A quantum spin-probe molecular microscope

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.

Multidimensional Spectroscopy of Nuclear Spin Clusters in Diamond

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

Mapping a 50-spin-qubit network through correlated sensing

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

Embedded nano spin sensor for in situ probing of gas adsorption inside porous organic frameworks

Spin-based sensors have attracted considerable attention owing to their high sensitivities. Herein, we developed a metallofullerene-based nano spin sensor to probe gas adsorption within porous organic frameworks. For this, spin-active metallofullerene, Sc3C2@C80, was selected and embedded into a nanopore of a pyrene-based covalent organic framework (Py-COF). Electron paramagnetic resonance (EPR) spectroscopy recorded the EPR signals of Sc3C2@C80 within Py-COF after adsorbing N2, CO, CH4, CO2, C3H6, and C3H8. Results indicated that the regularly changing EPR signals of embedded Sc3C2@C80 were associated with the gas adsorption performance of Py-COF. In contrast to traditional adsorption isotherm measurements, this implantable nano spin sensor could probe gas adsorption and desorption with in situ, real-time monitoring. The proposed nano spin sensor was also employed to probe the gas adsorption performance of a metal-organic framework (MOF-177), demonstrating its versatility. The nano spin sensor is thus applicable for quantum sensing and precision measurements.

Recent Developments of Nanodiamond Quantum Sensors for Biological Applications

Measuring certain quantities at the nanoscale is often limited to strict conditions such as low temperature or vacuum. However, the recently developed nanodiamond (ND) quantum sensing technology shows great promise for ultrasensitive diagnosis and probing subcellular parameters at ambient conditions. Atom defects (i.e., N, Si) within the ND lattice provide stable emissions and sometimes spin-dependent photoluminescence. These unique properties endow ND quantum sensors with the capacity to detect local temperature, magnetic fields, electric fields, or strain. In this review, some of the recent, most exciting developments in the preparation and application of ND sensors to solve current challenges in biology and medicine including ultrasensitive detection of virions and local sensing of pH, radical species, magnetic fields, temperature, and rotational movements, are discussed.

Chemical control of spin-lattice relaxation to discover a room temperature molecular qubit

The second quantum revolution harnesses exquisite quantum control for a slate of diverse applications including sensing, communication, and computation. Of the many candidates for building quantum systems, molecules offer both tunability and specificity, but the principles to enable high temperature operation are not well established. Spin-lattice relaxation, represented by the time constant T ₁, is the primary factor dictating the high temperature performance of quantum bits (qubits), and serves as the upper limit on qubit coherence times (T ₂). For molecular qubits at elevated temperatures (>100 K), molecular vibrations facilitate rapid spin-lattice relaxation which limits T ₂ to well below operational minimums for certain quantum technologies. Here we identify the effects of controlling orbital angular momentum through metal coordination geometry and ligand rigidity via π-conjugation on T ₁ relaxation in three four-coordinate Cu²⁺ S = ½ qubit candidates: bis(N,N'-dimethyl-4-amino-3-penten-2-imine) copper(ii) (Me₂Nac)₂ (1), bis(acetylacetone)ethylenediamine copper(ii) Cu(acacen) (2), and tetramethyltetraazaannulene copper(ii) Cu(tmtaa) (3). We obtain significant T ₁ improvement upon changing from tetrahedral to square planar geometries through changes in orbital angular momentum. T ₁ is further improved with greater π-conjugation in the ligand framework. Our electronic structure calculations reveal that the reduced motion of low energy vibrations in the primary coordination sphere slows relaxation and increases T ₁. These principles enable us to report a new molecular qubit candidate with room temperature T ₂ = 0.43 μs, and establishes guidelines for designing novel qubit candidates operating above 100 K.

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.

Investigation of Various Organic Radicals Dispersed in Polymethylmethacrylate Matrices Using the Electron Spin Resonance Spectroscopy Technique

The electron spin resonance (ESR) spectroscopy technique was used to study various organic radicals, such as 2,2,6,6-tetramethyl-1-piperidinyloxyl (TEMPO), 4-hydroxy-TEMPO (TEMPOL), 2-X-nitronylnitroxide (2-X-NN, X = Ph, NO₂Ph, or cyclohexyl), 4-Y-benzonitronylnitroxide (4-Y-PhBzNN, Y = Ph or NO₂Ph), and 2-Z-iminonitroxide (2-Z-IN, Z = Ph or NO₂Ph) dispersed in a polymethylmethacrylate (PMMA) matrix. The experiments were conducted at room temperature. The complex nature of the recorded ESR spectra could be attributed to the superposition of the rotational diffusion component of TEMPO (or TEMPOL) in the nanospace of the PMMA matrix with the rigid-limit component. A single component of the rigid-limit was observed for 2-X-NN and 4-Y-PhBzNN radicals dispersed in the PMMA matrix. The isotropic components of g and hyperfine ( A ) tensor, estimated by analyzing the solution spectra, were used to determine the g and A components of 4-Y-PhBzNN. Only the rotational diffusion component was observed for the 2-Z-IN radical. These results demonstrated that the PMMA matrix contains cylindrical nanospaces. Various radicals other than TEMPO derivatives could be used in the ESR spin probe technique as probe molecules for determining the structures, sizes, and shapes of the nanospaces.

A Label-Free Diamond Microfluidic DNA Sensor Based on Active Nitrogen-Vacancy Center Charge State Control

We propose a label-free biosensor concept based on the charge state manipulation of nitrogen-vacancy (NV) quantum color centers in diamond, combined with an electrochemical microfluidic flow cell sensor, constructed on boron-doped diamond. This device can be set at a defined electrochemical potential, locking onto the particular chemical reaction, whilst the NV center provides the sensing function. The NV charge state occupation is initially prepared by applying a bias voltage on a gate electrode and then subsequently altered by exposure to detected charged molecules. We demonstrate the functionality of the device by performing label-free optical detection of DNA molecules. In this experiment, a monolayer of strongly cationic charged polymer polyethylenimine is used to shift the charge state of near surface NV centers from negatively charged NV^- to neutral NV⁰ or dark positively charged NV⁺. Immobilization of negatively charged DNA molecules on the surface of the sensor restores the NV centers charge state back to the negatively charged NV^-, which is detected using confocal photoluminescence microscopy. Biochemical reactions in the microfluidic channel are characterized by electrochemical impedance spectroscopy. The use of the developed electrochemical device can also be extended to nuclear magnetic resonance spin sensing.

Ultra-high dynamic range quantum measurement retaining its sensitivity

Quantum sensors are highly sensitive since they capitalise on fragile quantum properties such as coherence, while enabling ultra-high spatial resolution. For sensing, the crux is to minimise the measurement uncertainty in a chosen range within a given time. However, basic quantum sensing protocols cannot simultaneously achieve both a high sensitivity and a large range. Here, we demonstrate a non-adaptive algorithm for increasing this range, in principle without limit, for alternating-current field sensing, while being able to get arbitrarily close to the best possible sensitivity. Therefore, it outperforms the standard measurement concept in both sensitivity and range. Also, we explore this algorithm thoroughly by simulation, and discuss the T⁻² scaling that this algorithm approaches in the coherent regime, as opposed to the T^−1/2 of the standard measurement. The same algorithm can be applied to any modulo-limited sensor.

Usually, quantum sensing protocols impose a trade-off between sensitivity and maximum range. Here, the authors demonstrate a non-adaptive algorithm for quantum sensors to measure AC fields with a large range for which the loss in sensitivity is negligible.

Pulse control protocols for preserving coherence in dipolar-coupled nuclear spin baths

Coherence of solid state spin qubits is limited by decoherence and random fluctuations in the spin bath environment. Here we develop spin bath control sequences which simultaneously suppress the fluctuations arising from intrabath interactions and inhomogeneity. Experiments on neutral self-assembled quantum dots yield up to a five-fold increase in coherence of a bare nuclear spin bath. Numerical simulations agree with experiments and reveal emergent thermodynamic behaviour where fluctuations are ultimately caused by irreversible conversion of coherence into many-body quantum entanglement. Simulations show that for homogeneous spin baths our sequences are efficient with non-ideal control pulses, while inhomogeneous bath coherence is inherently limited even under ideal-pulse control, especially for strongly correlated spin-9/2 baths. These results highlight the limitations of self-assembled quantum dots and advantages of strain-free dots, where our sequences can be used to control the fluctuations of a homogeneous nuclear spin bath and potentially improve electron spin qubit coherence.

Fluctuating nuclear spin ensembles are a significant decoherence mechanism for solid-state spin qubits. Here the authors introduce an approach to controlling and extending the coherence of a nuclear spin bath around self-assembled quantum dots and gain insight into the many-body dynamics.

Three-dimensional localization spectroscopy of individual nuclear spins with sub-Angstrom resolution

Nuclear magnetic resonance (NMR) spectroscopy is a powerful method for analyzing the chemical composition and molecular structure of materials. At the nanometer scale, NMR has the prospect of mapping the atomic-scale structure of individual molecules, provided a method that can sensitively detect single nuclei and measure inter-atomic distances. Here, we report on precise localization spectroscopy experiments of individual 13C nuclear spins near the central electronic sensor spin of a nitrogen-vacancy (NV) center in a diamond chip. By detecting the nuclear free precession signals in rapidly switchable external magnetic fields, we retrieve the three-dimensional spatial coordinates of the nuclear spins with sub-Angstrom resolution and for distances beyond 10 Å. We further show that the Fermi contact contribution can be constrained by measuring the nuclear g-factor enhancement. The presented method will be useful for mapping atomic positions in single molecules, an ambitious yet important goal of nanoscale nuclear magnetic resonance spectroscopy.

Optimal and secure measurement protocols for quantum sensor networks

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.

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.