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. .

Frame change technique for phase transient cancellation.

The precise control of complex quantum mechanical systems can unlock applications ranging from quantum simulation to quantum computation. Controlling strongly interacting many-body systems often relies on Floquet Hamiltonian engineering that is achieved by fast switching between Hamiltonian primitives via external control. For example, in our solid-state NMR system, we perform quantum simulation by modulating the natural Hamiltonian with control pulses. As the Floquet heating errors scale with the interpulse delay, δt, it is favorable to keep δt as short as possible, forcing our control pulses to be short duration and high power. Additionally, high-power pulses help to minimize undesirable evolution from occurring during the duration of the pulse. However, such pulses introduce an appreciable phase-transient control error, a form of unitary error. In this work, we detail our ability to diagnose the error, calibrate its magnitude, and correct it for π/2-pulses of arbitrary phase. We demonstrate the improvements gained by correcting for the phase transient error, using a method which we call the "frame-change technique", in a variety of experimental settings of interest. Given that the correction mechanism adds no real control overhead, we recommend that any resonance probe be checked for these phase transient control errors, and correct them using the frame-change technique.

Exponentially Enhanced Non-Hermitian Cooling.

Certain non-Hermitian systems exhibit the skin effect, whereby the wave functions become exponentially localized at one edge of the system. Such exponential amplification of wavefunction has received significant attention due to its potential applications in, e.g., classical and quantum sensing. However, the opposite edge of the system, featured by exponentially suppressed wave functions, remains largely unexplored. Leveraging this phenomenon, we introduce a non-Hermitian cooling mechanism, which is fundamentally distinct from traditional refrigeration or laser cooling techniques. Notably, non-Hermiticity will not amplify thermal excitations, but rather redistribute them. Hence, thermal excitations can be cooled down at one edge of the system, and the cooling effect can be exponentially enhanced by the number of auxiliary modes, albeit with a lower bound that depends on the dissipative interaction with the environment. Non-Hermitian cooling does not rely on intricate properties such as exceptional points or nontrivial topology, and it can apply to a wide range of excitations.

µeV-Deep Neutron Bound States in Nanocrystals.

The strong nuclear force gives rise to the widely studied neutron scattering states and MeV-energy nuclear bound states. Whether this same interaction could lead to low-energy bound states for a neutron in the nuclear force field of a cluster of nuclei is an open question. Here, we computationally demonstrate the existence of µeV-level neutronic bound states originating from the strong interactions in nanocrystals with a spatial extent of tens of nanometers. These negative-energy neutron wave functions depend on the size, dimension, and nuclear spin polarization of the nanoparticles, providing engineering degrees of freedom for the artificial neutronic "molecule".

Manipulating solid-state spin concentration through charge transport.

Solid-state defects are attractive platforms for quantum sensing and simulation, e.g., in exploring many-body physics and quantum hydrodynamics. However, many interesting properties can be revealed only upon changes in the density of defects, which instead is usually fixed in material systems. Increasing the interaction strength by creating denser defect ensembles also brings more decoherence. Ideally one would like to control the spin concentration at will while keeping fixed decoherence effects. Here, we show that by exploiting charge transport, we can take some steps in this direction, while at the same time characterizing charge transport and its capture by defects. By exploiting the cycling process of ionization and recombination of NV centers in diamond, we pump electrons from the valence band to the conduction band. These charges are then transported to modulate the spin concentration by changing the charge state of material defects. By developing a wide-field imaging setup integrated with a fast single photon detector array, we achieve a direct and efficient characterization of the charge redistribution process by measuring the complete spectrum of the spin bath with micrometer-scale spatial resolution. We demonstrate a two-fold concentration increase of the dominant spin defects while keeping the T2 of the NV center relatively unchanged, which also provides a potential experimental demonstration of the suppression of spin flip-flops via hyperfine interactions. Our work paves the way to studying many-body dynamics with temporally and spatially tunable interaction strengths in hybrid charge-spin systems.

Characterizing Temperature and Strain Variations with Qubit Ensembles for Their Robust Coherence Protection.

Solid-state spin defects, especially nuclear spins with potentially achievable long coherence times, are compelling candidates for quantum memories and sensors. However, their current performances are still limited by dephasing due to variations of their intrinsic quadrupole and hyperfine interactions. We propose an unbalanced echo to overcome this challenge by using a second spin to refocus variations of these interactions while preserving the quantum information stored in the nuclear spin free evolution. The unbalanced echo can be used to probe the temperature and strain distribution in materials. We develop first-principles methods to predict variations of these interactions and reveal their correlation over large temperature and strain ranges. Experiments performed in an ensemble of ∼10^{10} nuclear spins in diamond demonstrate a 20-fold dephasing time increase, limited by other noise sources. We further numerically show that our method can refocus even stronger noise variations than present in our experiments.

Communication-Efficient Quantum Algorithm for Distributed Machine Learning.

The growing demands of remote detection and an increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles two traditional machine learning problems, the least-square fitting and softmax regression problems, in the scenario where the dataset is distributed across two parties. Our quantum algorithm finds the model parameters with a communication complexity of O(log_{2}(N)/ε), where N is the number of data points and ε is the bound on parameter errors. Compared to classical and other quantum methods that achieve the same goal, our methods provide a communication advantage in the scaling with data volume. The core of our methods, the quantum bipartite correlator algorithm that estimates the correlation or the Hamming distance of two bit strings distributed across two parties, may be further applied to other information processing tasks.

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

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

Laser Cooling of Nuclear Magnons.

The initialization of nuclear spin to its ground state is challenging due to its small energy scale compared with thermal energy, even at cryogenic temperature. In this Letter, we propose an optonuclear quadrupolar effect, whereby two-color optical photons can efficiently interact with nuclear spins. Leveraging such an optical interface, we demonstrate that nuclear magnons, the collective excitations of nuclear spin ensemble, can be cooled down optically. Under feasible experimental conditions, laser cooling can suppress the population and entropy of nuclear magnons by more than 2 orders of magnitude, which could facilitate the application of nuclear spins in quantum information science.

Ion sensors with crown ether-functionalized nanodiamonds.

Alkali metal ions such as sodium and potassium cations play fundamental roles in biology. Developing highly sensitive and selective methods to both detect and quantify these ions is of considerable importance for medical diagnostics and bioimaging. Fluorescent nanoparticles have emerged as powerful tools for nanoscale imaging, but their optical properties need to be supplemented with specificity to particular chemical and biological signals in order to provide further information about biological processes. Nitrogen-vacancy (NV) centers in diamond are particularly attractive as fluorescence markers, thanks to their optical stability, biocompatibility and further ability to serve as highly sensitive quantum sensors of temperature, magnetic and electric fields in ambient conditions. In this work, by covalently grafting crown ether structures on the surface of nanodiamonds (NDs), we build sensors that are capable of detecting specific alkali ions such as sodium cations. We will show that the presence of these metal ions modifies the charge state of NV centers inside the ND, which can then be read out by measuring their photoluminescence spectrum. Our work paves the way for designing selective biosensors based on NV centers in diamond.

Bias in Error-Corrected Quantum Sensing.

The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side effect: it biases a sensor's output in realistic settings. If unaccounted for, this bias can systematically reduce a sensor's performance in experiment, and also give misleading values for the minimum detectable signal in theory. We analyze this effect in the experimentally motivated setting of continuous-time QEC, showing both how one can remedy it, and how incorrect results can arise when one does not.

A synthetic monopole source of Kalb-Ramond field in diamond.

Magnetic monopoles play a central role in areas of physics that range from electromagnetism to topological matter. String theory promotes conventional vector gauge fields of electrodynamics to tensor gauge fields and predicts the existence of more exotic tensor monopoles. Here, we report the synthesis of a tensor monopole in a four-dimensional parameter space defined by the spin degrees of freedom of a single solid-state defect in diamond. Using two complementary methods, we characterized the tensor monopole by measuring its quantized topological charge and its emanating Kalb-Ramond field. By introducing a fictitious external field that breaks chiral symmetry, we further observed an intriguing spectral transition, characterized by spectral rings protected by mirror symmetries. Our work demonstrates the possibility of emulating exotic topological structures inspired by string theory.

SARS-CoV-2 Quantum Sensor Based on Nitrogen-Vacancy Centers in Diamond.

The development of highly sensitive and rapid biosensing tools targeted to the highly contagious virus SARS-CoV-2 is critical to tackling the COVID-19 pandemic. Quantum sensors can play an important role because of their superior sensitivity and fast improvements in recent years. Here we propose a molecular transducer designed for nitrogen-vacancy (NV) centers in nanodiamonds, translating the presence of SARS-CoV-2 RNA into an unambiguous magnetic noise signal that can be optically read out. We evaluate the performance of the hybrid sensor, including its sensitivity and false negative rate, and compare it to widespread diagnostic methods. The proposed method is fast and promises to reach a sensitivity down to a few hundreds of RNA copies with false negative rate less than 1%. The proposed hybrid sensor can be further implemented with different solid-state defects and substrates, generalized to diagnose other RNA viruses, and integrated with CRISPR technology.

Observation of Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems.

Periodically driven (Floquet) quantum systems have recently been a focus of nonequilibrium physics by virtue of their rich dynamics. Time-periodic systems not only exhibit symmetries that resemble those in spatially periodic systems, but also display novel behavior that arises from symmetry breaking. Characterization of such dynamical symmetries is crucial, but often challenging due to limited driving strength and lack of an experimentally accessible characterization technique. Here, we show how to reveal dynamical symmetries, namely, parity, rotation, and particle-hole symmetries, by observing symmetry-induced Floquet selection rules. Notably, we exploit modulated driving to reach the strong light-matter coupling regime, and we introduce a protocol to experimentally extract the transition matrix elements between Floquet states from the system coherent evolution. By using nitrogen-vacancy centers in diamond as an experimental test bed, we execute our protocol to observe symmetry-protected dark states and dark bands, and coherent destruction of tunneling. Our work shows how one can exploit the quantum control toolkit to study dynamical symmetries that arise in the topological phases of strongly driven Floquet systems.

Nanoscale Vector AC Magnetometry with a Single Nitrogen-Vacancy Center in Diamond.

Detection of AC magnetic fields at the nanoscale is critical in applications ranging from fundamental physics to materials science. Isolated quantum spin defects, such as the nitrogen-vacancy center in diamond, can achieve the desired spatial resolution with high sensitivity. Still, vector AC magnetometry currently relies on using different orientations of an ensemble of sensors, with degraded spatial resolution, and a protocol based on a single NV is lacking. Here we propose and experimentally demonstrate a protocol that exploits a single NV to reconstruct the vectorial components of an AC magnetic field by tuning a continuous driving to distinct resonance conditions. We map the spatial distribution of an AC field generated by a copper wire on the surface of the diamond. The proposed protocol combines high sensitivity, broad dynamic range, and sensitivity to both coherent and stochastic signals, with broad applications in condensed matter physics, such as probing spin fluctuations.

Quantum Jarzynski Equality in Open Quantum Systems from the One-Time Measurement Scheme.

In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum thermodynamics. In this Letter, we introduce well-defined notions of guessed quantum heat and guessed quantum work, by exploiting the one-time measurement scheme, which only requires an initial energy measurement on the system alone. We derive a modified quantum Jarzynski equality and the principle of maximum work with respect to the guessed quantum work, which requires the knowledge of the system only. We further show the significance of guessed quantum heat and work by linking them to the problem of quantum hypothesis testing.

Identification and Control of Electron-Nuclear Spin Defects in Diamond.

We experimentally demonstrate an approach to scale up quantum devices by harnessing spin defects in the environment of a quantum probe. We follow this approach to identify, locate, and control two electron-nuclear spin defects in the environment of a single nitrogen-vacancy center in diamond. By performing spectroscopy at various orientations of the magnetic field, we extract the unknown parameters of the hyperfine and dipolar interaction tensors, which we use to locate the two spin defects and design control sequences to initialize, manipulate, and readout their quantum state. Finally, we create quantum coherence among the three electron spins, paving the way for the creation of genuine tripartite entanglement. This approach will be useful in assembling multispin quantum registers for applications in quantum sensing and quantum information processing.

Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator.

Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.

Emergent Prethermalization Signatures in Out-of-Time Ordered Correlations.

How a many-body quantum system thermalizes-or fails to do so-under its own interaction is a fundamental yet elusive concept. Here we demonstrate nuclear magnetic resonance observation of the emergence of prethermalization by measuring out-of-time ordered correlations. We exploit Hamiltonian engineering techniques to tune the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal out-of-time ordered correlations. At large fields, we observe an emergent conserved quantity due to prethermalization, which can be revealed by an early saturation of correlations. Our experiment not only demonstrates a new protocol to measure out-of-time ordered correlations, but also provides new insights in the study of quantum thermodynamics.

All-Optical Quantum Sensing of Rotational Brownian Motion of Magnetic Molecules.

Sensing the local environment through the motional response of small molecules lays the foundation of many fundamental technologies. The information on local viscosity, for example, is contained in the random rotational Brownian motions of molecules. However, detection of the motions is challenging for molecules with sub-nanometer scale or high motional rates. Here we propose and experimentally demonstrate a novel method of detecting fast rotational Brownian motions of small magnetic molecules. With electronic spins as sensors, we are able to detect changes in motional rates, which yield different noise spectra and therefore different relaxation signals of the sensors. As a proof-of-principle demonstration, we experimentally implemented this method to detect the motions of gadolinium (Gd) complex molecules with nitrogen-vacancy (NV) centers in nanodiamonds. With all-optical measurements of the NV centers' longitudinal relaxation, we distinguished binary solutions with varying viscosities. Our method paves a new way for detecting fast motions of sub-nanometer sized magnetic molecules with better spatial resolution than conventional optical methods. It also provides a new tool in designing better contrast agents in magnetic resonance imaging.