Nuclear spins in the solid state environment of diamond are highly coherent, but difficult to rapidly control due to the small nuclear gyromagnetic ratio. Here we demonstrate a more than 50-fold enhancement of the effective nuclear gyromagnetic ratio by coupling the nuclear spin to an electronic spin of a nitrogen-vacancy (NV) center in diamond. The enhancement allows for faster nuclear spin rotations and is in good agreement with second-order perturbation theory. The method may be applied to other systems with similar electron-nuclear spin interactions, such as phosphorous donors in silicon, opening up the possibility of fast and direct nuclear spin control in coupled spin systems.
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 relativ…
Hyperfine spectroscopy and fast, all-optical arbitrary state initialization and readout of a single, ten-level ${}^{73}$Ge vacancy nuclear spin qudit in diamond
We report a systematic study of the hyperfine interaction between the electron spin of a single nitrogen-vacancy (NV) defect in diamond and nearby $^{13}$C nuclear spins, by using pulsed electron spin resonance spectroscopy. We isolate a set of discrete values of the hyperfine coupling strength ranging from 14 MHz to 400 kHz and corresponding to $^{13}$C nuclear spins placed at different lattice sites of the diamond matrix. For each lattice site, the hyperfine interaction is further investigated through nuclear spin polarization measurements and by studying the magnetic field dependence of the…
Understanding the profile of a qubit's wavefunction is key to its quantum applications. Unlike conducting systems, where a scanning tunneling microscope can be used to probe the electron distribution, there is no direct method for solid-state-defect based qubits in wide-bandgap semiconductors. In this work, we use pressure as a tuning method and a nuclear spin as an atomic scale probe to monitor the hyperfine structure of negatively charged nitrogen vacancy (NV) centers in diamonds under pressure. We present a detailed study on the nearest-neighbor $^{13}C$ hyperfine splitting in the optically…
The nitrogen-vacancy (NV) center is a well utilized system for quantum technology, in particular quantum sensing and microscopy. Fully employing the NV center's capabilities for metrology requires a strong understanding of the behavior of the NV center with respect to changing temperature. Here, we probe the NV electronic spin density as the surrounding crystal temperature changes from 10 K to 700 K by examining its $^{13}$C hyperfine interactions. These results are corroborated with \textit{ab initio} calculations and demonstrate that the change in hyperfine interaction is small and dominated…
Coherent control and optical readout of the electron spin of the $^{29}$SiV$^{-}$ center in diamond has been demonstrated in literature, with exciting prospects for implementations as memory nodes and spin qubits. Nuclear spins may be even better suited for many applications in quantum information processing due to their long coherence times. Control of the $^{29}$SiV$^{-}$ nuclear spin using conventional NMR techniques is feasible, albeit at slow kilohertz rates due to the nuclear spin's low gyromagnetic ratio. In this work we theoretically demonstrate how indirect control using the electron …
Coherent population trapping (CPT) provides a highly sensitive means for probing the energy level structure of an atomic system. For a nitrogen vacancy center in diamond, the CPT offers an alternative to the standard optically-detected magnetic resonance method for measuring the hyperfine structure of the electronic ground states. We show that the nuclear spin dependent CPT measures directly the hyperfine splitting of these states due to the 14N nuclear spin. The CPT spectral response obtained in the presence of a strong microwave field, resonant or nearly resonant with a ground state spin tra…
We experimentally demonstrate high degree of polarization of 13C nuclear spins weakly interacting with nitrogen-vacancy (NV) centers in diamond. We combine coherent microwave excitation pulses with optical illumination to provide controlled relaxation and achieve a polarity-tunable, fast nuclear polarization of degree higher than 85% at room temperature for remote 13C nuclear spins exhibiting hyperfine interaction strength with NV centers of the order of 600 kHz. We show with the aid of numerical simulation that the anisotropic hyperfine tensor components naturally provide a route to control s…
The evolution of the polycrystalline pattern of electron paramagnetic resonance (EPR) spectra of intrinsic and induced paramagnetic centers in an ensemble of submicrometer diamond particles on diminishing average particle size is considered. Recent experimental data unambiguously demonstrate consistent reduction and then zeroing of typical hyperfine pattern from P1 centers on approaching a certain particle size and below it. These changes are accompanied by appearance and strengthening of new structureless signals. In small particles the electron wave function of a surface paramagnetic center …
We develop a quantum theory for a variety of nuclear spin dynamics such as dephasing, relaxation, squeezing, and narrowing due to the hyperfine interaction with a generic, dissipative electronic system. The first-order result of our theory reproduces and generalizes the nonlinear Hamiltonian for nuclear spin squeezing [M. S. Rudner, Phys. Rev. Lett. 107, 206806 (2011)]. The second-order result of our theory provides a good explanation to the experimentally observed $^{13}$C nuclear spin bath narrowing in diamond nitrogen-vacancy center [E. Togan, Nature 478, 497 (2011)
The negatively charged nitrogen-vacancy (NV$^-$) center in diamond is a model quantum system for university teaching labs due to its room-temperature compatibility and cost-effective operation. Based on the low-cost experimental setup that we have developed and described for the coherent control of the electronic spin (Sewani et al.), we introduce and explain here a number of more advanced experiments that probe the electron-nuclear interaction between the \nv electronic and the \NN~and \CC~nuclear spins. Optically-detected magnetic resonance (ODMR), Rabi oscillations, Ramsey fringe experiment…
Energy levels of nitrogen-vacancy centers in diamond were investigated using optically detected magnetic-resonance spectroscopy near the electronic ground-state level anticrossing (GSLAC) at an axial magnetic field around 102.4~mT in diamond samples with a nitrogen concentration of 1~ppm and 200~ppm. By applying radiowaves in the frequency ranges from 0 to 40 MHz and from 5.6 to 5.9 GHz, we observed transitions that involve energy levels mixed by the hyperfine interaction. We developed a theoretical model that describes the level mixing, transition energies, and transition strengths between th…
Progress with quantum technology has for a large part been realized with the nitrogen-vacancy centre in diamond. Part of its properties, however, are nonideal and this drives research into other spin-active crystal defects. Several of these come with much stronger energy scales for spin-orbit and hyperfine coupling, but how this affects their spin coherence is little explored. Vanadium in silicon carbide is such a system, with technological interest for its optical emission at a telecom wavelength and compatibility with semiconductor industry. Here we show coherent spin dynamics of an ensemble…
We present a theoretical scheme that allows to perform a universal set of holonomic gates on a two qubit register, formed by a $^{13}$C nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of $^{13}$C atoms allows to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.
Nuclear spins support long lived quantum coherence due to weak coupling to the environment, but are difficult to rapidly control using nuclear magnetic resonance (NMR) as a result of the small nuclear magnetic moment. We demonstrate a fast ~ 500 ns nuclear spin phase gate on a 14N nuclear spin qubit intrinsic to a nitrogen-vacancy (NV) center in diamond. The phase gate is enabled by the hyperfine interaction and off-resonance driving of electron spin transitions. Repeated applications of the phase gate bang-bang decouple the nuclear spin from the environment, locking the spin state for up to ~…
Nitrogen vacancy (NV-) color centers in diamond are a prime candidate for use in quantum information devices, owing to their spin-1 ground state, straightforward optical initialization and readout, and long intrinsic coherence times in a room-temperature solid. While the 13C nuclear spin is often a dominant source of magnetic noise, we observe transitions between electron-nuclear hyperfine states of NV- centers in 99% 13C diamond that are robust to decoherence. At magnetic field strengths ranging from 550 - 900 G, these transitions are observable by optically detected magnetic resonance (ODMR)…
We discuss the side resonances of optically detected magnetic resonance in diamond crystal and propose the new approach to the calculation of hyperfine interaction in composed system, consisted of negatively charged nitrogen-vacancy NV- center and nearby 13C nuclear spin. Energy levels and spin states are obtained by new method. The base of this method is the using of complete set of commuting operators. In zero magnetic field, predicted the existence of metastable excited state.
Solid-state magnetometers like the Nitrogen-Vacancy center in diamond have been of paramount importance for the development of quantum sensing with nanoscale spatial resolution. The basic protocol is a Ramsey sequence, that imprints an external static magnetic field into phase of the quantum sensor, which is subsequently readout. In this work we show that the hyperfine coupling between the Nitrogen-Vacancy and a nearby Carbon-13 can be used to set a post-selection protocol that leads to an enhancement of the sensitivity under realistic experimental conditions. We found that for an isotopically…
Continuous spectral hole burning and spin-level population oscillations are studied in an inhomogeneously broadened diamond-based spin ensemble composed of substitutional nitrogen and nitrogen-vacancy centres created through neutron irradiation and annealing. The burnt spectral features highlight a detuning-dependent homogeneous hole linewidth that is up to three orders of magnitude narrower than the total inhomogeneous ensemble linewidth. Continuous population oscillations are observed to quickly decay beyond a pump and probe detuning of 5 Hz, and are numerically modelled using a five-level s…
Generating robust entanglement among solid-state spins is key for applications in quantum information processing and precision sensing. We show here a dissipative approach to generate such entanglement among the hyperfine coupled electron nuclear spins using the rapid optical decay of electronic excited states. The combined dark state interference effects of the optical and microwave driving fields in the presence of spontaneous emission from the short-lived excited state leads to a dissipative formation of an entangled steady state. We show that the dissipative entanglement is generated for a…
The application of magnetic resonance (MR) spectroscopy at progressively smaller length scales may eventually permit "chemical imaging" of spins at the surfaces of materials and biological complexes. In particular, the negatively charged nitrogen-vacancy (NV-) centre in diamond has been exploited as an optical transducer for nanoscale nuclear magnetic resonance. However, the spectra of detected spins are generally broadened by their interaction with proximate paramagnetic NV- centres through coherent and incoherent mechanisms. Here we demonstrate a detection technique that can resolve the spec…
We report detection and coherent control of a single proton nuclear spin using an electronic spin of the nitrogen-vacancy (NV) center in diamond as a quantum sensor. In addition to determining the NV-proton hyperfine parameters by employing multipulse sequences, we polarize and coherently rotate the single proton spin, and detect an induced free precession. Observation of free induction decays is an essential ingredient for high resolution proton nuclear magnetic resonance, and the present work extends it to the atomic scale. We also discuss the origin of the proton as incorporation during che…
We study the coupling of a single nitrogen-vacancy center in diamond to a nearby single nitrogen defect at room temperature. The magnetic dipolar coupling leads to a splitting in the electron spin resonance frequency of the nitrogen-vacancy center, allowing readout of the state of a single nitrogen electron spin. At magnetic fields where the spin splitting of the two centers is the same we observe a strong polarization of the nitrogen electron spin. The amount of polarization can be controlled by the optical excitation power. We combine the polarization and the readout in time-resolved pump-pr…
Following the recent successful formation and manipulation of entangled $C^{13}$ atoms on the surface of Diamond we calculate the decoherence of the electron spin polarization in Diamond via a nonperturbative treatment of the time-dependent Greens function of the Central-Spin model, describing the phonon and Hyperfine couplings of the electron to a bath of $C^{13}$ atoms, for arbitrary initial polarizations, applied field strengths, and for up to eight entangled $C^{13}$ atoms. We compare these numerical results with the exact treatment available in the fully initially polarized limit of the n…
Pulsed ESR experiments are reported for ensembles of negatively-charged nitrogen-vacancy centers (NV$^-$) in diamonds at X-band magnetic fields (280-400 mT) and low temperatures (2-70 K). The NV$^-$ centers in synthetic type IIb diamonds (nitrogen impurity concentration $<1$~ppm) are prepared with bulk concentrations of $2\cdot 10^{13}$ cm$^{-3}$ to $4\cdot 10^{14}$ cm$^{-3}$ by high-energy electron irradiation and subsequent annealing. We find that a proper post-radiation anneal (1000$^\circ$C for 60 mins) is critically important to repair the radiation damage and to recover long electron spi…
Nitrogen-vacancy (NV) spin ensembles in diamond provide an advanced magnetic sensing platform, with applications in both the physical and life sciences. The development of isotopically engineered $^{15}$NV diamond offers advantages over naturally occurring $^{14}$NV for magnetometry, due to its simpler hyperfine structure. However, for sensing modalities requiring a bias magnetic field not aligned with the sensing NV axis, the absence of a quadrupole moment in the $^{15}$N nuclear spin leads to pronounced envelope modulation effects in time-dependent measurements of $^{15}$NV spin evolution. W…
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 having particularly strong hyperfine couplings. For 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 selec…
We present a thorough derivation of the excited state energy levels of the negatively charged $^{15}$N-V$^{-}$ center in diamond for the strong applied electric field case. We show that in the $^{15}$N-V$^{-}$ center a spin non-conserving two-photon $Λ$ transition exists that is mediated by the hyperfine interaction, which provides the possibility to write quantum information. Using second order perturbation theory we obtain a $Λ$ transition rate of the order of 10 MHz at room temperature, which allows for approximately $10^4$ quantum logic operations within the spin coherence time $τ_d(T=300 …
Spin complexes comprising the nitrogen-vacancy (NV) center and neighboring spins are being considered as a building block for a new generation of spintronic and quantum information processing devices. Because assembling identical spin clusters is difficult, new strategies are in order to determine individual node structures with the highest precision. Here we use a pulse protocol to monitor the time evolution of the 13C ensemble in the vicinity of a NV center. We observe long-lived time correlations in the nuclear spin dynamics, limited by NV spin-lattice relaxation. We use the host 14N spin a…
Color-center-hosting semiconductors are emerging as promising source materials for low-field dynamic nuclear polarization (DNP) at or near room temperature, but hyperfine broadening, susceptibility to magnetic field heterogeneity, and nuclear spin relaxation induced by other paramagnetic defects set practical constraints difficult to circumvent. Here, we explore an alternate route to color-center-assisted DNP using nitrogen-vacancy (NV) centers in diamond coupled to substitutional nitrogen impurities, the so-called P1 centers. Working near the level anti-crossing condition - where the P1 Zeema…
We study both theoretically and experimentally the free induction decay (FID) of the electron spin associated with a single nitrogen-vacancy defect in high purity diamond, where the main source of decoherence is the hyperfine interaction with a bath of $^{13}$C nuclear spins. In particular, we report a systematic study of the FID signal as a function of the strength of a magnetic field oriented along the symmetry axis of the defect. On average, an increment of the coherence time by a factor of $\sqrt{5/2}$ is observed at high magnetic field in diamond samples with a natural abundance of $^{13}…
Sensing single nuclear spins is a central challenge in magnetic resonance based imaging techniques. Although different methods and especially diamond defect based sensing and imaging techniques in principle have shown sufficient sensitivity, signals from single nuclear spins are usually too weak to be distinguished from background noise. Here, we present the detection and identification of remote single C-13 nuclear spins embedded in nuclear spin baths surrounding a single electron spins of a nitrogen-vacancy centre in diamond. With dynamical decoupling control of the centre electron spin, the…
A negatively charged nitrogen vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quant…
Deep cooling of electron and nuclear spins is equivalent to achieving polarization degrees close to 100% and is a key requirement in solid state quantum information technologies. While polarization of individual nuclear spins in diamond and SiC reaches 99% and beyond, it has been limited to 60-65% for the nuclei in quantum dots. Theoretical models have attributed this limit to formation of coherent "dark" nuclear spin states but experimental verification is lacking, especially due to the poor accuracy of polarization degree measurements. Here we measure the nuclear polarization in GaAs/AlGaAs …
A broad effort is underway to improve the sensitivity of nuclear magnetic resonance through the use of dynamic nuclear polarization. Nitrogen-vacancy (NV) centers in diamond offer an appealing platform because these paramagnetic defects can be optically polarized efficiently at room temperature. However, work thus far has been mainly limited to single crystals because most polarization transfer protocols are sensitive to misalignment between the NV and magnetic field axes. Here we study the spin dynamics of NV-13C pairs in the simultaneous presence of optical excitation and microwave frequency…
We experimentally demonstrate the use of a single electronic spin to measure the quantum dynamics of distant individual nuclear spins from within a surrounding spin bath. Our technique exploits coherent control of the electron spin, allowing us to isolate and monitor nuclear spins weakly coupled to the electron spin. Specifically, we detect the evolution of distant individual carbon-13 nuclear spins coupled to single nitrogen vacancy centers in a diamond lattice with hyperfine couplings down to a factor of 8 below the electronic spin bare dephasing rate. Potential applications to nanoscale mag…
We theoretically study the decoherence and the dynamical decoupling control of nitrogen-vacancy center electron spins in high-purity diamond, where the hyperfine interaction with $^{13}$C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flip-flops. The importance of different elementary processes…
We study the spin dynamics of diamond nitrogen vacancy (NV) centers in an oscillating magnetic field along the symmetry axis of the NV in the presence of transverse magnetic fields. It is well-known that the coupling between the otherwise degenerate Zeeman levels $|M_S=\pm1\rangle$ due to strain and electric fields is responsible for a Landau-Zener process near the pseudo-crossing of the adiabatic energy levels when the axial component of the oscillating magnetic field changes sign. We derive an effective two-level Hamiltonian for the NV system that includes coupling between the two levels via…
We report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to 13C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time T1 of the NV center at millikelvin temperatures in a non-destructive way.
Understanding fully the dynamics of coupled electron-nuclear spin systems, which are important for the development of long-lived qubits based on solid-state systems, remains a challenge. We show that in a singly charged semiconductor quantum dot with inhomogeneous hyperfine coupling, the nuclear spins relatively strongly coupled to the electron spin form a polarized core during the dynamical polarization process. The polarized core provides a protection effect against the electron spin relaxation, reducing the decay rate by a factor of $N_1$, the number of the nuclear spins in the polarized co…
This work introduces the so-called synchrosqueezed wavelet transform, to shed light on the dipolar fluctuations of a thermal ensemble of nuclear spins in a diamond crystal structure, hyperfine-coupled to a central spin. The raw time series of the nuclear spin bath coherent dynamics is acquired through the two-point correlation function computed using the cluster correlation expansion method. The dynamics can be conveniently analyzed according to zero-, single-, and double-quantum transitions derived from the dipolar pairwise spin flips. We show that in the early-time behavior when the coherenc…
We investigate the dynamic nuclear polarization process by frequently injecting polarized electron spins into a quantum dot. Due to the suppression of the direct dipolar and indirect electron-mediated nuclear spin interactions, by the frequently injected electron spins, the analytical predictions under the independent spin approximation agree well with quantum numerical simulations. Our results show that the acquired nuclear polarization is highly inhomogeneous, proportional to the square of the local electron-nuclear hyperfine interaction constant, if the injection frequency is high. Utilizin…
Optically interfaced spins in the solid promise scalable quantum networks. Robust and reliable optical properties have so far been restricted to systems with inversion symmetry. Here, we release this stringent constraint by demonstrating outstanding optical and spin properties of single silicon vacancy centres in silicon carbide. Despite the lack of inversion symmetry, the system's particular wave function symmetry decouples its optical properties from magnetic and electric fields, as well as from local strain. This provides a high-fidelity spin-to-photon interface with exceptionally stable an…
We propose a strategy to measure weak static magnetic fields with nitrogen-vacancy color center in diamond. Inspired by avian magnetoreception models, we consider the feasibility of utilizing quantum coherence phenomena to measure weak static magnetic fields. Nitrogen-vacancy (NV) color centers are regarded as the ideal platform to study quantum sciences as a result of its long coherence time up to a millisecond timescale. In high-purity diamond, hyperfine interaction with 13C nuclear spins dominates the decoherence process. In this paper, we numerically simulate the decoherence process betwee…
Hybrid qubit systems combining electronic spins with nearby ("proximate") nuclear spin registers offer a promising avenue towards quantum information processing, with even multi-spin error correction protocols recently demonstrated in diamond. However, for the important platform offered by spins of donor atoms in cryogenically-cooled silicon,decoherence mechanisms of $^{29}$Si proximate nuclear spins are not yet well understood.The reason is partly because proximate spins lie within a so-called "frozen core" region where the donor electronic hyperfine interaction strongly suppresses nuclear dy…
Erbium implanted silicon as a quantum technology platform has both telecommunications and integrated circuit (IC) processing compatibility. The electron spin coherence time of Er implanted Si with an Er concentration of 3X1017 cm-3 is measured to be ~10 μs at 5 K and the spin echo decay profile displays strong modulation due to super-hyperfine interaction with 29Si nuclei. Three independent measurements: temperature quenching of photoluminescence (PL), PL lifetime and photo-illuminated electron spin resonance (ESR) all indicate the presence of a previously unreported Er related defect state wh…
We use field-cycling-assisted dynamic nuclear polarization and continuous radio-frequency (RF) driving over a broad spectral range to demonstrate magnetic-field-dependent activation of nuclear spin transport from strongly-hyperfine-coupled 13C sites in diamond. We interpret our observations with the help of a theoretical framework where nuclear spin interactions are mediated by electron spins. In particular, we build on the results from a 4-spin toy model to show how otherwise localized nuclear spins must thermalize as they are brought in contact with a larger ancilla spin network. Further, by…
We consider the problem of determining the spectrum of an electronic spin via polarization transfer to coupled nuclear spins and their subsequent readout. This suggests applications for employing dynamic nuclear polarization (DNP) for "ESR-via-NMR". In this paper, we describe the theoretical basis for this process by developing a model for the evolution dynamics of the coupled electron-nuclear system through a cascade of Landau-Zener anti-crossings (LZ-LACs). We develop a method to map these traversals to the operation of an equivalent "Galton board". Here, LZ-LAC points serve as analogues to …
Similar to nitrogen-vacancy centers in diamond and impurity atoms in silicon, interstitial gallium deep paramagnetic centers in GaAsN have been proven to have useful characteristics for the development of spintronic devices. Among other interesting properties, under circularly polarized light, gallium centers in GaAsN act as spin filters that dynamically polarize free and bound electrons reaching record spin polarizations (100\%). Furthermore, the recent observation of the amplification of the spin filtering effect under a Faraday configuration magnetic field has suggested that the hyperfine i…
