Quantum nonlinear spectroscopy of single nuclear spins.

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

Quantum-assisted distortion-free audio signal sensing.

Quantum sensors are known for their high sensitivity in sensing applications. However, this sensitivity often comes with severe restrictions on other parameters which are also important. Examples are that in measurements of arbitrary signals, limitation in linear dynamic range could introduce distortions in magnitude and phase of the signal. High frequency resolution is another important feature for reconstructing unknown signals. Here, we demonstrate a distortion-free quantum sensing protocol that combines a quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the capability of reconstructing audio frequency signals with an extended linear dynamic range and high frequency resolution. Melody and speech based signals are used for demonstrating the features. The methods could broaden the horizon for quantum sensors towards applications, e.g. telecommunication in challenging environment, where low-distortion measurements are required at multiple frequency bands within a limited volume.

Heterodyne sensing of microwaves with a quantum sensor.

Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the 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 Hz for a 4 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 improved sensitivity, the Floquet dynamics allow robust control, independent from the system's resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.

Coherent electrical readout of defect spins in silicon carbide by photo-ionization at ambient conditions.

Quantum technology relies on proper hardware, enabling coherent quantum state control as well as efficient quantum state readout. In this regard, wide-bandgap semiconductors are an emerging material platform with scalable wafer fabrication methods, hosting several promising spin-active point defects. Conventional readout protocols for defect spins rely on fluorescence detection and are limited by a low photon collection efficiency. Here, we demonstrate a photo-electrical detection technique for electron spins of silicon vacancy ensembles in the 4H polytype of silicon carbide (SiC). Further, we show coherent spin state control, proving that this electrical readout technique enables detection of coherent spin motion. Our readout works at ambient conditions, while other electrical readout approaches are often limited to low temperatures or high magnetic fields. Considering the excellent maturity of SiC electronics with the outstanding coherence properties of SiC defects, the approach presented here holds promises for scalability of future SiC quantum devices.

Robust and Accurate Electric Field Sensing with Solid State Spin Ensembles.

Electron spins in solids constitute remarkable quantum sensors. Individual defect centers in diamond were used to detect individual nuclear spins with a nanometer scale resolution, and ensemble magnetometers rival SQUID and vapor cell magnetometers when taking into account room-temperature operation and size. NV center spins can also detect electric field vectors, despite their weak coupling to electric fields. Here, we employ ensembles of NV center spins to measure macroscopic AC electric fields with high precision. We utilize low strain, 12C enriched diamond to achieve the maximum sensitivity and tailor the spin Hamiltonian via the proper magnetic field adjustment to map out the AC electric field strength and polarization and arrive at refined electric field coupling constants. For high-precision measurements, we combine classical lock-in detection with aspects from quantum phase estimation for the effective suppression of technical noise. Eventually, this enables t-1/2 uncertainty scaling of the electric field strength over extended averaging periods, enabling us to reach a precision down to 10-7 V/µm for an AC electric field with a frequency of 2 kHz and an amplitude of 0.012 V/ µm.

Triple nitrogen-vacancy centre fabrication by C5N4Hn ion implantation.

Quantum information processing requires quantum registers based on coherently interacting quantum bits. The dipolar couplings between nitrogen vacancy (NV) centres with nanometre separation makes them a potential platform for room-temperature quantum registers. The fabrication of quantum registers that consist of NV centre arrays has not advanced beyond NV pairs for several years. Further scaling up of coupled NV centres by using nitrogen implantation through nanoholes has been hampered because the shortening of the separation distance is limited by the nanohole size and ion straggling. Here, we demonstrate the implantation of C5N4Hn from an adenine ion source to achieve further scaling. Because the C5N4Hn ion may be regarded as an ideal point source, the separation distance is solely determined by straggling. We successfully demonstrate the fabrication of strongly coupled triple NV centres. Our method may be extended to fabricate small quantum registers that can perform quantum information processing at room temperature.

Photoelectrical imaging and coherent spin-state readout of single nitrogen-vacancy centers in diamond.

Nitrogen-vacancy (NV) centers in diamond have become an important instrument for quantum sensing and quantum information science. However, the readout of NV spin state requires bulky optical setups, limiting fabrication of miniaturized compact devices for practical use. Here we realized photoelectrical detection of magnetic resonance as well as Rabi oscillations on a single-defect level. Furthermore, photoelectrical imaging of individual NV centers at room temperature was demonstrated, surpassing conventional optical readout methods by providing high imaging contrast and signal-to-noise ratio. These results pave the way toward fully integrated quantum diamond devices.

Probing Quantum Thermalization of a Disordered Dipolar Spin Ensemble with Discrete Time-Crystalline Order.

We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving, and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.

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

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

Nonvolatile nuclear spin memory enables sensor-unlimited nanoscale spectroscopy of small spin clusters.

In nanoscale metrology, dissipation of the sensor limits its performance. Strong dissipation has a negative impact on sensitivity, and sensor-target interaction even causes relaxation or dephasing of the latter. The weak dissipation of nitrogen-vacancy (NV) sensors in room temperature diamond enables detection of individual target nuclear spins, yet limits the spectral resolution of nuclear magnetic resonance (NMR) spectroscopy to several hundred Hertz, which typically prevents molecular recognition. Here, we use the NV intrinsic nuclear spin as a nonvolatile classical memory to store NMR information, while suppressing sensor back-action on the target using controlled decoupling of sensor, memory, and target. We demonstrate memory lifetimes up to 4 min and apply measurement and decoupling protocols, which exploit such memories efficiently. Our universal NV-based sensor device records single-spin NMR spectra with 13 Hz resolution at room temperature.Dissipation of the sensor is a limiting factor in metrology. Here, Pfender et al. suppress this effect employing the nuclear spin of an NV centre for robust intermediate storage of classical NMR information, allowing then to record single-spin NMR spectra with 13 Hz resolution at room temperature.

Protecting a Diamond Quantum Memory by Charge State Control.

In recent years, solid-state spin systems have emerged as promising candidates for quantum information processing. Prominent examples are the nitrogen-vacancy (NV) center in diamond, phosphorus dopants in silicon (Si:P), rare-earth ions in solids, and VSi-centers in silicon-carbide. The Si:P system has demonstrated that its nuclear spins can yield exceedingly long spin coherence times by eliminating the electron spin of the dopant. For NV centers, however, a proper charge state for storage of nuclear spin qubit coherence has not been identified yet. Here, we identify and characterize the positively charged NV center as an electron-spin-less and optically inactive state by utilizing the nuclear spin qubit as a probe. We control the electronic charge and spin utilizing nanometer scale gate electrodes. We achieve a lengthening of the nuclear spin coherence times by a factor of 4. Surprisingly, the new charge state allows switching of the optical response of single nodes facilitating full individual addressability.

Nanoscale nuclear magnetic resonance with chemical resolution.

Nuclear magnetic resonance (NMR) spectroscopy is a key analytical technique in chemistry, biology, and medicine. However, conventional NMR spectroscopy requires an at least nanoliter-sized sample volume to achieve sufficient signal. We combined the use of a quantum memory and high magnetic fields with a dedicated quantum sensor based on nitrogen vacancy centers in diamond to achieve chemical shift resolution in 1H and 19F NMR spectroscopy of 20-zeptoliter sample volumes. We demonstrate the application of NMR pulse sequences to achieve homonuclear decoupling and spin diffusion measurements. The best measured NMR linewidth of a liquid sample was ~1 part per million, mainly limited by molecular diffusion. To mitigate the influence of diffusion, we performed high-resolution solid-state NMR by applying homonuclear decoupling and achieved a 20-fold narrowing of the NMR linewidth.

Observation of discrete time-crystalline order in a disordered dipolar many-body system.

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic 'time-crystalline' phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Here we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. This order is remarkably stable to perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.

Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble.

We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and nonexponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.

Local and bulk (13)C hyperpolarization in nitrogen-vacancy-centred diamonds at variable fields and orientations.

Polarizing nuclear spins is of fundamental importance in biology, chemistry and physics. Methods for hyperpolarizing (13)C nuclei from free electrons in bulk usually demand operation at cryogenic temperatures. Room temperature approaches targeting diamonds with nitrogen-vacancy centres could alleviate this need; however, hitherto proposed strategies lack generality as they demand stringent conditions on the strength and/or alignment of the magnetic field. We report here an approach for achieving efficient electron-(13)C spin-alignment transfers, compatible with a broad range of magnetic field strengths and field orientations with respect to the diamond crystal. This versatility results from combining coherent microwave- and incoherent laser-induced transitions between selected energy states of the coupled electron-nuclear spin manifold. (13)C-detected nuclear magnetic resonance experiments demonstrate that this hyperpolarization can be transferred via first-shell or via distant (13)Cs throughout the nuclear bulk ensemble. This method opens new perspectives for applications of diamond nitrogen-vacancy centres in nuclear magnetic resonance, and in quantum information processing.

Single spin optically detected magnetic resonance with 60-90 GHz (E-band) microwave resonators.

Magnetic resonance with ensembles of electron spins is commonly performed around 10 GHz, but also at frequencies above 240 GHz and in corresponding magnetic fields of over 9 T. However, experiments with single electron and nuclear spins so far only reach into frequency ranges of several 10 GHz, where existing coplanar waveguide structures for microwave (MW) delivery are compatible with single spin readout techniques (e.g., electrical or optical readout). Here, we explore the frequency range up to 90 GHz, with magnetic fields of up to ≈3 T for single spin magnetic resonance in conjunction with optical spin readout. To this end, we develop MW resonators with optical single spin access. In our case, rectangular 60-90 GHz (E-band) waveguides guarantee low-loss supply of microwaves to the resonators. Three dimensional cavities, as well as coplanar waveguide resonators, enhance MW fields by spatial and spectral confinement with a MW efficiency of 1.36 mT/√W. We utilize single nitrogen vacancy (NV) centers as hosts for optically accessible spins and show that their properties regarding optical spin readout known from smaller fields (<0.65 T) are retained up to fields of 3 T. In addition, we demonstrate coherent control of single nuclear spins under these conditions. Furthermore, our results extend the applicable magnetic field range of a single spin magnetic field sensor. Regarding spin based quantum registers, high fields lead to a purer product basis of electron and nuclear spins, which promises improved spin lifetimes. For example, during continuous single-shot readout, the (14)N nuclear spin shows second-long longitudinal relaxation times.

Fluorescence Polarization Switching from a Single Silicon Vacancy Colour Centre in Diamond.

Single-photon emitters with stable and uniform photoluminescence properties are important for quantum technology. However, in many cases, colour centres in diamond exhibit spectral diffusion and photoluminescence intensity fluctuation. It is therefore essential to investigate the dynamics of colour centres at the single defect level in order to enable the on-demand manipulation and improved applications in quantum technology. Here we report the polarization switching, intensity jumps and spectral shifting observed on a negatively charged single silicon-vacancy colour centre in diamond. The observed phenomena elucidate the single emitter dynamics induced by photoionization of nearby electron donors in the diamond.

Investigation of the silicon vacancy color center for quantum key distribution.

Single photon sources (SPS) are crucial for quantum key distribution. Here we demonstrate a stable triggered SPS at 738 nm with linewidth less than 5 nm at room temperature based on a negatively charged single silicon vacancy color center. Thanks to the short photon duration of about 1.3-1.7 ns, by using high repetition pulsed excitation at 30 MHz, the triggered single photon source generates 16.6 kcounts/s. And we discuss the feasibility of this triggered SPS in the application of quantum key distribution.

All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond.

The silicon-vacancy (SiV-) color center in diamond has attracted attention because of its unique optical properties. It exhibits spectral stability and indistinguishability that facilitate efficient generation of photons capable of demonstrating quantum interference. Here we show optical initialization and readout of electronic spin in a single SiV- center with a spin relaxation time of T1=2.4±0.2 ms. Coherent population trapping (CPT) is used to demonstrate coherent preparation of dark superposition states with a spin coherence time of T2⋆=35±3 ns. This is fundamentally limited by orbital relaxation, and an understanding of this process opens the way to extend coherence by engineering interactions with phonons. Hyperfine structure is observed in CPT measurements with the 29Si isotope which allows access to nuclear spin. These results establish the SiV- center as a solid-state spin-photon interface.

Magnetic resonance identification of hydrogen at a zinc vacancy in ZnO.

Hydrogen (H) at a zinc vacancy (VZn) in ZnO is identified by electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM). In ZnO irradiated by 2 MeV electrons, a doublet EPR spectrum, labelled S1, is observed. The doublet structure and the accompanying weak satellites are shown to be the allowed and forbidden lines of the hyperfine structure due to the dipolar interaction between an electron spin S = 1/2 and a nuclear spin I = 1/2 of (1)H located at a VZn. The involvement of a single H atom in the S1 defect is further confirmed by the observation of the nuclear Zeeman frequency of (1)H in ESEEM experiments. We show that at a VZn, H prefers to make a short O-H bond with one O neighbour and is off the substitutional site, forming a low symmetry C1 defect. In this partly H passivated VZn, the unpaired electron localizes on the p orbital of another O neighbour of VZn, and not on the H.