Selective Detection of Dynamics-Complete Set of Correlations via Quantum Channels.

Correlations of fluctuations are essential to understanding many-body systems and key information for advancing quantum technologies. To fully describe the dynamics of a physical system, all time-ordered correlations (TOCs), i.e., the dynamics-complete set of correlations are needed. The current measurement techniques can only access a limited set of TOCs, and there has been no systematic and feasible solution for extracting the dynamic-complete set of correlations hitherto. Here we propose a platform-universal protocol to selectively detect arbitrary types of TOCs via quantum channels. In our method, the quantum channels are synthesized with various controls, and engineer the evolution of a sensor-target system along a specific path that corresponds to a desired correlation. Using nuclear magnetic resonance, we experimentally demonstrate this protocol by detecting a specific type of fourth-order TOC that has never been accessed previously. We also show that the knowledge of the TOCs can be used to significantly improve the precision of quantum optimal control. Our method provides a new toolbox for characterizing the quantum many-body states and quantum noise, and hence for advancing the fields of quantum sensing and quantum computing.

Detection of Quantum Signals Free of Classical Noise via Quantum Correlation.

Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application, especially in quantum sensing. Here, we propose a signal-nature-based (not signal-pattern-based) approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. We design a novel protocol to extract the quantum correlation signal and use it to single out the signal of a remote nuclear spin from its overwhelming classical noise backgrounds, which is impossible to be accomplished by conventional filter methods. Our Letter demonstrates the quantum or classical nature as a new degree of freedom in quantum sensing. The further generalization of this quantum nature-based method opens a new direction in quantum research.

Nanothermometry with Enhanced Sensitivity and Enlarged Working Range Using Diamond Sensors.

Nanothermometry is increasingly demanded in frontier research in physics, chemistry, materials science and engineering, and biomedicine. An ideal thermometer should have features of reliable temperature interpretation, high sensitivity, fast response, minimum disturbance of the target's temperature, applicability in a variety of environments, and a large working temperature range. For applications in nanosystems, high spatial resolution is also desirable. Such requirements impose great challenges in nanothermometry since the shrinking of the sensor volume usually leads to a reduction in sensitivity.Diamond with nitrogen-vacancy (NV) centers provides opportunities for nanothermometry. NV center spins have sharp resonances due to their superb coherence. NV centers are multimodal sensors. They can directly sense magnetic fields, electric fields, temperature, pressure, and nuclear spins and, through proper transduction, measure other quantities such as the pH and deformation. In particular, their spin resonance frequencies vary with temperature, making them a promising thermometer. The high thermal conductivity, high hardness, chemical stability, and biocompatibility of diamond enable reliable and fast temperature sensing in complex environments ranging from erosive liquids to live systems. Chemical processing of diamond surfaces allows various functionalities such as targeting. The small size and the targeting capability of nanodiamonds then enable site-specific temperature sensing with nanoscale spatial resolution. However, the sensitivity of NV-based nanothermometry is yet to meet the requirement of practical systems with a large gap of a few orders of magnitude. On the other hand, although NV-based quantum sensing works well from 0.3 to 600 K, extending the sensing scheme to high temperature remains challenging due to uncertainty in identifying the exact physical limits and possible solution at elevated temperatures.This Account focuses on our efforts to enhance the temperature sensitivity and widen the working temperature range of diamond-based nanothermometry. We start with explaining the working principle and features of NV-based thermometry with examples of applications. Then a transducer-based concept is introduced with practical schemes to improve the sensitivity of the nanodiamond thermometer. Specifically, we show that the temperature signal can be transduced and amplified by adopting hybrid structures of nanodiamond and magnetic nanoparticles, which results in a record temperature sensitivity of 76 µK/√Hz. We also demonstrate quantum sensing with NV at high temperatures of up to 1000 K by adopting a pulsed heating-cooling scheme to carry out the spin polarization and readout at room temperature and the spin manipulation (sensing) at high temperatures. Finally, unsolved problems and future endeavors of diamond nanothermometry are discussed.

Quantum nonlinear spectroscopy of single nuclear spins.

Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.

Near-Surface

Impurity spins in crystal matrices are promising components in quantum technologies, particularly if they can maintain their spin properties when close to surfaces and material interfaces. Here, we investigate an attractive candidate for microwave-domain applications, the spins of group-VI ^{125}Te^{+} donors implanted into natural Si at depths as shallow as 20 nm. We show that surface band bending can be used to ionize such near-surface Te to spin-active Te^{+} state, and that optical illumination can be used further to control the Te donor charge state. We examine spin activation yield, spin linewidth, and relaxation (T_{1}) and coherence times (T_{2}) and show how a zero-field 3.5 GHz "clock transition" extends spin coherence times to over 1 ms, which is about an order of magnitude longer than other near-surface spin systems.

Revealing Capillarity in AFM Indentation of Cells by Nanodiamond-Based Nonlocal Deformation Sensing.

Nanoindentation based on atomic force microscopy (AFM) can measure the elasticity of biomaterials and cells with high spatial resolution and sensitivity, but relating the data to quantitative mechanical properties depends on information on the local contact, which is unclear in most cases. Here, we demonstrate nonlocal deformation sensing on biorelevant soft matters upon AFM indentation by using nitrogen-vacancy centers in nanodiamonds, providing data for studying both the elasticity and capillarity without requiring detailed knowledge about the local contact. Using fixed HeLa cells for demonstration, we show that the apparent elastic moduli of the cells would have been overestimated if the capillarity was not considered. In addition, we observe that both the elastic moduli and the surface tensions are reduced after depolymerization of the actin cytoskeleton in cells. This work demonstrates that the nanodiamond sensing of nonlocal deformation with nanometer precision is particularly suitable for studying mechanics of soft biorelevant materials.

Ultra-sensitive hybrid diamond nanothermometer.

Nitrogen-vacancy (NV) centers in diamond are promising quantum sensors because of their long spin coherence time under ambient conditions. However, their spin resonances are relatively insensitive to non-magnetic parameters such as temperature. A magnetic-nanoparticle-nanodiamond hybrid thermometer, where the temperature change is converted to the magnetic field variation near the Curie temperature, were demonstrated to have enhanced temperature sensitivity ([Formula: see text]) (Wang N, Liu G-Q and Leong W-H et al. Phys Rev X 2018; 8: 011042), but the sensitivity was limited by the large spectral broadening of ensemble spins in nanodiamonds. To overcome this limitation, here we show an improved design of a hybrid nanothermometer using a single NV center in a diamond nanopillar coupled with a single magnetic nanoparticle of copper-nickel alloy, and demonstrate a temperature sensitivity of [Formula: see text]. This hybrid design enables detection of 2 mK temperature changes with temporal resolution of 5 ms. The ultra-sensitive nanothermometer offers a new tool to investigate thermal processes in nanoscale systems.

Association of Nanodiamond Rotation Dynamics with Cell Activities by Translation-Rotation Tracking.

Correlated translation-orientation tracking of single particles can provide important information for understanding the dynamics of live systems and their interaction with the probes. However, full six-dimensional (6D) motion tracking has yet to be achieved. Here, we developed synchronized 3D translation and 3D rotation tracking of single diamond particles based on nitrogen-vacancy center sensing. We first performed 6D tracking of diamond particles attached to a giant plasma membrane vesicle to demonstrate the method. Quantitative analysis of diamond particles' motion allowed elimination of the geometric effect and revealed the net rotation on the vesicle. 6D tracking was then applied to measure live cell dynamics. Motion characteristics of nanodiamonds on cell membranes under various controlled physiological conditions suggest that the nanodiamonds' rotation is associated with cell metabolic activities. Our technique extends the toolbox of single particle tracking and provides a unique solution to problems where correlated analysis of translation and rotation is critical.

Characterization of Arbitrary-Order Correlations in Quantum Baths by Weak Measurement.

Correlations of fluctuations are the driving forces behind the dynamics and thermodynamics in quantum many-body systems. For qubits embedded in a quantum bath, the correlations in the bath are key to understanding and combating decoherence-a critical issue in quantum information technology. However, there is no systematic method for characterizing the many-body correlations in quantum baths beyond the second order or the Gaussian approximation. Here we present a scheme to characterize the correlations in a quantum bath to arbitrary order. The scheme employs a weak measurement of the bath via the projective measurement of a central system. The bath correlations, including both the "classical" and the "quantum" parts, can be reconstructed from the correlations of the measurement outputs. The possibility of full characterization of many-body correlations in a quantum bath forms the basis for optimizing quantum control against decoherence in realistic environments, for studying the quantum characteristics of baths, and for the quantum sensing of correlated clusters in quantum baths.

Nanometer-precision non-local deformation reconstruction using nanodiamond sensing.

Spatially resolved information about material deformation upon loading is critical to evaluating mechanical properties of materials, and to understanding mechano-response of live systems. Existing techniques may access local properties of materials at nanoscale, but not at locations away from the force-loading positions. Moreover, interpretation of the local measurement relies on correct modeling, the validation of which is not straightforward. Here we demonstrate an approach to evaluating non-local material deformation based on the integration of nanodiamond orientation sensing and atomic force microscopy nanoindentation. This approach features a 5 nm precision in the loading direction and a sub-hundred nanometer lateral resolution, high enough to disclose the surface/interface effects in the material deformation. The non-local deformation profile can validate the models needed for mechanical property determination. The non-local nanometer-precision sensing of deformation facilitates studying mechanical response of complex material systems ranging from impact transfer in nanocomposites to mechano-response of live systems.

Coherent quantum control of nitrogen-vacancy center spins near 1000 kelvin.

Quantum coherence control usually requires low temperature environments. Even for nitrogen-vacancy center spins in diamond, a remarkable exception, the coherence signal is limited to about 700 K due to the quench of the spin-dependent fluorescence at a higher temperature. Here we overcome this limit and demonstrate quantum coherence control of the electron spins of nitrogen-vacancy centers in nanodiamonds at temperatures near 1000 K. The scheme is based on initialization and readout of the spins at room temperature and control at high temperature, which is enabled by pulse laser heating and rapid diffusion cooling of nanodiamonds on amorphous carbon films. Using the diamond magnetometry based on optically detected magnetic resonance up to 800 K, we observe the magnetic phase transition of a single nickel nanoparticle at about 615 K. This work enables nano-thermometry and nano-magnetometry in the high-temperature regime.

High-resolution spectroscopy of single nuclear spins via sequential weak measurements.

Nuclear magnetic resonance (NMR) of single spins have recently been detected by quantum sensors. However, the spectral resolution has been limited by the sensor's relaxation to a few kHz at room temperature. This can be improved by using quantum memories, at the expense of sensitivity. In contrast, classical signals can be measured with exceptional spectral resolution by using continuous measurement techniques, without compromising sensitivity. When applied to single-spin NMR, it is critical to overcome the impact of back action inherent of quantum measurement. Here we report sequential weak measurements on a single 13C nuclear spin. The back-action causes the spin to undergo a quantum dynamics phase transition from coherent trapping to coherent oscillation. Single-spin NMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. These results enable the use of measurement-correlation schemes for the detection of very weakly coupled single spins.

Hybrid nanodiamond quantum sensors enabled by volume phase transitions of hydrogels.

Diamond nitrogen-vacancy (NV) center-based magnetometry provides a unique opportunity for quantum bio-sensing. However, NV centers are not sensitive to parameters such as temperature and pressure, and immune to many biochemical parameters such as pH and non-magnetic biomolecules. Here, we propose a scheme that can potentially enable the measurement of various biochemical parameters using diamond quantum sensing, by employing stimulus-responsive hydrogels as a spacing transducer in-between a nanodiamond (ND, with NV centers) and magnetic nanoparticles (MNPs). The volume phase transition of hydrogel upon stimulation leads to sharp variation in the separation distance between the MNPs and the ND. This in turn changes the magnetic field that the NV centers can detect sensitively. We construct a temperature sensor under this hybrid scheme and show the proof-of-the-principle demonstration of reversible temperature sensing. Applications in the detection of other bio-relevant parameters are envisioned if appropriate types of hydrogels can be engineered.

2 + 1 dimensional de Sitter universe emerging from the gauge structure of a nonlinear quantum system.

Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical surfaces in the parameter space. We find that these critical surfaces result in a new type of gauge field singularity, namely, a conic singularity that resembles the big bang of a 2 + 1 dimensional de Sitter universe, with the fundamental frequency of Bogoliubov excitations acting as the cosmic scale, and mode softening at the critical surface, where the fundamental frequency vanishes, causing a causal singularity. Such conic singularity may be observed in various systems such as Bose-Einstein condensates and molecular magnets. This finding offers a new approach to quantum simulation of fundamental physics.

Anchored but not internalized: shape dependent endocytosis of nanodiamond.

Nanoparticle-cell interactions begin with the cellular uptake of the nanoparticles, a process that eventually determines their cellular fate. In the present work, we show that the morphological features of nanodiamonds (NDs) affect both the anchoring and internalization stages of their endocytosis. While a prickly ND (with sharp edges/corners) has no trouble of anchoring onto the plasma membrane, it suffers from difficult internalization afterwards. In comparison, the internalization of a round ND (obtained by selective etching of the prickly ND) is not limited by its lower anchoring amount and presents a much higher endocytosis amount. Molecular dynamics simulation and continuum modelling results suggest that the observed difference in the anchoring of round and prickly NDs likely results from the reduced contact surface area with the cell membrane of the former, while the energy penalty associated with membrane curvature generation, which is lower for a round ND, may explain its higher probability of the subsequent internalization.

Single-Shot Readout of a Nuclear Spin Weakly Coupled to a Nitrogen-Vacancy Center at Room Temperature.

Single-shot readout of qubits is required for scalable quantum computing. Nuclear spins are superb quantum memories due to their long coherence time, but are difficult to be read out in a single shot due to their weak interaction with probes. Here we demonstrate single-shot readout of a weakly coupled ^{13}C nuclear spin at room temperature, which is unresolvable in traditional protocols. States of the weakly coupled nuclear spin are trapped and read out projectively by sequential weak measurements, which are implemented by dynamical decoupling pulses. A nuclear spin coupled to the nitrogen-vacancy (NV) center with strength 330 kHz is read out in 200 ms with a fidelity of 95.5%. This work provides a general protocol for single-shot readout of weakly coupled qubits at room temperature and therefore largely extends the range of physical systems for scalable quantum computing.

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths.

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.