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Refrigeration limits are of fundamental and practical importance. We here show that quantum systems can be cooled below existing incoherent cooling bounds by employing coherent virtual qubits, even if the amount of coherence is incompletely known. Virtual subsystems, that do not necessarily correspond to a natural eigensubspace of a system, are a key conceptual tool in quantum information science and quantum thermodynamics. We derive universal coherent cooling limits and introduce specific protocols to reach them. As an illustration, we propose a generalized algorithmic cooling protocol that outperforms its current incoherent counterpart. Our results provide a general framework to investigate the performance of coherent refrigeration processes., Comment: 6+8 pages, 3+6 figures

Nanoelectrical and photonic integration of quantum optical components is crucial for scalable solid-state quantum technologies. Silicon carbide stands out as a material with mature quantum defects and a wide variety of applications in semiconductor industry. Here, we study the behaviour of single silicon vacancy (V2) colour centres in a metal-semiconductor (Au/Ti/4H-SiC) epitaxial wafer device, operating in a Schottky diode configuration. We explore the depletion of free carriers in the vicinity of the defect, as well as electrical tuning of the defect optical transition lines. By detecting single charge traps, we investigate their impact on V2 optical line width. Additionally, we investigate the charge-photon-dynamics of the V2 centre and find its dominating photon-ionisation processes characteristic rate and wavelength dependence. Finally, we probe the spin coherence properties of the V2 system in the junction and demonstrate several key protocols for quantum network applications. Our work shows the first demonstration of low temperature integration of a Schottky device with optical microstructures for quantum applications and paves the way towards fundamentally scalable and reproducible optical spin defect centres in solids.

Solid-state spin systems hold great promise for quantum information processing and the construction of quantum networks. However, the considerable inhomogeneity of spins in solids poses a significant challenge to the scaling of solid-state quantum systems. A practical protocol to individually control and entangle spins remains elusive. To this end, we propose a hybrid spin-phonon architecture based on spin-embedded SiC optomechanical crystal (OMC) cavities, which integrates photonic and phononic channels allowing for interactions between multiple spins. With a Raman-facilitated process, the OMC cavities support coupling between the spin and the zero-point motion of the OMC cavity mode reaching 0.57 MHz, facilitating phonon preparation and spin Rabi swap processes. Based on this, we develop a spin-phonon interface that achieves a two-qubit controlled-Z gate with a simulated fidelity of $96.80\%$ and efficiently generates highly entangled Dicke states with over $99\%$ fidelity, by engineering the strongly coupled spin-phonon dark state which is robust against loss from excited state relaxation as well as spectral inhomogeneity of the defect centers. This provides a hybrid platform for exploring spin entanglement with potential scalability and full connectivity in addition to an optical link, and offers a pathway to investigate quantum acoustics in solid-state systems.

The nitrogen-vacancy (NV) center in diamond is a promising candidate for various quantum applications, such as quantum sensing. High sensitivity in NV-based magnetic sensing requires a diamond sample with a high density of NV centers and a long electron spin dephasing time. In this work, we propose a systematic measurement method for determining the electron spin dephasing time of NV center ensembles and analyze the contributions to the dephasing time from various sources, including NV-NV interactions, strain distribution, $^{13}C$ nuclear spin, and P1 electron spin. We demonstrate the effectiveness of our method on a series of high-performance diamond samples and provide a comprehensive understanding of dephasing sources, enabling the optimization of NV-based quantum sensing applications.

Quantum networks and distributed quantum computers rely on entanglement generation between photons and long-lived quantum memories. For large-scale architectures, one of the most crucial parameters is the efficiency at which entanglement can be created and detected. Here, we maximize the efficiency for the detection of hybrid entanglement between a nuclear spin qubit in diamond with a photonic time-bin qubit. Our approach relies on an optimal implementation of the photonic qubit analyzer, for which we use a high-speed electro-optic deflector to direct photons deterministically along the optimal interferometer paths. This way, we completely eliminate all cases in which photons are randomly lost due to the propagation in the wrong interferometer path. In this first demonstration experiment, we use nitrogen-vacancy center in diamond, for which we immediately demonstrate the presence of the entanglement. An extension to other spin-photon entanglement systems is straightforward. Further, our scheme can be used in the framework of quantum repeater networks, including spectral and temporal multiplexing strategies. Our results thus pave the way for the future high-performance quantum networks.

Critical parameters are the key to superconductivity research, and reliable instrumentations can facilitate the study. Traditionally, one has to use several different measurement techniques to measure critical parameters separately. In this work, we develop the use of a single species of quantum sensor to determine and estimate several critical parameters with the help of independent simulation data. We utilize the nitrogen-vacancy (NV) center in the diamond, which recently emerged as a promising candidate for probing exotic features in condensed matter physics. The non-invasive and highly stable nature provides extraordinary opportunities to solve scientific problems in various systems. Using a high-quality single-crystalline YBa$_{2}$Cu$_{4}$O$_{8}$ (YBCO) as a platform, we demonstrate the use of diamond particles and a bulk diamond to probe the Meissner effect. The evolution of the vector magnetic field, the $H-T$ phase diagram, and the map of fluorescence contour are studied via NV sensing. Our results reveal different critical parameters, including lower critical field $H_{c1}$, upper critical field $H_{c2}$, and critical current density $j_{c}$, as well as verifying the unconventional nature of this high-temperature superconductor YBCO. Therefore, NV-based quantum sensing techniques have huge potential in condensed matter research.

Magnetic auto-oscillations are damping-compensated magnetization precessions. They can be generated in spin Hall nano-oscillators (SHNO) among others. Current research on these devices is dedicated to create next generation energy-efficient hardware for communication technologies. However, the underlying physics governing the formation of auto-oscillation modes, their output power and line width in a single SHNO device have remained elusive so far. We image the sources of magnetic auto-oscillations in a metallic SHNO using a single spin quantum sensor. We directly measure the microwave field generated by an auto-oscillation spot at the nanoscale by driving the electron spin resonance transition of the sensor spin, enabling faster acquisition speed (100 ms/pixel). Instead of being defined by the points of the largest antidamping only, we experimentally demonstrate for the first time with quantitative magnetometry that the auto-oscillation spots are determined by the positions of the magnetic field minima. The latter act as local potential wells for confining spin-waves, thus supporting large amplitude auto-oscillations. By comparing the magnitude of the magnetic stray field at these spots, we decipher the different frequencies of the auto-oscillation modes. The insights gained regarding the interaction between auto-oscillation modes and spin-wave potential wells enable advanced engineering of real devices.

Solid state quantum emitters are a prime candidate in distributed quantum technologies since they inherently provide a spin-photon interface. An ongoing challenge in the field, however, is the low photon extraction due to the high refractive index of typical host materials. This challenge can be overcome using photonic structures. Here, we report the integration of V2 centers in a cavity-based optical antenna. The structure consists of a silver-coated, 135 nm thin 4H-SiC membrane functioning as a planar cavity with a broadband resonance yielding a theoretical photon collection enhancement factor of 34. The planar geometry allows us to identify over 20 single V2 centers at room temperature with a mean (maximum) count rate enhancement factor of 9 (15). Moreover, we observe 10 V2 centers with a mean absorption linewidth below 80MHz at cryogenic temperatures. These results demonstrate a photon collection enhancement that is robust to the lateral emitter position.

We present a protocol for the ground-state cooling of a tripartite hybrid quantum system, in which a macroscopic oscillator acts as a mediator between a single probe spin and a remote spin ensemble. In the presence of weak dispersive coupling between the spins and the oscillator, cooling of the oscillator and the ensemble spins can be achieved by exploiting the feedback from frequent measurements of the single probe spin. We explore the parameter regimes necessary to cool the ensemble, the oscillator, or both to their thermal ground states. This novel cooling protocol shows that, even with only weak dispersive coupling, energy transfer-like effects can be obtained by simply manipulating the probe spin. These results not only contribute to the development of a practical solution for cooling/polarizing large spin ensembles, but also provide a relatively simple means of tuning the dynamics of a hybrid system. The proposed cooling protocol thus has broader implications for advancing various quantum technology applications, such as macroscopic quantum state generation and remote sensing.

Nuclear spins in solids offer a promising avenue for developing scalable quantum hardware. Leveraging nearby single-color centers, these spins can be efficiently addressed at the single-site level through spin resonance. However, characterising individual nuclear spins is quite cumbersome since the characterisation protocols may differ depending on the strength of the hyperfine coupling, necessitating tailored approaches and experimental conditions. While modified electron spin Hahn echoes like CPMG and XY8 pulse sequences are commonly employed, they encounter significant limitations in scenarios involving spin-1/2 systems, strongly coupled spins, or nuclear spin baths comprising distinct isotopes. Here, we present a more straightforward approach for determining the hyperfine interactions among each nuclear and the electron spin. This method holds promise across diverse platforms, especially for emerging S=1/2 group IV defects in diamond (e.g., SiV, GeV, SnV, PbV) or silicon (T-centre, P-donors). We provide a theoretical framework and adapt it for color-centers exhibiting various spins. Through simulations conducted on nuclear spin clusters, we evaluate different protocols and compare their performance using the Fisher information matrix and Cramer Rao bounds., Comment: 10 pages, 5 figures, preprint

Enzymes are cellular protein machines using a variety of conformational changes to power fast biochemical catalysis. Our goal is to exploit the single-spin properties of the luminescent NV (nitrogen-vacancy) center in nanodiamonds to reveal the dynamics of an active enzyme complex at physiological conditions with the highest spatio-temporal resolution. Specifically attached to the membrane enzyme FoF1-ATP synthase, the NV sensor will report the adenosine triphosphate (ATP)-driven full rotation of Fo motor subunits in ten consecutive 36{\deg} steps. Conformational dynamics are monitored using either a double electron-electron resonance scheme or NV- magnetometry with optical readout or using NV- relaxometry with a superparamagnetic nanoparticle as the second marker attached to the same enzyme. First, we show how all photophysical parameters like individual size, charge, brightness, spectral range of fluorescence and fluorescence lifetime can be determined for the NV- center in a single nanodiamond held in aqueous solution by a confocal anti-Brownian electrokinetic trap (ABEL trap). Stable photon count rates of individual nanodiamonds and the absence of blinking allow for observation times of single nanodiamonds in solution exceeding hundreds of seconds. For the proposed quantum sensing of nanometer-sized distance changes within an active enzyme, we show that local magnetic field fluctuations can be detected all-optically by analyzing fluorescence lifetime changes of the NV- center in each nanodiamond in solution., Comment: 14 pages, 5 figures

Emitters in high refractive index materials like 4H-SiC suffer from reduced detection of photons because of losses caused by total internal reflection. Thus, integration into efficient nanophotonic structures which couple the emission of photons to a well defined waveguide mode can significantly enhance the photon detection efficiency. In addition, interfacing this waveguide to a classical fiber network is of similar importance to detect the photons and perform experiments. Here, we show a waveguide fiber interface in SiC. By careful measurements we determine efficiencies exceeding 93 % for the transfer of photons from SiC nanobeams to fibers. We use this interface to create a bright single photon source based on waveguide integrated V2 defects in 4H-SiC and achieve an overall photon count rate of 181 kilo-counts per second. We observe and quantify the strain induced shift of the ground state spin states and demonstrate coherent control of the electron spin with a coherence time of T2=42.5 $\rm\mu$s.

Test of {macroscopic realism} (MR) is key to understanding the foundation of quantum mechanics. Due to the existence of the {non-invasive measurability} loophole and other interpretation loopholes, however, such test remains an open question. Here we propose a general inequality based on high-order correlations of measurements for a loophole-free test of MR at the weak signal limit. Importantly, the inequality is established using the statistics of \textit{raw data} recorded by classical devices, without requiring a specific model for the measurement process, so its violation would falsify MR without the interpretation loophole. The non-invasive measurability loophole is also closed, since the weak signal limit can be verified solely by measurement data (using the relative scaling behaviors of different orders of correlations). We demonstrate that the inequality can be broken by a quantum spin model. The inequality proposed here provides an unambiguous test of the MR principle and is also useful to characterizing {quantum coherence}.

Quantum state readout is a key requirement for a successful qubit platform. In this work we demonstrate a high fidelity quantum state readout of a V2 center nuclear spin based on a repetitive readout technique. We demonstrate up to 99.5$\,\%$ readout fidelity and 99$\,\%$ for state preparation. Using this efficient readout we initialise the nuclear spin by measurement and demonstrate its Rabi and Ramsey nutation. Finally, we use the nuclear spin as a long lived memory for quantum sensing application of weakly coupled diatomic nuclear spin bath., Comment: 9 pages

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.

Nuclear spins with hyperfine coupling to single electron spins are highly valuable quantum bits. In this work we probe and characterise the particularly rich nuclear spin environment around single silicon vacancy color-centers (V2) in 4H-SiC. By using the electron spin-3/2 qudit as a 4 level sensor, we identify several groups of $^{29}$Si and $^{13}$C nuclear spins through their hyperfine interaction. We extract the major components of their hyperfine coupling via optical detected nuclear resonance, and assign them to shell groups in the crystal via the DFT simulations. We utilise the ground state level anti-crossing of the electron spin for dynamic nuclear polarization and achieve a nuclear spin polarization of up to $98\pm6\,\%$. We show that this scheme can be used to detect the nuclear magnetic resonance signal of individual spins and demonstrate their coherent control. Our work provides a detailed set of parameters for future use of SiC as a multi-qubit memory and quantum computing platform., Comment: 9 pages, 4 figures, 1 SM

Colour centres in silicon carbide emerge as a promising semiconductor quantum technology platform with excellent spin-optical coherences.However, recent efforts towards maximising the photonic efficiency via integration into nanophotonic structures proved to be challenging due to reduced spectral stabilities. Here, we provide a large-scale systematic investigation on silicon vacancy centres in thin silicon carbide membranes with thicknesses down to $0.25\,\rm\mu m$. Our membrane fabrication process involves a combination of chemical mechanical polishing, reactive ion etching, and subsequent annealing. This leads to highly reproducible membranes with roughness values of $3-4\,\rm\r{A}$, as well as negligible surface fluorescence. We find that silicon vacancy centres show close-to lifetime limited optical linewidths with almost no signs of spectral wandering down to membrane thicknesses of $0.7 \,\rm\mu m$. For silicon vacancy centres in thinner membranes down to $0.25\,\rm\mu m$, we observe spectral wandering, however, optical linewidths remain below $200\,\rm MHz$, which is compatible with spin-selective excitation schemes. Our work clearly shows that silicon vacancy centres can be integrated into sub-micron silicon carbide membranes, which opens the avenue towards obtaining the necessary improvements in photon extraction efficiency based on nanophotonic structuring., Comment: 10 pages, 4 figures, plus supplementary information

The negatively-charged silicon vacancy center ($\rm V_{Si}^-$) in silicon carbide (SiC) is an emerging color center for quantum technology covering quantum sensing, communication, and computing. Yet, limited information currently available on the internal spin-optical dynamics of these color centers prevents us achieving the optimal operation conditions and reaching the maximum performance especially when integrated within quantum photonics. Here, we establish all the relevant intrinsic spin dynamics of negatively charged $\rm V_{Si}^-$ center in 4H-SiC by an in-depth electronic fine structure modeling including intersystem-crossing and deshelving mechanisms. With carefully designed spin-dependent measurements, we obtain all previously unknown spin-selective radiative and non-radiative decay rates. To showcase the relevance of our work for integrated quantum photonics, we use the obtained rates to propose a realistic implementation of time-bin entangled multi-photon GHZ and cluster state generation. We find that up to 3-photon GHZ/cluster states are readily within reach using the existing nanophotonic cavity technology., Comment: 37 pages, 6 figures. Document includes Supplementary Information

The constant interplay and information exchange between cells and their micro-environment are essential to their survival and ability to execute biological functions. To date, a few leading technologies such as traction force microscopy, have been broadly used in measuring cellular forces. However, the considerable limitations, regarding the sensitivity and ambiguities in data interpretation, are hindering our thorough understanding of mechanobiology. Herein, we propose an innovative approach, namely quantum-enhanced diamond molecular tension microscopy (QDMTM), to precisely quantify the integrin-based cell adhesive forces. Specifically, we construct a force sensing platform by conjugating the magnetic nanotags labeled, force-responsive polymer to the surface of diamond membrane containing nitrogen vacancy (NV) centers. Thus, the coupled mechanical information can be quantified through optical readout of spin relaxation of NV centers modulated by those magnetic nanotags. To validate QDMTM, we have carefully performed corresponding measurements both in control and real cell samples. Particularly, we have obtained the quantitative cellular adhesion force mapping by correlating the measurement with established theoretical model. We anticipate that our method can be routinely used in studying important issues like cell-cell or cell-material interactions and mechanotransduction., Comment: 51 pages, 20 figures

Charge state instabilities have been a bottleneck for the implementation of solid-state spin systems and pose a major challenge to the development of spin-based quantum technologies. Here we investigate the stabilization of negatively charged nitrogen-vacancy (NV$^-$) centers in phosphorus-doped diamond at liquid helium temperatures. Photoionization of phosphorous donors in conjunction with charge diffusion at the nanoscale enhances NV$^0$ to NV$^-$ conversion and stabilizes the NV$^-$ charge state without the need for an additional repump laser. The phosphorus-assisted stabilization is explored and confirmed both with experiments and our theoretical model. Stable photoluminescence-excitation spectra are obtained for NV$^-$ centers created during the growth. The fluorescence is continuously recorded under resonant excitation to real-time monitor the charge state and the ionization and recombination rates are extracted from time traces. We find a linear laser power dependence of the recombination rate as opposed to the conventional quadratic dependence, which is attributed to the photo-ionization of phosphorus atoms., Comment: 8 pages, 4 figures

Spatial, momentum and energy separation of electronic spins in condensed matter systems guides the development of novel devices where spin-polarized current is generated and manipulated. Recent attention on a set of previously overlooked symmetry operations in magnetic materials leads to the emergence of a new type of spin splitting, enabling giant and momentum-dependent spin polarization of energy bands on selected antiferromagnets. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here, we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet MnTe$_2$, the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic (AFM) ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, stems from the intrinsic AFM order instead of spin-orbit coupling (SOC). Our finding demonstrates a new type of quadratic spin texture induced by time-reversal breaking, placing AFM spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials., Comment: Version 3, 49 pages, 4 main figures, 13 extended data figures and 2 extended data tables. Nature in press (2024)

Recently, the negatively charged nitrogen-vacancy (NV) center has emerged as a robust and versatile quantum sensor in pressurized environments. There are two popular ways to implement NV sensing in a diamond anvil cell (DAC), which is a conventional workhorse in the high-pressure community: create implanted NV centers (INVs) at the diamond anvil tip or immerse NV-enriched nano-diamonds (NDs) in the pressure medium. Nonetheless, there are limited studies on comparing the local stress environments experienced by these sensor types as well as their performances as pressure gauges. In this work, by probing the NV energy levels with the optically detected magnetic resonance (ODMR) method, we experimentally reveal a dramatic difference in the partially reconstructed stress tensors of INVs and NDs incorporated in the same DAC. Our measurement results agree with computational simulations, concluding that INVs perceive a more non-hydrostatic environment dominated by a uniaxial stress along the DAC axis. This provides insights on the suitable choice of NV sensors for specific purposes and the stress distribution in a DAC. We further propose some possible methods, such as using NDs and nanopillars, to extend the maximum working pressure of quantum sensing based on ODMR spectroscopy, since the maximum working pressure could be restricted by non-hydrostaticity of the pressure environment. Moreover, we explore more sensing applications of the NV center by studying how pressure modifies different aspects of the NV system. We perform a photoluminescence study using both INVs and NDs to determine the pressure dependence of the zero-phonon line, which helps developing an all-optical pressure sensing protocol with the NV center. We also characterize the spin-lattice relaxation ($T_1$) time of INVs under pressure to lay a foundation for robust pulsed measurements with NV centers in pressurized environments.

Ideal projective quantum measurement makes the system state collapse in one of the observable operator eigenstates $|\phi_\alpha\rangle$, making it a powerful tool for preparing the system in the desired pure state. Nevertheless, experimental realisations of projective measurement are not ideal. During the measurement time needed to overcome the classical noise of the apparatus, the system state is often (slightly) perturbed, which compromises the fidelity of initialisation. In this paper, we propose an analytical model to analyse the initialisation fidelity of the system performed by the single-shot readout. We derive a method to optimise parameters for the three most used cases of photon counting based readouts for NV colour centre in diamond, charge state, nuclear spin and low temperature electron spin readout. Our work is of relevance for the accurate description of initialisation fidelity of the quantum bit when the single-shot readout is used for initialisation via post-selection or real-time control.

Single color centers in solid have emerged as promising physical platforms for quantum information science. Creating these centers with excellent quantum properties is a key foundation for further technological developments. In particular, the microscopic understanding of the spin bath environments is the key to engineer color centers for quantum control. In this work, we propose and demonstrate a distinct high-temperature annealing (HTA) approach for creating high-quality nitrogen vacancy (NV) centers in implantation-free diamonds. Simultaneously using the created NV centers as probes for their local environment we verify that no damage was microscopically induced by the HTA. Nearly all single NV centers created in ultra-low-nitrogen-concentration membranes possess stable and Fourier-transform-limited optical spectra. Furthermore, HTA strongly reduces noise sources naturally grown in ensemble samples, and leads to more than three-fold improvements of decoherence time and sensitivity. We also verify that the vacancy activation and defect reformation, especially H3 and P1 centers, can explain the reconfiguration between spin baths and color centers. This novel approach will become a powerful tool in vacancy-based quantum technology.

Nanoscale nuclear magnetic resonance (NMR) signals can be measured through hyperfine interaction to paramagnetic electron sensor spins. A heterodyne approach is widely used to overcome the electron spin lifetime limit in spectral resolution. It uses a series of modified Hahn echo pulse sequences applied coherently with precession signal resulting in a subsampled NMR signal. Due to challenges with applying high electron Rabi frequencies its application is limited to low fields, thus the full potential of the method is not yet exploited at high magnetic fields, beneficial for NMR. Here we present heterodyne detection utilizing a series of phase coherent electron nuclear double resonance sensing blocks which extends nanoscale NMR protocols to arbitrary magnetic fields. We demonstrate this principle on a single NV center, both with an intrinsic $^{14}$N and a weekly coupled $^{13}$C nuclear spin in the bath surrounding single NV centres. We compare our protocol to existing heterodyne protocols and discuss its prospects. This work paves the way towards high field nanoscale heterodyne NMR protocols with NV centres which is crucial for reducing sample volumes and improving chemical resolution., Comment: 27 pages, 11 figures

The ability to perform high-precision optical measurements is paramount to science and engineering. Laser interferometry enables interaction-free sensing with a precision ultimately limited by shot noise. Quantum optical sensors can surpass this limit, but single- or multi-photon schemes are challenged by low experimental sampling rates, while squeezed-light approaches require complex optical setups and sophisticated time gating. Here, we introduce a simple method that infers optical phase shifts through standard intensity measurements while still maintaining the quantum advantage in the measurement precision. Capitalising on the robustness and high sampling rates of our device, we implement a quantum optical microphone in the audio band. Its performance is benchmarked against a classical laser microphone in a standardised medically-approved speech recognition test on 45 subjects. We find that quantum-recorded words improve the speech recognition threshold by $-0.57\, \text{dB}_{\text{SPL}}$, thus making the quantum advantage audible. Not only do these results open the door towards applications in quantum nonlinear interferometry, but they also show that quantum phenomena can be experienced by humans., Comment: 8 pages, 4 figures

Color centers in silicon carbide are emerging candidates for distributed spin-based quantum applications due to the scalability of host materials and the demonstration of integration into nanophotonic resonators. Recently, silicon vacancy centers in silicon carbide have been identified as a promising system with excellent spin and optical properties. Here, we in-depth study the spin-optical dynamics of single silicon vacancy center at hexagonal lattice sites, namely V1, in 4H-polytype silicon carbide. By utilizing resonant and above-resonant sub-lifetime pulsed excitation, we determine spin-dependent excited-state lifetimes and intersystem-crossing rates. Our approach to inferring the intersystem-crossing rates is based on all-optical pulsed initialization and readout scheme, and is applicable to spin-active color centers with similar dynamics models. In addition, the optical transition dipole strength and the quantum efficiency of V1 defect are evaluated based on coherent optical Rabi measurement and local-field calibration employing electric-field simulation. The measured rates well explain the results of spin-state polarization dynamics, and we further discuss the altered photoemission dynamics in resonant enhancement structures such as radiative lifetime shortening and Purcell enhancement. By providing a thorough description of V1 center's spin-optical dynamics, our work provides deep understanding of the system which guides implementations of scalable quantum applications based on silicon vacancy centers in silicon carbide., Comment: 32 pages, 12 figures

Randomness is a very important resource for cryptography, algorithms, and scientific simulations. Since all classical processes are considered to be intrinsically deterministic, we must build quantum random number generators which utilize quantum processes to generate true randomness. Quantum random number generators have been realized in different quantum systems, including quantum optical systems, and trapped ions. Here we present a proof-of-concept random number generator based on a nuclear spin system for the first time. The state preparation and measurements are performed with high-fidelity operations in our system. The entropy of randomness in the experimental data is quantified by two dimension witness certification protocols, which require no detailed models to describe the experimental devices but only some general assumptions, such as the limited dimensionality and the independence of the experimental devices., Comment: With the agreement of my coauthors, I would like to withdraw the manuscript "Self-testing randomness from a nuclear spin system". Major modification is needed, the randomness certification models need to be clearer explained, and some experimental procedures need more details to be understood in the manuscript

The continuous scaling of semiconductor-based technologies to micron and sub-micron regimes has resulted in higher device density and lower power dissipation. Many physical phenomena such as self-heating or current leakage become significant at such scales, and mapping current densities to reveal these features is decisive for the development of modern electronics. However, advanced non-invasive technologies either offer low sensitivity or poor spatial resolution and are limited to two-dimensional spatial mapping. Here we use near-surface nitrogen-vacancy centres in diamond to probe Oersted fields created by current flowing within a multi-layered integrated circuit in pre-development. We show the reconstruction of the three-dimensional components of the current density with a magnitude down to about $\approx 10 \,\rm \mu A / \mu m^2$ and sub-micron spatial resolution at room temperature. We also report the localisation of currents in different layers and observe anomalous current flow in an electronic chip. Our method provides, therefore a decisive step toward three-dimensional current mapping in technologically relevant nanoscale electronics chips., Comment: Featured in Parker, M., Imaging circuits in three dimensions. Nat Electron 7, 94 (2024)

Quantum sensors are keeping the cutting-edge sensitivities in metrology. However, for high-sensitive measurements of arbitrary signals, limitations in linear dynamic range could introduce distortions when sensing the frequency, magnitude and phase of unknown signals. Here, we overcome these limitations with advanced sensing protocol that combines quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the ability to sense radio signals with a 98 dB linear dynamic range, a 31 pT/Hz$^{1/2}$ sensitivity, and arbitrary frequency resolution. Further, we perform the quantum-assisted distortion-free audio signal (melody, speech) sensing with high fidelity. The methods developed here could broaden the horizon for quantum sensors towards applications in telecommunication, where high-fidelity and low-distortion at multiple frequency bands within small sensing volumes are required., Comment: 30 pages, 7 figures

We investigate, theoretically and experimentally, the thermodynamic performance of a minimal three-qubit heat-bath algorithmic cooling refrigerator. We analytically compute the coefficient of performance, the cooling power and the polarization of the target qubit for an arbitrary number of cycles, taking realistic experimental imperfections into account. We determine their fundamental upper bounds in the ideal reversible limit and show that these values may be experimentally approached using a system of three qubits in a nitrogen-vacancy center in diamond., Comment: 6 pages, 4 figures. With supplemental material of 6 pages, 4 figures. Content of published version

Nonlinear spectroscopy is widely used for studying physical systems. Conventional nonlinear optical spectroscopy and magnetic resonance spectroscopy, which use classical probes such as electromagnetic waves, can only access certain types of correlations in a quantum system. The idea of quantum nonlinear spectroscopy was recently proposed to use quantum probes such as entangled photons to achieve sensitivities and resolutions beyond the classical limits. It is shown that quantum sensing can extract arbitrary types and orders of correlations in a quantum system by first quantum-entangling a sensor and the object and then measuring the sensor. Quantum sensing has been applied to achieve nuclear magnetic resonance (NMR) of single atoms and the second-order correlation spectroscopy has been adopted to enhance the spectral resolution. However, quantum nonlinear spectroscopy (i.e., the measurement of higher-order correlations) of single nuclear spins is still elusive. Here we demonstrate the extraction of fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via an atomic quantum sensor, namely, a nitrogen-vacancy center in diamond. We show that 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. The measured fourth-order correlation unambiguously differentiates a single nuclear spin and a random-phased AC field. 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., Comment: 23 pages and 4 figures

Shallow nitrogen-vacancy (NV) centers in diamond are promising for nano-magnetometry for they can be placed proximate to targets. To study the intrinsic magnetic properties, zero-field magnetometry is desirable. However, for shallow NV centers under zero field, the strain near diamond surfaces would cause level anti-crossing between the spin states, leading to clock transitions whose frequencies are insensitive to magnetic signals. Furthermore, the charge noises from the surfaces would induce extra spin decoherence and hence reduce the magnetic sensitivity. Here we demonstrate that the relatively strong hyperfine coupling (130 MHz) from a first-shell 13C nuclear spin can provide an effective bias field to an NV center spin so that the clock-transition condition is broken and the charge noises are suppressed. The hyperfine bias enhances the dc magnetic sensitivity by a factor of 22 in our setup. With the charge noises suppressed by the strong hyperfine field, the ac magnetometry under zero field also reaches the limit set by decoherence due to the nuclear spin bath. In addition, the 130 MHz splitting of the NV center spin transitions allows relaxometry of magnetic noises simultaneously at two well-separated frequencies (~2.870 +/- 0.065 GHz), providing (low-resolution) spectral information of high-frequency noises under zero field. The hyperfine-bias enhanced zero-field magnetometry can be combined with dynamical decoupling to enhance single-molecule magnetic resonance spectroscopy and to improve the frequency resolution in nanoscale magnetic resonance imaging.

Optically addressable spin defects in silicon carbide (SiC) are an emerging platform for quantum information processing. Lending themselves to modern semiconductor nanofabrication, they promise scalable high-efficiency spin-photon interfaces. We demonstrate here nanoscale fabrication of silicon vacancy centres (VSi) in 4H-SiC without deterioration of their intrinsic spin-optical properties. In particular, we show nearly transform limited photon emission and record spin coherence times for single defects generated via ion implantation and in triangular cross section waveguides. For the latter, we show further controlled operations on nearby nuclear spin qubits, which is crucial for fault-tolerant quantum information distribution based on cavity quantum electrodynamics., Comment: 18 pages, 4 figures

The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state purity and yield a low-entropy steady state of the bath. The purified bath state persists long after the measurements are completed. Such purification enables the exploitation of spin baths as long-lived quantum memories or as quantum-enhanced sensors. The experiment involved a repeatedly probed defect center dephased by a nuclear spin bath in a diamond at low-temperature., Comment: 4 figures

We show here through experiments and exact analytical models the emergence of discrete time translation symmetry breaking in non-interacting systems. These time-periodic structures become stable against perturbations only in the presence of their interaction with the ancillary quantum system and display subharmonic response over a range of rotation angle errors. We demonstrate this effect for central spin and spin-mechanical systems, where the ancillary induced interaction among the spins stabilizes the spin dynamics against finite errors. Further, we extend these studies and show the possibility to even achieve non-local (remote) synchronization of such Floquet crystals., Comment: 6 pages, 3 figures

We measure diffusion of organic molecules located a few nanometers from the diamond surface. To study molecular diffusion, we perform local detection of nuclear magnetic resonance, based on single shallow Nitrogen-Vacancy (NV) centers in diamond. Specifically, we demonstrate measurements of translational diffusion coefficient of phospholipids in an artificial cell membrane by employing correlation spectroscopy. An analysis of correlation decay curves using different diffusion models shows, that a simple 2D diffusion model gives satisfactory diffusion coefficients, although the choice of the model affects the extracted numbers. We find significant differences among the diffusion coefficients measured by different single NV centers, which we attribute to local heterogeneities of the lipid layers, likely caused by the supporting diamond substrate.

Point defects in insulators are considered promising candidates for quantum technologies. In keeping with this, we present an extensive optically-detected magnetic resonance (ODMR) study at room-temperature on individual TR12 centers (ZPL at 471nm), which are known in the literature since 1956. In this work we found TR12 centers to show a strong ODMR signal under optical saturation. These observed defects were created in high-purity epitaxial layers of diamond by standard irradiation and annealing processes. From the analysis of the ODMR spectra along with antibunching measurements and coherent population trapping, we proposed the energy level structure of TR12 center, consisting of ground state and excited state singlets complemented by a metastable triplet in between. Mapping the fluorescence dependence of the center on an external magnetic field and on the polarization of laser excitation, allows us to identify twelve inequivalent orientations for TR12 centers. This includes the exact orientations of the dipole transition and the triplet axes in the diamond lattice in full agreement with the results of modeling based on the proposed level structure. Furthermore, a static Jahn-Teller effect was detected through fluorescence switching between two levels at low optical excitation power, directly observable in the real-time fluorescence signal for various polarization of laser excitation. Based on these results we discuss the prospects of the TR12 center in diamond for quantum sensing and quantum information processing., Comment: 12 pages, 8 figures

The ability to follow the dynamics of a quantum system in a quantitative manner is of key importance for quantum technology. Despite its central role, justifiable deduction of the quantum dynamics of a single quantum system in terms of a macroscopical observable remains a challenge. Here we show that the relation between the readout signal of a single electron spin and the quantum dynamics of the single nuclear spin is given by a parameter related to the measurement strength. We determine this measurement strength in independent experiments and use this value to compare our analysis of the quantum dynamics with experimental results. We prove the validity of our approach by measuring violations of the Leggett-Garg inequality.

Electro-optical control of on-chip photonic devices is an essential tool for efficient integrated photonics. Lithium niobate on insulator (LNOI) is an emerging platform for on-chip photonics due to its large electro-optic coefficient and high nonlinearity [1]. Integrating quantum emitters into LNOI would extend their versatile use in classic photonics to quantum computing and communication [2, 3]. Here, we incorporate single rare-earth ions (REI) quantum emitters in electro-optical tunable lithium niobite (LN) thin films and demonstrate control of LN microcavities coupled to REI over a frequency range of 160 GHz with 5 \mus switching speed. Dynamical control of the cavities enables the modulation of the Purcell enhancement of the REIs with short time constants. Using the Purcell enhancement, we show evidence of detecting single Yb3+ ions in LN cavities. Coupling quantum emitters in fast tunable photonic devices is an efficient method to shape the waveform of the emitter [4]. It also offers a platform to encode quantum information in the integration of a spectral-temporal-spatial domain to achieve high levels of channel multiplexing, as well as an approach to generate deterministic single-photon sources [5, 6].

Optically active solid-state spin registers have demonstrated their unique potential in quantum computing, communication and sensing. Realizing scalability and increasing application complexity requires entangling multiple individual systems, e.g. via photon interference in an optical network. However, most solid-state emitters show relatively broad spectral distributions, which hinders optical interference experiments. Here, we demonstrate that silicon vacancy centres in semiconductor silicon carbide (SiC) provide a remarkably small natural distribution of their optical absorption/emission lines despite an elevated defect concentration of $\approx 0.43\,\rm \mu m^{-3}$. In particular, without any external tuning mechanism, we show that only 13 defects have to be investigated until at least two optical lines overlap within the lifetime-limited linewidth. Moreover, we identify emitters with overlapping emission profiles within diffraction limited excitation spots, for which we introduce simplified schemes for generation of computationally-relevant Greenberger-Horne-Zeilinger (GHZ) and cluster states. Our results underline the potential of the CMOS-compatible SiC platform toward realizing networked quantum technology applications., Comment: 7 pages, 4 figures

Point defects in crystals provide important building blocks for quantum applications. To initialize, control, and read-out their quantum states, an efficient optical interface for addressing defects with photons is required. However, conventional confocal fluorescence microscopy with high refractive index crystals has limited photon collection efficiency and spatial resolution. Here, we demonstrate high resolution, high contrast imaging for defects qubits using microsphere-assisted confocal microscopy. A microsphere provides an excellent optical interface for point defects with a magnified virtual image that improves spatial resolution up to ~${\lambda}$/5 as well as an optical signal-to-noise ratio by four times. These features enable individual optical addressing of single photons and single spins of spatially-unresolved defects in conventional confocal microscopy with improved signal contrast. The combined optical tweezers show the possibility of positioning or scanning the microspheres for deterministic coupling and wide-field imaging of defects. The approach does not require any complicated fabrication and additional optical system but uses simple micro-optics off-the-shelf. From these distinctive advantages of the microspheres, our approach can provide an efficient way for imaging and addressing closely-spaced defects with higher resolution and sensitivity., Comment: 20 pages, 5 figures

Nitrogen vacancy (NV) centers in diamond have developed into a powerful solid-state platform for compact quantum sensors. However, high sensitivity measurements usually come with additional constraints on the pumping intensity of the laser and the pulse control applied. Here, we demonstrate high sensitivity NV ensemble based magnetic field measurements with low-intensity optical excitation. DC magnetometry methods like, e.g., continuous-wave optically detected magnetic resonance and continuously excited Ramsey measurements combined with lock-in detection, are compared to get an optimization. Gradiometry is also investigated as a step towards unshielded measurements of unknown gradients. The magnetometer demonstrates a minimum detectable field of 0.3-0.7 pT in a 73 s measurement by further applying a flux guide with a sensing dimension of 2 mm, corresponding to a magnetic field sensitivity of 2.6-6 pT/Hz^0.5. Combined with our previous efforts on the diamond AC magnetometry, the diamond magnetometer is promising to perform wide bandwidth magnetometry with picotesla sensitivity and a cubic-millimeter sensing volume under ambient conditions., Comment: 20 pages, 12 figures

Nitrogen-vacancy (NV) centers in diamond can be used as quantum sensors to image the magnetic field with nanoscale resolution. However, nanoscale electric-field mapping has not been achieved so far because of the relatively weak coupling strength between NV and electric field. Using individual shallow NVs, here we succeeded to quantitatively image the contours of electric field from a sharp tip of a qPlus-based atomic force microscope (AFM), and achieved a spatial resolution of ~10 nm. Through such local electric fields, we demonstrated electric control of NV's charge state with sub-5 nm precision. This work represents the first step towards nanoscale scanning electrometry based on a single quantum sensor and may open up new possibility of quantitatively mapping local charge, electric polarization, and dielectric response in a broad spectrum of functional materials at nanoscale., Comment: 32 pages, 5 figures

Magnetic-domain structure and dynamics play an important role in understanding and controlling the magnetic properties of two-dimensional magnets, which are of interest to both fundamental studies and applications[1-5]. However, the probe methods based on the spin-dependent optical permeability[1,2,6] and electrical conductivity[7-10] can neither provide quantitative information of the magnetization nor achieve nanoscale spatial resolution. These capabilities are essential to image and understand the rich properties of magnetic domains. Here, we employ cryogenic scanning magnetometry using a single-electron spin of a nitrogen-vacancy center in a diamond probe to unambiguously prove the existence of magnetic domains and study their dynamics in atomically thin CrBr$_3$. The high spatial resolution of this technique enables imaging of magnetic domains and allows to resolve domain walls pinned by defects. By controlling the magnetic domain evolution as a function of magnetic field, we find that the pinning effect is a dominant coercivity mechanism with a saturation magnetization of about 26~$\mu_B$/nm$^2$ for bilayer CrBr$_3$. The magnetic-domain structure and pinning-effect dominated domain reversal process are verified by micromagnetic simulation. Our work highlights scanning nitrogen-vacancy center magnetometry as a quantitative probe to explore two-dimensional magnetism at the nanoscale.

Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However the spectral resolution in such protocols is limited ultimately by sensor lifetime. Here we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW-signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally we achieve a spectral resolution below $1\ \rm{Hz}$ for a $4\ \rm{GHz}$ signal far below the sensor lifetime limit of kilohertz. Furthermore we show control over the interaction of the MW-field with the two level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to highest sensitivity, the Floquet dynamics allows robust control independent from the systems resonance frequency. Our work is important for future studies in sensing weak microwave signals in wide frequency range with high spectral resolution.

The Quantum Fourier Transformation ($QFT$) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance the performance of a quantum sensor. We implement the $QFT$ algorithm in a hybrid quantum register consisting of a nitrogen-vacancy (NV) center electron spin and three nuclear spins. The $QFT$ runs on the nuclear spins and serves to process the sensor - NV electron spin signal. We demonstrate $QFT$ for quantum (spins) and classical signals (radio frequency (RF) ) with near Heisenberg limited precision scaling. We further show the application of $QFT$ for demultiplexing the nuclear magnetic resonance (NMR) signal of two distinct target nuclear spins. Our results mark the application of a complex quantum algorithm in sensing which is of particular interest for high dynamic range quantum sensing and nanoscale NMR spectroscopy experiments.

The prototype of a quantum random number generator is a single photon which impinges onto a beam splitter and is then detected by single photon detectors at one of the two output paths. Prior to detection, the photon is in a quantum mechanical superposition state of the two possible outcomes with - ideally - equal amplitudes until its position is determined by measurement. When the two output modes are observed by a single photon detector, the generated clicks can be interpreted as ones and zeros - and a raw random bit stream is obtained. Here we implement such a random bit generator based on single photons from a defect center in diamond. We investigate the single photon emission of the defect center by an anti-bunching measurement. This certifies the "quantumness" of the supplied photonic input state, while the random "decision" is still based on the vacuum fluctuations at the open port of the beam-splitter. Technical limitations, such as intensity fluctuations, mechanical drift, and bias are discussed. A number of ways to suppress such unwanted effects, and an a priori entropy estimation are presented. The single photon nature allows for a characterization of the non-classicality of the source, and allows to determine a background fraction. Due to the NV-center's superior stability and optical properties, we can operate the generator under ambient conditions around the clock. We present a true 24/7 operation of the implemented random bit generator., Comment: 21 pages, 4 figures

Single-photon emitting devices have been identified as an important building block for applications in quantum information and quantum communication. They allow to transduce and collect quantum information over a long distance via photons as so called flying qubits. In addition, substrates like silicon carbide provides an excellent material platform for electronic devices. In this work we combine these two features and show that one can drive single photon emitters within a silicon carbide p-i-n-diode. To achieve this, we specifically designed a lateral oriented diode. We find a variety of new color centers emitting non-classical lights in VIS and NIR range. One type of emitter can be electrically excited, demonstrating that silicon carbide can act as an ideal platform for electrically controllable single photon sources.