor assemblies with submicroscale resolutions (down to 400 nm) and large fields of view (>1 mm). By embedding NV center-containing nanoparticles in exemplary structures, we demonstrate high sensitivity optical sensing of temperature and magnetic fields at the microscale. Our work showcases the potential for integrating quantum sensors with advanced manufacturing techniques, facilitating the incorporation of sensors into existing microfluidic and electronic platforms, and opening new avenues for widespread utilization of quantum sensors in various applications.

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.

Electron-to-nuclear spectral mapping via dynamic nuclear polarization.

We report on a strategy to indirectly read out the spectrum of an electronic spin via polarization transfer to nuclear spins in its local environment. The nuclear spins are far more abundant and have longer lifetimes, allowing for repeated polarization accumulation in them. Subsequent nuclear interrogation can reveal information about the electronic spectral density of states. We experimentally demonstrate the method by reading out the ESR spectrum of nitrogen vacancy center electrons in diamond via readout of lattice 13C nuclei. Spin-lock control on the 13C nuclei yields a significantly enhanced signal-to-noise ratio for the nuclear readout. Spectrally mapped readout presents operational advantages in being background-free and immune to crystal orientation and optical scattering. We harness these advantages to demonstrate applications in underwater magnetometry. The physical basis for the "one-to-many" spectral map is itself intriguing. To uncover its origin, we develop a theoretical model that maps the system dynamics, involving traversal of a cascaded structure of Landau-Zener anti-crossings, to the operation of a tilted "Galton board." This work points to new opportunities for "ESR-via-NMR" in dilute electronic systems and in hybrid electron-nuclear quantum memories and sensors.

Carbon-13 dynamic nuclear polarization in diamond via a microwave-free integrated cross effect.

Color-center-hosting semiconductors are emerging as promising source materials for low-field dynamic nuclear polarization (DNP) at or near room temperature, but hyperfine broadening, susceptibility to magnetic field heterogeneity, and nuclear spin relaxation induced by other paramagnetic defects set practical constraints difficult to circumvent. Here, we explore an alternate route to color-center-assisted DNP using nitrogen-vacancy (NV) centers in diamond coupled to substitutional nitrogen impurities, the so-called P1 centers. Working near the level anticrossing condition-where the P1 Zeeman splitting matches one of the NV spin transitions-we demonstrate efficient microwave-free 13C DNP through the use of consecutive magnetic field sweeps and continuous optical excitation. The amplitude and sign of the polarization can be controlled by adjusting the low-to-high and high-to-low magnetic field sweep rates in each cycle so that one is much faster than the other. By comparing the 13C DNP response for different crystal orientations, we show that the process is robust to magnetic field/NV misalignment, a feature that makes the present technique suitable to diamond powders and settings where the field is heterogeneous. Applications to shallow NVs could capitalize on the greater physical proximity between surface paramagnetic defects and outer nuclei to efficiently polarize target samples in contact with the diamond crystal.

Dynamics of frequency-swept nuclear spin optical pumping in powdered diamond at low magnetic fields.

A broad effort is underway to improve the sensitivity of NMR through the use of dynamic nuclear polarization. Nitrogen vacancy (NV) centers in diamond offer an appealing platform because these paramagnetic defects can be optically polarized efficiently at room temperature. However, work thus far has been mainly limited to single crystals, because most polarization transfer protocols are sensitive to misalignment between the NV and magnetic field axes. Here we study the spin dynamics of NV-13C pairs in the simultaneous presence of optical excitation and microwave frequency sweeps at low magnetic fields. We show that a subtle interplay between illumination intensity, frequency sweep rate, and hyperfine coupling strength leads to efficient, sweep-direction-dependent 13C spin polarization over a broad range of orientations of the magnetic field. In particular, our results strongly suggest that finely tuned, moderately coupled nuclear spins are key to the hyperpolarization process, which makes this mechanism distinct from other known dynamic polarization channels. These findings pave the route to applications where powders are intrinsically advantageous, including the hyperpolarization of target fluids in contact with the diamond surface or the use of hyperpolarized particles as contrast agents for in vivo imaging.

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.

Quantum interpolation for high-resolution sensing.

Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.

Two-Electron-Spin Ratchets as a Platform for Microwave-Free Dynamic Nuclear Polarization of Arbitrary Material Targets.

Optically pumped color centers in semiconductor powders can potentially induce high levels of nuclear spin polarization in surrounding solids or fluids at or near ambient conditions, but complications stemming from the random orientation of the particles and the presence of unpolarized paramagnetic defects hinder the flow of polarization beyond the defect's host material. Here, we theoretically study the spin dynamics of interacting nitrogen-vacancy (NV) and substitutional nitrogen (P1) centers in diamond to show that outside protons spin-polarize efficiently upon a magnetic field sweep across the NV-P1 level anticrossing. The process can be interpreted in terms of an NV-P1 spin ratchet, whose handedness, and hence the sign of the resulting nuclear polarization, depends on the relative timing of the optical excitation pulse. Further, we find that the polarization transfer mechanism is robust to NV misalignment relative to the external magnetic field, and efficient over a broad range of electron-electron and electron-nuclear spin couplings, even if proxy spins feature short coherence or spin-lattice relaxation times. Therefore, these results pave the route toward the dynamic nuclear polarization of arbitrary spin targets brought in proximity with a diamond powder under ambient conditions.

Imaging Sequences for Hyperpolarized Solids.

Hyperpolarization is one of the approaches to enhance Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI) signal by increasing the population difference between the nuclear spin states. Imaging hyperpolarized solids opens up extensive possibilities, yet is challenging to perform. The highly populated state is normally not replenishable to the initial polarization level by spin-lattice relaxation, which regular MRI sequences rely on. This makes it necessary to carefully "budget" the polarization to optimize the image quality. In this paper, we present a theoretical framework to address such challenge under the assumption of either variable flip angles or a constant flip angle. In addition, we analyze the gradient arrangement to perform fast imaging to overcome intrinsic short decoherence in solids. Hyperpolarized diamonds imaging is demonstrated as a prototypical platform to test the theory.

Nanoscale Vector dc Magnetometry via Ancilla-Assisted Frequency Up-Conversion.

Sensing static magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging, and materials science. Even more beneficial would be full vector magnetometry with nanoscale spatial resolution. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with nitrogen vacancy (NV) centers in diamond. Achieving vector magnetometry has, however, often required using an ensemble of sensors or degrading the sensitivity. Here we introduce a hybrid magnetometry platform, consisting of a sensor and an ancillary qubit, that allows vector magnetometry of static fields. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear spin qubit. In particular, sensing transverse fields relies on frequency up-conversion of the dc fields through the ancillary qubit, allowing quantum lock-in detection with low-frequency noise rejection. In combination with the Ramsey detection of longitudinal fields, our frequency up-conversion scheme delivers a sensitive technique for vector dc magnetometry at the nanoscale.

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.

Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks.

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

Optical and electronic spin properties of fluorescent micro- and nanodiamonds upon prolonged ultrahigh-temperature annealing.

High-temperature annealing is a promising but still mainly unexplored method for enhancing spin properties of negatively charged nitrogen-vacancy (NV) centers in diamond particles. After high-energy irradiation, the formation of NV centers in diamond particles is typically accomplished via annealing at temperatures in the range of 800-900 °C for 1-2 h to promote vacancy diffusion. Here, we investigate the effects of conventional annealing (900 °C for 2 h) against annealing at a much higher temperature of 1600 °C for the same annealing duration for particles ranging in size from 100 nm to 15 µm using electron paramagnetic resonance and optical characterization. At this high temperature, the vacancy-assisted diffusion of nitrogen can occur. Previously, the annealing of diamond particles at this temperature was performed over short time scales because of concerns of particle graphitization. Our results demonstrate that particles that survive this prolonged 1600 °C annealing show increased NV T1 and T2 electron spin relaxation times in 1 and 15 µm particles, due to the removal of fast relaxing spins. Additionally, this high-temperature annealing also boosts magnetically induced fluorescence contrast of NV centers for particle sizes ranging from 100 nm to 15 µm. At the same time, the content of NV centers is decreased fewfold and reaches a level of <0.5 ppm. The results provide guidance for future studies and the optimization of high-temperature annealing of fluorescent diamond particles for applications relying on the spin properties of NV centers in the host crystals.

High field magnetometry with hyperpolarized nuclear spins.

Quantum sensors have attracted broad interest in the quest towards sub-micronscale NMR spectroscopy. Such sensors predominantly operate at low magnetic fields. Instead, however, for high resolution spectroscopy, the high-field regime is naturally advantageous because it allows high absolute chemical shift discrimination. Here we demonstrate a high-field spin magnetometer constructed from an ensemble of hyperpolarized 13C nuclear spins in diamond. They are initialized by Nitrogen Vacancy (NV) centers and protected along a transverse Bloch sphere axis for minute-long periods. When exposed to a time-varying (AC) magnetic field, they undergo secondary precessions that carry an imprint of its frequency and amplitude. For quantum sensing at 7T, we demonstrate detection bandwidth up to 7 kHz, a spectral resolution < 100mHz, and single-shot sensitivity of 410pT[Formula: see text]. This work anticipates opportunities for microscale NMR chemical sensors constructed from hyperpolarized nanodiamonds and suggests applications of dynamic nuclear polarization (DNP) in quantum sensing.

Optically pumped spin polarization as a probe of many-body thermalization.

Disorder and many body interactions are known to impact transport and thermalization in competing ways, with the dominance of one or the other giving rise to fundamentally different dynamical phases. Here we investigate the spin diffusion dynamics of 13C in diamond, which we dynamically polarize at room temperature via optical spin pumping of engineered color centers. We focus on low-abundance, strongly hyperfine-coupled nuclei, whose role in the polarization transport we expose through the integrated impact of variable radio-frequency excitation on the observable bulk 13C magnetic resonance signal. Unexpectedly, we find good thermal contact throughout the nuclear spin bath, virtually independent of the hyperfine coupling strength, which we attribute to effective carbon-carbon interactions mediated by the electronic spin ensemble. In particular, observations across the full range of hyperfine couplings indicate the nuclear spin diffusion constant takes values up to two orders of magnitude greater than that expected from homo-nuclear spin couplings.

Orientation-independent room temperature optical 13C hyperpolarization in powdered diamond.

Dynamic nuclear polarization via contact with electronic spins has emerged as an attractive route to enhance the sensitivity of nuclear magnetic resonance beyond the traditional limits imposed by magnetic field strength and temperature. Among the various alternative implementations, the use of nitrogen vacancy (NV) centers in diamond-a paramagnetic point defect whose spin can be optically polarized at room temperature-has attracted widespread attention, but applications have been hampered by the need to align the NV axis with the external magnetic field. We overcome this hurdle through the combined use of continuous optical illumination and a microwave sweep over a broad frequency range. As a proof of principle, we demonstrate our approach using powdered diamond with which we attain bulk 13C spin polarization in excess of 0.25% under ambient conditions. Remarkably, our technique acts efficiently on diamond crystals of all orientations and polarizes nuclear spins with a sign that depends exclusively on the direction of the microwave sweep. Our work paves the way toward the use of hyperpolarized diamond particles as imaging contrast agents for biosensing and, ultimately, for the hyperpolarization of nuclear spins in arbitrary liquids brought in contact with their surface.