Publications

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.

Characterizing the time over which quantum coherence survives is critical for any implementation of quantum bits, memories, and sensors. The usual method for determining a quantum system's decoherence rate involves a suite of experiments probing the entire expected range of this parameter, and extracting the resulting estimation in postprocessing. Here we present an adaptive multiparameter Bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales (T1, T2∗ - , and T2) and the corresponding decay exponent of a quantum system in real time, using information gained in preceding experiments. This approach reduces the time required to reach a given uncertainty by a factor up to an order of magnitude, depending on the specific experiment, compared to the standard protocol of curve fitting. A further speedup of a factor approximately 2 can be realized by performing our optimization with respect to sensitivity as opposed to variance.

Spin-based quantum information processing makes extensive use of spin-state manipulation. This ranges from dynamical decoupling of nuclear spins in quantum sensing experiments to applying logical gates on qubits in a quantum processor. Fast manipulation of spin states is highly desirable for accelerating experiments, enhancing sensitivity, and applying elaborate pulse sequences. Strong driving using intense radio-frequency (RF) fields can, therefore, facilitate fast manipulation and enable broadband excitation of spin species. In this work, we present an antenna for strong driving in quantum sensing experiments and theoretically address challenges of the strong driving regime. First, we designed and implemented a micron-scale planar spiral RF antenna capable of delivering intense fields to a sample. The planar antenna is tailored for quantum sensing experiments using the diamonds nitrogen-vacancy (NV) center and should be applicable to other solid-state defects. The antenna has a broad bandwidth of 22 MHz, is compatible with scanning probes, and is suitable for cryogenic and ultrahigh vacuum conditions. We measure the magnetic field induced by the antenna and estimate a field-to-current ratio of 113 ± 16 G/A, representing a six-fold increase in efficiency compared to the state-of-the-art, crucial for cryogenic experiments. We demonstrate the antenna by driving Rabi oscillations in ¹H spins of an organic sample on the diamond surface and measure ¹H Rabi frequencies of over 500 kHz, i.e. π -pulses shorter than 1 μ s an order of magnitude faster than previously reported in NV-based nuclear magnetic resonance (NMR). Finally, we discuss the implications of driving spins with a field tilted from the transverse plane in a regime where the driving amplitude is comparable to the spin-state splitting, such that the rotating wave approximation does not describe the dynamics well. We present a simple recipe to optimize pulse fidelity in this regime based on a phase and offset-shifted sine drive, which may be optimized in situ without numerical optimization procedures or precise modeling of the experiment. We consider this approach in a range of driving amplitudes and show that it is particularly efficient in the case of a tilted driving field. The results presented here constitute a foundation for implementing fast nuclear spin control in various systems.

To use batteries as large-scale energy storage systems it is necessary to measure and understand their degradation in-situ and in-operando. As a batterys degradation is often the result of molecular processes inside the electrolyte, a sensing platform which allows to measure the ions with a high spatial resolution is needed. Primary candidates for such a platform are NV-centers in diamonds. We propose to use a single NV-center to deduce the electric field distribution generated by the ions inside the electrolyte through microwave pulse sequences. We show that the electric field can be reconstructed with great accuracy by using a protocol which includes different variations of the free induction decay to obtain the mean electric field components and a pulse sequence consisting of three polarized π-pulses to measure the electric fields standard deviation σ E . From a semi-analytical ansatz we find that for a lithium ion battery there is a direct relationship between σ E and the ionic concentration. Our results show that it is therefore possible to use NV-centers as sensors to measure both the electric field distribution and the local ionic concentration inside electrolytes.

Quantum sensors can potentially achieve the Heisenberg limit of sensitivity over a large dynamic range using quantum algorithms. The adaptive phase estimation algorithm (PEA) is one example that was proven to achieve such high sensitivities with single-shot readout (SSR) sensors. However, using the adaptive PEA on a non-SSR sensor is not trivial due to the low contrast nature of the measurement. The standard approach to account for the averaged nature of the measurement in this PEA algorithm is to use a method based on majority voting. Although it is easy to implement, this method is more prone to mistakes due to noise in the measurement. To reduce these mistakes, a binomial distribution technique from a batch selection was recently shown theoretically to be superior, as all ranges of outcomes from an averaged measurement are considered. Here we apply, for the first time, real-time non-adaptive PEA on a non-SSR sensor with the binomial distribution approach. We compare the mean square error of the binomial distribution method to the majority-voting approach using the nitrogen-vacancy center in diamond at ambient conditions as a non-SSR sensor. Our results suggest that the binomial distribution approach achieves better accuracy with the same sensing times. To further shorten the sensing time, we propose an adaptive algorithm that controls the readout phase and, therefore, the measurement basis set. We show by numerical simulation that adding the adaptive protocol can further improve the accuracy in a future real-time experiment.

Nitrogen vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use the longitudinal relaxation time T₁ of single NV centers to investigate the spin dynamics of nanometer-thin flakes of α-RuCl₃ at room temperature. We observe a significant reduction in the T₁ in the presence of α-RuCl₃ in the proximity of NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal planes. Furthermore, the T₁ time exhibits a monotonic increase with an applied magnetic field. We associate this trend with the alteration of the spin and charge noise in α-RuCl₃ under an external magnetic field. These findings suggest that the influence of the spin dynamics of α-RuCl₃ on the T₁ of the NV center can be used to gain information about the material itself and the technique to be used on other 2D materials.

Fluorescent nanodiamonds have been used to a large extent in various biological systems due to their robust nature, their inert properties, and the relative ease of modifying their surface for attachment to different functional groups. Within a given batch, however, each nanodiamond is indistinguishable from its neighbors and, so far, one could only rely on fluorescence statistics for some global information about the ensemble. Here, we propose and measure the possibility of adding another layer of unique information, relying on the coupling between the strain in the nanodiamond and the spin degree-of-freedom in the nitrogen-vacancy center in diamond. We show that the large variance in axial and transverse strain can be encoded to an individual radio frequency identity for a cluster of nanodiamonds. When using single nanodiamonds, this unique fingerprint can then be potentially tracked in real-time in, e.g., cells, as their size is compatible with metabolism intake. From a completely different aspect, in clusters of nanodiamonds, this can already serve as a platform for anti-counterfeiting measures.

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.

Mapping the positions of single electron spins is a highly desired capability for applications such as nanoscale magnetic resonance imaging and quantum network characterization. Here, we demonstrate a method based on rotating an external magnetic field to identify the precise location of single electron spins in the vicinity of a quantum spin sensor. We use a nitrogen-vacancy center in diamond as a quantum sensor and modulate the dipolar coupling to a proximate electron spin in the crystal by varying the magnetic field vector. The modulation of the dipolar coupling contains information on the coordinates of the spin, from which we extract its position with an uncertainty of 0.9 Å. We show that the method can be used to locate electron spins with nanometer precision up to 10 nm away from the sensor. We discuss the applicability of the method to mapping hyperfine coupled electron spins and show that it may be applied to locating nitroxide radicals. The magnetic tomography method can be utilized for distance measurements for studying the structure of individual molecules.

A plethora of single-photon emitters have been identified in the atomic layers of two-dimensional van der Waals materials¹⁸. Here, we report on a set of isolated optical emitters embedded in hexagonal boron nitride that exhibit optically detected magnetic resonance. The defect spins show an isotropic g_e-factor of ~2 and zero-field splitting below 10 MHz. The photokinetics of one type of defect is compatible with ground-state electron-spin paramagnetism. The narrow and inhomogeneously broadened magnetic resonance spectrum differs significantly from the known spectra of in-plane defects. We determined a hyperfine coupling of ~10 MHz. Its angular dependence indicates an unpaired, out-of-plane delocalized π-orbital electron, probably originating from substitutional impurity atoms. We extracted spinlattice relaxation times T₁ of 1317 μs with estimated spin coherence times T₂ of less than 1 μs. Our results provide further insight into the structure, composition and dynamics of single optically active spin defects in hexagonal boron nitride.

Radical pairs and the dynamics they undergo are prevalent in many chemical and biological systems. Specifically, it has been proposed that the radical-pair mechanism results from a relatively strong hyperfine interaction with its intrinsic nuclear spin environment. While the existence of this mechanism is undisputed, the nanoscale details remain to be experimentally shown. Here, we analyze the role of a quantum sensor in detecting the spin dynamics (non-Markovian) of individual radical pairs in the presence of a weak magnetic field. We show how quantum control methods can be used to set apart the dynamics of the radical-pair mechanism at various stages of the evolution. We expect these findings to have implications to the understanding of the physical mechanism in magnetoreception and other biochemical processes with a microscopic detail.

Atomic spins for quantum technologies need to be individually addressed and positioned with nanoscale precision. C₆₀ fullerene cages offer a robust packaging for atomic spins, while allowing in-situ physical positioning at the nanoscale. However, achieving single-spin level readout and control of endofullerenes has so far remained elusive. In this work, we demonstrate electron paramagnetic resonance on an encapsulated nitrogen spin (¹⁴N@C₆₀) within a C₆₀ matrix using a single near-surface nitrogen vacancy (NV) center in diamond at 4.7 K. Exploiting the strong magnetic dipolar interaction between the NV and endofullerene electronic spins, we demonstrate radio-frequency pulse controlled Rabi oscillations and measure spin-echos on an encapsulated spin. Modeling the results using second-order perturbation theory reveals an enhanced hyperfine interaction and zero-field splitting, possibly caused by surface adsorption on diamond. These results demonstrate the first step towards controlling single endofullerenes, and possibly building large-scale endofullerene quantum machines, which can be scaled using standard positioning or self-assembly methods.

Coupled micro- and nanomechanical oscillators are of fundamental and technical interest for emerging quantum technologies. Upon interfacing with long-lived solid-state spins, the coherent manipulation of the quantum hybrid system becomes possible even at ambient conditions. Although the ability of these systems to act as a quantum bus inducing long-range spin-spin interactions has been known, the possibility to coherently couple electron/nuclear spins to the common modes of multiple oscillators and map their mechanical motion to spin-polarization has not been experimentally demonstrated. We here report experiments on interfacing spins to the common modes of a coupled cantilever system and show their correlation by translating ultralow forces induced by radiation from one oscillator to a distant spin. Further, we analyze the coherent spin-spin coupling induced by the common modes and estimate the entanglement generation among distant spins.

Low-dimensional wide bandgap semiconductors open a new playing field in quantum optics using sub-bandgap excitation. In this field, hexagonal boron nitride (h-BN) has been reported to host single quantum emitters (QEs), linking QE density to perimeters. Furthermore, curvature/perimeters in transition metal dichalcogenides (TMDCs) have demonstrated a key role in QE formation. We investigate a curvature-Abundant BN system-quasi one-dimensional BN nanotubes (BNNTs) fabricated via a catalyst-free method. We find that non-Treated BNNT is an abundant source of stable QEs and analyze their emission features down to single nanotubes, comparing dispersed/suspended material. Combining high spatial resolution of a scanning electron microscope, we categorize and pin-point emission origin to a scale of less than 20 nm, giving us a one-To-one validation of emission source with dimensions smaller than the laser excitation wavelength, elucidating nano-Antenna effects. Two emission origins emerge: hybrid/entwined BNNT. By artificially curving h-BN flakes, similar QE spectral features are observed. The impact on emission of solvents used in commercial products and curved regions is also demonstrated. The 'out of the box' availability of QEs in BNNT, lacking processing contamination, is a milestone for unraveling their atomic features. These findings open possibilities for precision engineering of QEs, puts h-BN under a similar 'umbrella' of TMDC's QEs and provides a model explaining QEs spatial localization/formation using electron/ion irradiation and chemical etching.

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 (

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.

Newly discovered van der Waals materials like MoS₂, WSe₂, hexagonal boron nitride (h-BN), and recently C₂N have sparked intensive research to unveil the quantum behavior associated with their 2D structure. Of great interest are 2D materials that host single quantum emitters. h-BN, with a band gap of 5.95 eV, has been shown to host single quantum emitters which are stable at room temperature in the UV and visible spectral range. In this paper we investigate correlations between h-BN structural features and emitter location from bulk down to the monolayer at room temperature. We demonstrate that chemical etching and ion irradiation can generate emitters in h-BN. We analyze the emitters' spectral features and show that they are dominated by the interaction of their electronic transition with a single Raman active mode of h-BN. Photodynamics analysis reveals diverse rates between the electronic states of the emitter. The emitters show excellent photo stability even under ambient conditions and in monolayers. Comparing the excitation polarization between different emitters unveils a connection between defect orientation and the h-BN hexagonal structure. The sharp spectral features, color diversity, room-temperature stability, long-lived metastable states, ease of fabrication, proximity of the emitters to the environment, outstanding chemical stability, and biocompatibility of h-BN provide a completely new class of systems that can be used for sensing and quantum photonics applications.

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.

To study the magnetic dynamics of superparamagnetic nanoparticles, we use scanning probe relaxometry and dephasing of the nitrogen vacancy (NV) center in diamond, characterizing the spin noise of a single 10 nm magnetite particle. Additionally, we show the anisotropy of the NV sensitivitys dependence on the applied decoherence measurement method. By comparing the change in relaxation (T₁) and dephasing (T₂) time in the NV center when scanning a nanoparticle over it, we are able to extract the nanoparticles diameter and distance from the NV center using an Ornstein-Uhlenbeck model for the nanoparticles fluctuations. This scanning probe technique can be used in the future to characterize different spin label substitutes for both medical applications and basic magnetic nanoparticle behavior.

Superconducting quantum interference devices (SQUIDs) can be used to detect weak magnetic fields and have traditionally been the most sensitive magnetometers available. However, because of their relatively large effective size (on the order of 1 μm), the devices have so far been unable to achieve the level of sensitivity required to detect the field generated by the spin magnetic moment (μ B) of a single electron. Here we show that nanoscale SQUIDs with diameters as small as 46 nm can be fabricated on the apex of a sharp tip. The nano-SQUIDs have an extremely low flux noise of 50 nΦ 0 Hz -1/2 and a spin sensitivity of down to 0.38 μ B Hz -1/2, which is almost two orders of magnitude better than previous devices. They can also operate over a wide range of magnetic fields, providing a sensitivity of 0.6 μ B Hz -1/2 at 1 T. The unique geometry of our nano-SQUIDs makes them well suited to scanning probe microscopy, and we use the devices to image vortices in a type II superconductor, spaced 120 nm apart, and to record magnetic fields due to alternating currents down to 50 nT.

We describe a new type of scanning probe microscope based on a superconducting quantum interference device (SQUID) that resides on the apex of a sharp tip. The SQUID-on-tip is glued to a quartz tuning fork which allows scanning at a tip-sample separation of a few nm. The magnetic flux sensitivity of the SQUID is 1.8 μΦ ₀/√Hz and the spatial resolution is about 200 nm, which can be further improved. This combination of high sensitivity, spatial resolution, bandwidth, and the very close proximity to the sample provides a powerful tool for study of dynamic magnetic phenomena on the nanoscale. The potential of the SQUID-on-tip microscope is demonstrated by imaging of the vortex lattice and of the local ac magnetic response in superconductors.

We present a SQUID of novel design, which is fabricated on the tip of a pulled quartz tube in a simple 3-step evaporation process without need for any additional processing, patterning, or lithography. The resulting devices have SQUID loops with typical diameters in the range 75-300 nm. They operate in magnetic fields up to 0.6 T and have flux sensitivity of 1.8 μΦ₀/Hz^1/2 and magnetic field sensitivity of 10 ^-7 T/Hz^1/2, which corresponds to a spin sensitivity of 65 μ_B/Hz^1/2 for aluminum SQUIDs. The shape of the tip and the small area of the SQUID loop, together with its high sensitivity, make our device an excellent tool for scanning SQUID microscopy: With the SQUID-on-tip glued to a tine of a quartz tuning fork, we have succeeded in obtaining magnetic images of a patterned niobium film and of vortices in a superconducting film in a magnetic field.

A nanometer-sized superconducting quantum interference device (nanoSQUlD) is fabricated on the apex of a sharp quartz tip and integrated into a scanning SQUID microscope. A simple self-aligned fabrication method results in nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An aluminum nanoSQUID with an effective area of 0.034 μm² displays flux sensitivity of 1.8 x 10^-6 Φ_o/Hz^1/2 and operates in fields as high as 0.6 T. With projected spin sensitivity of 65 μ_B/Hz^1/2and high bandwidth, the SQUID on a tip is a highly promising probe for nanoscale magnetic imaging and spectroscopy.

Using micron-sized thermometers and Hall bars, we report time resolved studies of the local temperature and local magnetization for two types of magnetic avalanches (abrupt spin reversals) in the molecular magnet Mn12 acetate, corresponding to avalanches of the main slow-relaxing crystalline form and avalanches of the fast-relaxing minor species that exists in all as-grown crystals of this material. An experimental protocol is used that allows the study of each type of avalanche without triggering avalanches in the other, and of both types of avalanches simultaneously. In samples prepared magnetically to enable both types of avalanches, minor species avalanches are found to act as a catalyst for the major species avalanches.

Using a wire heater to ignite magnetic avalanches in fixed magnetic field applied along the easy axis of single crystals of the molecular magnet Mn12 acetate, we report fast local measurements of the temperature and time-resolved measurements of the local magnetization as a function of magnetic field. In addition to confirming maxima in the velocity of propagation, we find that avalanches trigger at a threshold temperature which exhibits pronounced minima at resonant magnetic fields, demonstrating that thermally assisted quantum tunneling plays an important role in the ignition as well as the propagation of magnetic avalanches in molecular magnets.