Immunomagnetic microscopy of tumor tissues using quantum sensors in diamond.

Histological imaging is essential for the biomedical research and clinical diagnosis of human cancer. Although optical microscopy provides a standard method, it is a persistent goal to develop new imaging methods for more precise histological examination. Here, we use nitrogen-vacancy centers in diamond as quantum sensors and demonstrate micrometer-resolution immunomagnetic microscopy (IMM) for human tumor tissues. We immunomagnetically labeled cancer biomarkers in tumor tissues with magnetic nanoparticles and imaged them in a 400-nm resolution diamond-based magnetic microscope. There is barely magnetic background in tissues, and the IMM can resist the impact of a light background. The distribution of biomarkers in the high-contrast magnetic images was reconstructed as that of the magnetic moment of magnetic nanoparticles by employing deep-learning algorithms. In the reconstructed magnetic images, the expression intensity of the biomarkers was quantified with the absolute magnetic signal. The IMM has excellent signal stability, and the magnetic signal in our samples had not changed after more than 1.5 y under ambient conditions. Furthermore, we realized multimodal imaging of tumor tissues by combining IMM with hematoxylin-eosin staining, immunohistochemistry, or immunofluorescence microscopy in the same tissue section. Overall, our study provides a different histological method for both molecular mechanism research and accurate diagnosis of human cancer.

Imaging the Magnetic Anisotropy in Ultrathin Fe4GeTe2 with a Nitrogen-Vacancy Magnetometer.

Two-dimensional (2D) FenGeTe2, with n = 3, 4, and 5, has been realized in experiments, showing strong magnetic anisotropy with enhanced critical temperature (Tc). The understanding of its magnetic anisotropy is crucial for the exploration of more stable 2D magnets and its spintronic applications. Here, we report a quantitative reconstruction of the magnetization magnitude and its direction in ultrathin Fe4GeTe2 using nitrogen vacancy centers. Through imaging stray magnetic fields, we identified the spin-flop transition at approximately 80 K, resulting in a change of the easy axis from the out-of-plane direction to the in-plane direction. Moreover, by analyzing the thermally activated escape behavior of the magnetization near Tc in terms of the Ginzburg-Landau model, we observed the in-plane magnetic anisotropy effect and the formation capability of magnetic domains at ∼0.4 µm2 µT-1. Our findings contribute to the quantitative understanding of the magnetic anisotropy effect in a vast range of 2D van der Waals magnets.

Single-Shot Readout of a Solid-State Electron Spin Qutrit.

Quantum systems usually feature a rich multilevel structure with promising resources for developing superior quantum technologies compared with their binary counterpart. Single-shot readout of these high-dimensional quantum systems is essential for exploiting their potential. Although there have been various high-spin systems, the single-shot readout of the overall state of high-spin systems remains a challenging issue. Here we demonstrate a reliable single-shot readout of spin qutrit state in a low-temperature solid-state system utilizing a binary readout scheme. We achieve a single-shot readout of an electron spin qutrit associated with a single nitrogen-vacancy center in diamond with an average fidelity of 87.80%. We use this spin qutrit system to verify quantum contextuality, a fundamental test of quantum mechanics. We observe a violation of the noncontextual hidden variable inequality with the developed single-shot readout in contrast to the conventional binary readout. These results pave the way for developing quantum information processing based on spin qutrits.

Digital Magnetic Detection of Biomolecular Interactions with Single Nanoparticles.

Biomolecular interactions compose a fundamental element of all life forms and are the biological basis of many biomedical assays. However, current methods for detecting biomolecular interactions have limitations in sensitivity and specificity. Here, using nitrogen-vacancy centers in diamond as quantum sensors, we demonstrate digital magnetic detection of biomolecular interactions with single magnetic nanoparticles (MNPs). We first developed a single-particle magnetic imaging (SiPMI) method on 100 nm-sized MNPs with negligible magnetic background, high signal stability, and accurate quantification. The single-particle method was performed on biotin-streptavidin interactions and DNA-DNA interactions in which a single-base mismatch was specifically differentiated. Subsequently, SARS-CoV-2-related antibodies and nucleic acids were examined by a digital immunomagnetic assay derived from SiPMI. In addition, a magnetic separation process improved the detection sensitivity and dynamic range by more than 3 orders of magnitude and also the specificity. This digital magnetic platform is applicable to extensive biomolecular interaction studies and ultrasensitive biomedical assays.

99.92%-Fidelity cnot Gates in Solids by Noise Filtering.

Inevitable interactions with the reservoir largely degrade the performance of entangling gates, which hinders practical quantum computation from coming into existence. Here, we experimentally demonstrate a 99.920(7)%-fidelity controlled-not gate by suppressing the complicated noise in a solid-state spin system at room temperature. We found that the fidelity limited at 99% in previous works results from considering only static classical noise, and, thus, in this work, a complete noise model is constructed by also considering the time dependence and the quantum nature of the spin bath. All noises in the model are dynamically corrected by an exquisitely designed shaped pulse, giving the resulting error below 10^{-4}. The residual gate error is mainly originated from the longitudinal relaxation and the waveform distortion that can both be further reduced technically. Our noise-resistant method is universal and will benefit other solid-state spin systems.

Excited-State Spectroscopy of Spin Defects in Hexagonal Boron Nitride.

A negatively charged boron vacancy (VB-) color center in hexagonal boron nitride has recently been proposed as a promising quantum sensor due to its excellent properties. However, the spin level structure of the VB- color center is still unclear, especially for the excited state. Here we measured and confirmed the excited-state spin transitions of VB- using an optically detected magnetic resonance (ODMR) technique. The zero-field splitting of the excited state is 2.06 GHz, the transverse splitting is 93.1 MHz, and the g factor is 2.04. Moreover, negative peaks in fluorescence intensity and ODMR contrast at the level anticrossing point were observed, and they further confirmed that the spin transitions we measured came from the excited state. Our work deepens the understanding of the excited-state structure of VB- and promotes VB--based quantum sensing applications.

Biocompatible Nanotomography of Tightly Focused Light.

Tightly focusing a spatially modulated laser beam lays the foundations for advanced optical techniques, such as a holographic optical tweezer and deterministic super-resolution imaging. Precisely mapping the subwavelength features of those highly confined fields is critical to improving the spatial resolution, especially in highly scattering biotissues. However, current techniques characterizing focal fields are mostly limited to conditions such as under a vacuum and on a glass surface. An optical probe with low cytotoxicity and resistance to autofluorescence is the key to achieving in vivo applications. Here, we use a newly emerging quantum reference beacon, the nitrogen-vacancy (NV) center in the nanodiamond, to characterize the focal field of the near-infrared (NIR) laser focus in Caenorhabditis elegans (C. elegans). This biocompatible background-free focal field mapping technique has the potential to optimize in vivo optical imaging and manipulation.

Spin Quantum Heat Engine Quantified by Quantum Steering.

Following the rising interest in quantum information science, the extension of a heat engine to the quantum regime by exploring microscopic quantum systems has seen a boon of interest in the last decade. Although quantum coherence in the quantum system of the working medium has been investigated to play a nontrivial role, a complete understanding of the intrinsic quantum advantage of quantum heat engines remains elusive. We experimentally demonstrate that the quantum correlation between the working medium and the thermal bath is critical for the quantum advantage of a quantum Szilárd engine, where quantum coherence in the working medium is naturally excluded. By quantifying the nonclassical correlation through quantum steering, we reveal that the heat engine is quantum when the demon can truly steer the working medium. The average work obtained by taking different ways of work extraction on the working medium can be used to verify the real quantum Szilárd engine.

Publisher Correction: Single-DNA electron spin resonance spectroscopy in aqueous solutions.

In the version of this paper originally published online, the ORCID ID for Peter Z. Qin was incorrectly assigned to Zhuoyang Qin. In addition, the ORCID for Fazhan Shi was omitted. These errors have been corrected in the print, PDF, and HTML versions of the paper.

Single-DNA electron spin resonance spectroscopy in aqueous solutions.

Magnetic resonance spectroscopy of single biomolecules under near-physiological conditions could substantially advance understanding of their biological function, but this approach remains very challenging. Here we used nitrogen-vacancy centers in diamonds to detect electron spin resonance spectra of individual, tethered DNA duplexes labeled with a nitroxide spin label in aqueous buffer solutions at ambient temperatures. This work paves the way for magnetic resonance studies on single biomolecules and their intermolecular interactions in native-like environments.

Identity Test of Single NV

Atomiclike defects in solids are not considered to be identical owing to the imperfections of host lattice. Here, we found that even under ambient conditions, negatively charged nitrogen-vacancy (NV^{-}) centers in diamond could still manifest identical at Hz-precision level, corresponding to a 10^{-7}-level relative precision, while the lattice strain can destroy the identity by tens of Hz. All parameters involved in the NV^{-}-^{14}N Hamiltonian are determined by formulating six nuclear frequencies at 10-mHz-level precision and measuring them at Hz-level precision. The most precisely measured parameter, the ^{14}N quadrupole coupling P, is given by -494 575 4.9(8) Hz, whose precision is improved by nearly 4 orders of magnitude compared with previous measurements. We offer an approach for performing precision measurements in solids and deepening our understandings of NV centers as well as other solid-state defects. Besides, these high-precision results imply a potential application of a robust and integrated atomiclike clock based on ensemble NV centers.

Nanoscale Electrometry Based on a Magnetic-Field-Resistant Spin Sensor.

The nitrogen-vacancy (NV) center is a potential atomic-scale spin sensor for electric field sensing. However, its natural susceptibility to the magnetic field hinders effective detection of the electric field. Here we propose a robust electrometric method utilizing continuous dynamic decoupling (CDD) technique. During the CDD period, the NV center evolves in a dressed frame, where the sensor is resistant to magnetic fields but remains sensitive to electric fields. As an example, we use this method to isolate the electric noise from a complex electromagnetic environment near diamond surface via measuring the dephasing rate between dressed states. By reducing the surface electric noise with different covered liquids, we observe an unambiguous relation between the dephasing rate and the relative dielectric permittivity of the liquid, which enables a quantitative investigation of electric noise model near the diamond surface.

Quantum Simulation for Three-Dimensional Chiral Topological Insulator.

Quantum simulation, as a state-of-the-art technique, provides a powerful way to explore topological quantum phases beyond natural limits. Nevertheless, it is usually hard to simulate both the bulk and surface topological physics at the same time to reveal their correspondence. Here we build up a quantum simulator using nitrogen-vacancy center to investigate a three-dimensional (3D) chiral topological insulator, and demonstrate the study of both the bulk and surface topological physics by quantum quenches. First, a dynamical bulk-surface correspondence in momentum space is observed, showing that the bulk topology of the 3D phase uniquely corresponds to the nontrivial quench dynamics emerging on 2D momentum hypersurfaces called band inversion surfaces (BISs). This is the momentum-space counterpart of the bulk-boundary correspondence in real space. Further, the symmetry protection of the 3D chiral phase is uncovered by measuring dynamical spin textures on BISs, which exhibit perfect (broken) topology when the chiral symmetry is preserved (broken). Finally, we measure the topological charges to characterize directly the bulk topology and identify an emergent dynamical topological transition when varying the quenches from deep to shallow regimes. This work demonstrates how a full study of topological phases can be achieved in quantum simulators.

Constraints on a Spin-Dependent Exotic Interaction between Electrons with Single Electron Spin Quantum Sensors.

A new laboratory bound on the axial-vector mediated interaction between electron spins at micrometer scale is established with single nitrogen-vacancy (NV) centers in diamond. A single crystal of p-terphenyl doped pentacene-d_{14} under laser pumping provides the source of polarized electron spins. Based on the measurement of polarization signal via nitrogen-vacancy centers, we set a constraint for the exotic electron-electron coupling g_{A}^{e}g_{A}^{e}, within the force range from 10 to 900 µm. The obtained upper bound of the coupling at 500 µm is |g_{A}^{e}g_{A}^{e}/4πℏc|≤1.8×10^{-19}, which is one order of magnitude more stringent than a previous experiment. Our result shows that the NV center can be a promising platform for searching for new particles predicted by theories beyond the standard model.

Experimental Observation of a Generalized Thouless Pump with a Single Spin.

Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.

Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum.

The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of measurement outcomes for a pair of noncommuting observables. In this work, we study the preparation uncertainty for the angular momentum, especially for spin-1/2. We derive uncertainty relations encompassing the triple components of angular momentum and show that, compared with the relations involving only two components, a triple constant 2/sqrt[3] often arises. Intriguingly, this constant is the same for the position and momentum case. Experimental verification is carried out on a single spin in diamond, and the results confirm the triple constant in a wide range of experimental parameters.

Experimental Adiabatic Quantum Factorization under Ambient Conditions Based on a Solid-State Single Spin System.

The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian S_{z}I_{z} on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.

Experimental Time-Optimal Universal Control of Spin Qubits in Solids.

Quantum control of systems plays an important role in modern science and technology. The ultimate goal of quantum control is to achieve high-fidelity universal control in a time-optimal way. Although high-fidelity universal control has been reported in various quantum systems, experimental implementation of time-optimal universal control remains elusive. Here, we report the experimental realization of time-optimal universal control of spin qubits in diamond. By generalizing a recent method for solving quantum brachistochrone equations [X. Wang et al., Phys. Rev. Lett. 114, 170501 (2015)], we obtained accurate minimum-time protocols for multiple qubits with fixed qubit interactions and a constrained control field. Single- and two-qubit time-optimal gates are experimentally implemented with fidelities of 99% obtained via quantum process tomography. Our work provides a time-optimal route to achieve accurate quantum control and unlocks new capabilities for the emerging field of time-optimal control in general quantum systems.

Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances.

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.

Direct Measurement of Topological Numbers with Spins in Diamond.

Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.