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The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682-686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator.

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected logical qubit using a diamond quantum processor. We encode the logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements, and apply corrections by real-time feedback. The actively error-corrected qubit is robust against errors and encoded quantum superposition states are preserved beyond the natural dephasing time of the best physical qubit in the encoding. These results establish a powerful platform to investigate error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

Nuclear quadrupolar resonance (NQR) spectroscopy reveals chemical bonding patterns in materials and molecules through the unique coupling between nuclear spins and local fields. However, traditional NQR techniques require macroscopic ensembles of nuclei to yield a detectable signal, which obscures molecule-to-molecule variations. Solid-state spin qubits, such as the nitrogen-vacancy (NV) center in diamond, facilitate the detection and control of individual nuclei through their local magnetic couplings. Here, we use NV centers to perform NQR spectroscopy on their associated nitrogen-14 ( 14 N) nuclei at room temperature. In mapping the nuclear quadrupolar Hamiltonian, we resolve minute variations between individual nuclei. The measurements reveal correlations between the Hamiltonian parameters associated with the NV center's electronic and nuclear spin states, as well as a previously unreported symmetry-breaking quadrupolar term. We further design pulse sequences to initialize, read out, and control the quantum evolution of the 14 N nuclear state using the nuclear quadrupolar Hamiltonian.

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., (Creative Commons Attribution license.)

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., (© 2024. The Author(s).)

Solid-state spin qubits is a promising platform for quantum computation and quantum networks 1,2 . Recent experiments have demonstrated high-quality control over multi-qubit systems 3-8 , elementary quantum algorithms 8-11 and non-fault-tolerant error correction 12-14 . Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations 15-18 . Overcoming imperfections in this way remains an important outstanding challenge for quantum science 15,19-27 . Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits 28-30 . We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. Although future improvements in fidelity and the number of qubits will be required to suppress logical error rates below the physical error rates, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards quantum information processing based on solid-state spins., (© 2022. The Author(s).)

The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.

A promising approach for multi-qubit quantum registers is to use optically addressable spins to control multiple dark electron-spin defects in the environment. While recent experiments have observed signatures of coherent interactions with such dark spins, it is an open challenge to realize the individual control required for quantum information processing. Here, we demonstrate the heralded initialisation, control and entanglement of individual dark spins associated to multiple P1 centers, which are part of a spin bath surrounding a nitrogen-vacancy center in diamond. We realize projective measurements to prepare the multiple degrees of freedom of P1 centers-their Jahn-Teller axis, nuclear spin and charge state-and exploit these to selectively access multiple P1s in the bath. We develop control and single-shot readout of the nuclear and electron spin, and use this to demonstrate an entangled state of two P1 centers. These results provide a proof-of-principle towards using dark electron-nuclear spin defects as qubits for quantum sensing, computation and networks.

The neutral charge state plays an important role in quantum information and sensing applications based on nitrogen-vacancy centers. However, the orbital and spin dynamics remain unexplored. Here, we use resonant excitation of single centers to directly reveal the fine structure, enabling selective addressing of spin-orbit states. Through pump-probe experiments, we find the orbital relaxation time (430 ns at 4.7 K) and measure its temperature dependence up to 11.8 K. Finally, we reveal the spin relaxation time (1.5 s) and realize projective high-fidelity single-shot readout of the spin state (≥98%).

Efficiently detecting and characterizing individual spins in solid-state hosts is an essential step to expand the fields of quantum sensing and quantum information processing. While selective detection and control of a few 13 C nuclear spins in diamond have been demonstrated using the electron spin of nitrogen-vacancy (NV) centers, a reliable, efficient, and automatic characterization method is desired. Here, we develop an automated algorithmic method for decomposing spectral data to identify and characterize multiple nuclear spins in diamond. We demonstrate efficient nuclear spin identification and accurate reproduction of hyperfine interaction components for both virtual and experimental nuclear spectroscopy data. We conduct a systematic analysis of this methodology and discuss the range of hyperfine interaction components of each nuclear spin that the method can efficiently detect. The result demonstrates a systematic approach that automatically detects nuclear spins with the aid of computational methods, facilitating the future scalability of devices.

Nuclear magnetic resonance (NMR) is a powerful method for determining the structure of molecules and proteins 1 . Whereas conventional NMR requires averaging over large ensembles, recent progress with single-spin quantum sensors 2-9 has created the prospect of magnetic imaging of individual molecules 10-13 . As an initial step towards this goal, isolated nuclear spins and spin pairs have been mapped 14-21 . However, large clusters of interacting spins-such as those found in molecules-result in highly complex spectra. Imaging these complex systems is challenging because it requires high spectral resolution and efficient spatial reconstruction with sub-ångström precision. Here we realize such atomic-scale imaging using a single nitrogen vacancy centre as a quantum sensor, and demonstrate it on a model system of 27 coupled 13 C nuclear spins in diamond. We present a multidimensional spectroscopy method that isolates individual nuclear-nuclear spin interactions with high spectral resolution (less than 80 millihertz) and high accuracy (2 millihertz). We show that these interactions encode the composition and inter-connectivity of the cluster, and develop methods to extract the three-dimensional structure of the cluster with sub-ångström resolution. Our results demonstrate a key capability towards magnetic imaging of individual molecules and other complex spin systems 9-13 .

We report on the realization and application of nondestructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by a single-shot nondestructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the maximally mixed state. Furthermore, we implement a single-shot version of the Greenberger-Horne-Zeilinger experiment that can generate a quantum versus classical contradiction in each run. Finally, we test a state-independent noncontextuality inequality in eight dimensions. The techniques and insights developed are relevant for fundamental tests as well as for quantum information protocols such as quantum error correction.

Single electron spins coupled to multiple nuclear spins provide promising multi-qubit registers for quantum sensing and quantum networks. The obtainable level of control is determined by how well the electron spin can be selectively coupled to, and decoupled from, the surrounding nuclear spins. Here we realize a coherence time exceeding a second for a single nitrogen-vacancy electron spin through decoupling sequences tailored to its microscopic nuclear-spin environment. First, we use the electron spin to probe the environment, which is accurately described by seven individual and six pairs of coupled carbon-13 spins. We develop initialization, control and readout of the carbon-13 pairs in order to directly reveal their atomic structure. We then exploit this knowledge to store quantum states in the electron spin for over a second by carefully avoiding unwanted interactions. These results provide a proof-of-principle for quantum sensing of complex multi-spin systems and an opportunity for multi-qubit quantum registers with long coherence times.

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.

Single defect centers in diamond have emerged as a powerful platform for quantum optics experiments and quantum information processing tasks. Connecting spatially separated nodes via optical photons into a quantum network will enable distributed quantum computing and long-range quantum communication. Initial experiments on trapped atoms and ions as well as defects in diamond have demonstrated entanglement between two nodes over several meters. To realize multi-node networks, additional quantum bit systems that store quantum states while new entanglement links are established are highly desirable. Such memories allow for entanglement distillation, purification and quantum repeater protocols that extend the size, speed and distance of the network. However, to be effective, the memory must be robust against the entanglement generation protocol, which typically must be repeated many times. Here we evaluate the prospects of using carbon nuclear spins in diamond as quantum memories that are compatible with quantum networks based on single nitrogen vacancy (NV) defects in diamond. We present a theoretical framework to describe the dephasing of the nuclear spins under repeated generation of NV spin-photon entanglement and show that quantum states can be stored during hundreds of repetitions using typical experimental coupling parameters. This result demonstrates that nuclear spins with weak hyperfine couplings are promising quantum memories for quantum networks.

Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward, quantum teleportation is achieved upon each attempt with an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing., (Copyright © 2014, American Association for the Advancement of Science.)

Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing. Pioneering experiments selected defects with favourably located nuclear spins with particularly strong hyperfine couplings. To progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here, we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single- and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes.

Quantum entanglement between spatially separated objects is one of the most intriguing phenomena in physics. The outcomes of independent measurements on entangled objects show correlations that cannot be explained by classical physics. As well as being of fundamental interest, entanglement is a unique resource for quantum information processing and communication. Entangled quantum bits (qubits) can be used to share private information or implement quantum logical gates. Such capabilities are particularly useful when the entangled qubits are spatially separated, providing the opportunity to create highly connected quantum networks or extend quantum cryptography to long distances. Here we report entanglement of two electron spin qubits in diamond with a spatial separation of three metres. We establish this entanglement using a robust protocol based on creation of spin-photon entanglement at each location and a subsequent joint measurement of the photons. Detection of the photons heralds the projection of the spin qubits onto an entangled state. We verify the resulting non-local quantum correlations by performing single-shot readout on the qubits in different bases. The long-distance entanglement reported here can be combined with recently achieved initialization, readout and entanglement operations on local long-lived nuclear spin registers, paving the way for deterministic long-distance teleportation, quantum repeaters and extended quantum networks.

Multipolar transitions other than electric dipoles are generally too weak to be observed at optical frequencies in single quantum emitters. For example, fluorescent molecules and quantum dots have dimensions much smaller than the wavelength of light and therefore emit predominantly as electric dipoles. Here we demonstrate controlled emission of a quantum dot into multipolar radiation through selective coupling to a linear nanowire antenna. The antenna resonance tailors the interaction of the quantum dot with light, effectively creating a hybrid nanoscale source beyond the simple Hertz dipole. Our findings establish a basis for the controlled driving of fundamental modes in nanoantennas and metamaterials, for the understanding of the coupling of quantum emitters to nanophotonic devices such as waveguides and nanolasers, and for the development of innovative quantum nano-optics components with properties not found in nature.

We experimentally isolate, characterize, and coherently control up to six individual nuclear spins that are weakly coupled to an electron spin in diamond. Our method employs multipulse sequences on the electron spin that resonantly amplify the interaction with a selected nuclear spin and at the same time dynamically suppress decoherence caused by the rest of the spin bath. We are able to address nuclear spins with interaction strengths that are an order of magnitude smaller than the electron spin dephasing rate. Our results provide a route towards tomography with single-nuclear-spin sensitivity and greatly extend the number of available quantum bits for quantum information processing in diamond.

Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle quantum bit (qubit) can be efficiently insulated from the outside world by dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protecting qubit coherence during a multi-qubit gate is a non-trivial problem: in general, the decoupling disrupts the interqubit dynamics and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, in which different types of qubit evolve and decohere at very different rates. Here we present the integration of dynamical decoupling into quantum gates for a standard hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates using a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We also perform Grover's quantum search algorithm, and achieve fidelities of more than 90% even though the algorithm run-time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly allow decoherence-protected interface gates between different types of solid-state qubit. Ultimately, quantum gates with integrated decoupling may reach the accuracy threshold for fault-tolerant quantum information processing with solid-state devices.

Tremendous advances in the study of magnetic light-matter interactions have recently been achieved using man-made nanostructures that exhibit and exploit an optical magnetic response. However, naturally occurring emitters can also exhibit magnetic resonances in the form of optical-frequency magnetic-dipole transitions. Here we quantify the magnetic nature of light emission using energy- and momentum-resolved spectroscopy, and leverage a pair of spectrally close electric- and magnetic-dipole transitions in trivalent europium to probe vacuum fluctuations in the electric and magnetic fields at the nanometre scale. These results reveal a new tool for nano-optics: an atomic-size quantum emitter that interacts with the magnetic component of light.

Optical antennas link objects to light. Here we derive an analytical model for the interaction of dipolar transitions with radiation through nanorod antenna modes, by modeling nanorods as cavities. The model includes radiation damping, accurately describes the complete emission process, and is summarized in a phase-matching equation. We analytically discuss the quantitative evolution of antenna modes, in particular the gradual emergence of subradiant, super-radiant, and dark modes, as antennas become increasingly more bound, i.e., plasmonic. Our description is valid for the interaction of nanorods with light in general and is thus widely applicable.

Nanoscale quantum emitters are key elements in quantum optics and sensing. However, efficient optical excitation and detection of such emitters involves large solid angles because their interaction with freely propagating light is omnidirectional. Here, we present unidirectional emission of a single emitter by coupling to a nanofabricated Yagi-Uda antenna. A quantum dot is placed in the near field of the antenna so that it drives the resonant feed element of the antenna. The resulting quantum-dot luminescence is strongly polarized and highly directed into a narrow forward angular cone. The directionality of the quantum dot can be controlled by tuning the antenna dimensions. Our results show the potential of optical antennas to communicate energy to, from, and between nano-emitters.

The active steering of the pathways taken by chemical reactions and the optimization of energy conversion processes provide striking examples of the coherent control of quantum interference through the use of shaped laser pulses. Experimentally, coherence is usually established by synchronizing a subset of molecules in an ensemble with ultra-short laser pulses. But in complex systems where even chemically identical molecules exist with different conformations and in diverse environments, the synchronized subset will have an intrinsic inhomogeneity that limits the degree of coherent control that can be achieved. A natural-and, indeed, the ultimate-solution to overcoming intrinsic inhomogeneities is the investigation of the behaviour of one molecule at a time. The single-molecule approach has provided useful insights into phenomena as diverse as biomolecular interactions, cellular processes and the dynamics of supercooled liquids and conjugated polymers. Coherent state preparation of single molecules has so far been restricted to cryogenic conditions, whereas at room temperature only incoherent vibrational relaxation pathways have been probed. Here we report the observation and manipulation of vibrational wave-packet interference in individual molecules at ambient conditions. We show that adapting the time and phase distribution of the optical excitation field to the dynamics of each molecule results in a high degree of control, and expect that the approach can be extended to achieve single-molecule coherent control in other complex inhomogeneous systems.

We present spatially resolved spectral mode mapping of resonant plasmon gap antennas using two-photon luminescence microspectroscopy. The obtained maps are in good agreement with 3D calculations of the antenna modes. The evolution of the modal field with wavelength, both in the gap and along the two coupled gold nanowires forming the antenna, is directly visualized. At resonance, the luminescence for the gap area is enhanced at least 80 times and a comparison with the antenna extremities shows a dynamical charge redistribution due to the near-field coupling between the two arms.

We demonstrate by 3D numerical calculations that the interaction of a single quantum emitter with the electromagnetic field is both enhanced and directed by a nano-optical Yagi-Uda antenna. The single emitter is coupled in the near field to the resonant plasmon mode of the feed element, enhancing both excitation and emission rates. The angular emission of the coupled system is highly directed and determined by the antenna mode. Arbitrary control over the main direction of emission is obtained, regardless of the orientation of the emitter. The directivity is even more increased by the presence of a dielectric substrate, making such antennas a promising candidate for compact easy-to-address planar sensors.

We present reversible and a-priori control of the polarization of a photon emitted by a single molecule by introducing a nanoscale metal object in its near field. It is experimentally shown that, with the metal close to the emitter, the polarization ratio of the emission can be varied by a factor of 2. The tunability of polarization decays, when the metal is displaced by typically 30 nm. Calculations based on the multiple multipole method agree well with our experiments and predict even further enhancement with a suitable nanoantenna design.

We present a resonant optical nanoantenna positioned at the end of a metal-coated glass fiber near-field probe. Antenna resonances, excitation conditions, and field localization are directly probed in the near field by single fluorescent molecules and compared to finite integration technique simulations. It is shown that the antenna is equivalent to its radio frequency analogue, the monopole antenna. For the right antenna length and local excitation conditions, antenna resonances occur that lead to an enhanced localized field near the antenna apex. Direct mapping of this field with single fluorescent molecules reveals a spatial localization of 25 nm, demonstrating the importance of such antennas for nanometer resolution optical microscopy.