Although a nuclear spin is weakly coupled to its environment, due to its small gyromagnetic ratio, its coherence time is limited by the hyperfine coupling to a nearby noisy electron. Here, we propose to utilize continuous dynamical decoupling to refocus the coupling to the electron. If the random phase accumulated by the nuclear spin through the reduced coupling terms is sufficient small, we can increase the nuclear coherence time. Initially, we demonstrate this on a simple case with a two-level electron spin, while taking all relevant hyperfine coupling terms and noise terms into account. We then extend the analysis to a nitrogen-vacancy center in diamond having a three level structure.
Isolated nuclear spins offer a promising building block for quantum information processing systems, but their weak interactions often impede preparation, control, and detection. Hyperfine coupling to a proximal electronic spin can enhance each of these processes. Using the electronic spin of the nitrogen-vacancy center as an intermediary, we demonstrate robust initialization, single-qubit manipulation, and direct optical readout of 13C, 15N, and 14N nuclear spins in diamond. These results pave the way for nitrogen nuclear spin based quantum information architectures in diamond.
We report a versatile method to efficiently polarize single nuclear spins in diamond, which is based on optical pumping of a single NV color center and mediated by a level-anti crossing in its excited state. A nuclear spin polarization higher than 98% is achieved at room temperature for the 15N nuclear spin associated to the NV center, corresponding to $μ$K effective nuclear spin temperature. We then show simultaneous deterministic initialization of two nuclear spins (13C and 15N) in close vicinity to a NV defect. Such robust control of nuclear spin states is a key ingredient for further scali…
By removing a $^{12}C$ atom from the tetrahedral configuration of the diamond, replace it by a $^{13}C$ atom, and repeating this in a linear direction, it is possible to have a linear chain of nuclear spins one half and to build a solid state quantum computer. One qubit rotation and controlled-not (CNOT) quantum gates are obtained immediately from this configuration, and CNOT quantum gate is used to determined the design parameters of this quantum computer.
Efficiently detecting and characterizing individual spins in solid-state hosts is an essential step to expand the fields of quantum sensing and quantum information processing. While selective detection and control of a few 13C nuclear spins in diamond have been demonstrated using the electron spin of nitrogen-vacancy (NV) centers, a reliable, efficient, and automatic characterization method is desired. Here, we develop an automated algorithmic method for decomposing spectral data to identify and characterize multiple nuclear spins in diamond. We demonstrate efficient nuclear spin identificatio…
We report polarization of a dense nuclear-spin ensemble in diamond and its dependence on magnetic field and temperature. The polarization method is based on the transfer of electron spin polarization of negatively charged nitrogen vacancy color centers to the nuclear spins via the excited-state level anti-crossing of the center. We polarize 90% of the 14N nuclear spins within the NV centers, and 70% of the proximal 13C nuclear spins with hyperfine interaction strength of 13-14 MHz. Magnetic-field dependence of the polarization reveals sharp decrease in polarization at specific field values cor…
Nuclear spins in solids exhibit long coherence times due to the small nuclear gyromagnetic ratio. This weak environmental coupling comes at the expense of slow quantum gate operations, which should be as fast as possible for many applications in quantum information processing and sensing. In this work, we use nitrogen-vacancy (NV) centers in diamond to probe the nuclear spins within dark paramagnetic nitrogen defects (P1 centers) in the diamond lattice. The gyromagnetic ratio of the P1 nuclear spin is augmented by hyperfine coupling to the electron spin, resulting in greatly enhanced coupling …
Nuclear spin ensembles in diamond are promising candidates for quantum sensing applications, including rotation sensing. Here we perform a characterization of the optically detected nuclear-spin transitions associated with the 14N nuclear spin within diamond nitrogen vacancy (NV) centers. We observe nuclear-spin-dependent fluorescence with the contrast of optically detected 14N nuclear Rabi oscillations comparable to that of the NV electron spin. Using Ramsey spectroscopy, we investigate the temperature and magnetic-field dependence of the nuclear spin transitions in the 77.5-420 K and 350-675…
We propose a protocol that achieves arbitrary N-qubit interactions between nuclear spins and that can measure directly nuclear many-body correlators by appropriately making the nuclear spins interact with a nitrogen vacancy (NV) center electron spin. The method takes advantage of recently introduced dynamical decoupling techniques and demonstrates that action on the electron spin is sufficient to fully exploit nuclear spins as robust quantum registers. Our protocol is general, being applicable to other nuclear spin based platforms with electronic spin defects acting as mediators as the case of…
The coherent behavior of the single electron and single nuclear spins of a defect center in diamond and a 13C nucleus in its vicinity, respectively, are investigated. The energy levels associated with the hyperfine coupling of the electron spin of the defect center to the 13C nuclear spin are analyzed. Methods of magnetic resonance together with optical readout of single defect centers have been applied in order to observe the coherent dynamics of the electron and nuclear spins. Long coherence times, in the order of microseconds for electron spins and tens of microseconds for nuclear spins, re…
We report on Fourier spectroscopy experiments performed with near-surface nitrogen-vacancy centers in a diamond chip. By detecting the free precession of nuclear spins rather than applying a multipulse quantum sensing protocol, we are able to unambiguously identify the NMR species devoid of harmonics. We further show that by engineering different Hamiltonians during free precession, the hyperfine coupling parameters as well as the nuclear Larmor frequency can be selectively measured with high precision (here 5 digits). The protocols can be combined to demonstrate two-dimensional Fourier spectr…
We investigate nuclear spin hyperpolarization from nitrogen vacancy centers in isotopically enriched diamonds with $^{13}$C concentrations up to 100%. $^{13}$C enrichment leads to hyperfine structure of the nitrogen vacancy electron spin resonance spectrum and as a result the spectrum of dynamic nuclear polarization. We show that strongly-coupled $^{13}$C spins in the first shell surrounding a nitrogen vacancy center generate resolved hyperfine splittings, but do not act as an intermediary in the transfer of hyperpolarization of bulk nuclear spins. High levels of $^{13}$C enrichment are desira…
Precise characterization of a hyperfine interaction is a prerequisite for high fidelity manipulations of electron and nuclear spins belonging to a hybrid qubit register in diamond. Here, we demonstrate a novel scheme for determining a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes, by applying it to the system of a Nitrogen Vacancy (NV) center and a $^{13}$C nuclear spin in the 1$^{\mathrm{st}}$ shell. The zero-quantum Ramsey fringe, analogous to the quantum beat in a $Λ$-type level structure, particularly enhances the measurement precision for non-secular hyperfin…
We address a problem of generating a robust entangling gate between electronic and nuclear spins in the system of a single nitrogen-vacany centre coupled to a nearest Carbon-13 atom in diamond against certain types of systematic errors such as pulse-length and off-resonance errors. We analyse the robustness of various control schemes: sequential pulses, composite pulses and numerically-optimised pulses. We find that numerically-optimised pulses, produced by the gradient ascent pulse engineering algorithm (GRAPE), are more robust than the composite pulses and the sequential pulses. The optimise…
Recently, magnetic field sensors based on an electron spin of a nitrogen vacancy (NV) center in diamond have been studied both from an experimental and theoretical point of view. This system provides a nanoscale magnetometer, and it is possible to detect a precession of a single spin. In this paper, we propose a sensor consisting of an electron spin and a nuclear spin in diamond. Although the electron spin has a reasonable interaction strength with magnetic field, the coherence time of the spin is relatively short. On the other hand, the nuclear spin has a longer life time while the spin has a…
In this work, we demonstrate initialization and readout of nuclear spins via a negatively charged silicon-vacancy (SiV) electron spin qubit. Under Hartmann-Hahn conditions the electron spin polarization is coherently transferred to the nuclear spin. The readout of the nuclear polarization is observed via the fluorescence of the SiV. We also show that the coherence time of the nuclear spin (6 ms) is limited by the electron spin-lattice relaxation due to the hyperfine coupling to the electron spin. This work paves the way towards realization of building blocks of quantum hardware with an efficie…
In this article we investigate the dynamics of a single negatively charged nitrogen-vacancy center (NV-) coupled to the spin of the nucleus of a 15-nitrogen atom and show that high fidelity gate operations are possible without the need for complicated composite pulse sequences. These operations include both the electron and nuclear spin rotations, as well as an entangling gate between them. These are experimentally realizable gates with current technology of sufficiently high fidelities that they can be used to build graph states for quantum information processing tasks.
We experimentally demonstrate an approach to scale up quantum devices by harnessing spin defects in the environment of a quantum probe. We follow this approach to identify, locate, and control two electron-nuclear spin defects in the environment of a single nitrogen-vacancy center in diamond. By performing spectroscopy at various orientations of the magnetic field, we extract the unknown parameters of the hyperfine and dipolar interaction tensors, which we use to locate the two spin defects and design control sequences to initialize, manipulate, and readout their quantum state. We finally crea…
High-Sensitivity Optical Detection of Electron-Nuclear Spin Clusters in Diamond
École Normale Supérieure, PSL Research University, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院、PSL研究大学、法国国家科学研究中心、索邦大学、巴黎西岱大学）；Laboratoire Charles Coulomb, Université de Montpellier, CNRS（夏尔·库隆实验室、蒙彼利埃大学、法国国家科学研究中心）
A rotation sensor is one of the key elements of inertial navigation systems and compliments most cellphone sensor sets used for various applications. Currently, inexpensive and efficient solutions are mechanoelectronic devices, which nevertheless lack long-term stability. Realization of rotation sensors based on spins of fundamental particles may become a drift-free alternative to such devices. Here, we carry out a proof-of-concept experiment, demonstrating rotation measurements on a rotating setup utilizing nuclear spins of an ensemble of NV centers as a sensing element with no stationary ref…
Initializing a set of qubits to a given quantum state is a basic prerequisite for the physical implementation of quantum-information protocols. Here, we discuss the polarization of the electronic and nuclear spin in a single nitrogen vacancy center in diamond. Our initialization scheme uses a sequence of laser, microwave and radio-frequency pulses, and we optimize the pumping parameters of the laser pulse. A rate equation model is formulated that explains the effect of the laser pulse on the spin system. We have experimentally determined the population of the relevant spin states as a function…
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, …
Nuclear spins in certain solids couple weakly to their environment, making them attractive candidates for quantum information processing and inertial sensing. When coupled to the spin of an optically-active electron, nuclear spins can be rapidly polarized, controlled and read via lasers and radiofrequency fields. Possessing coherence times of several milliseconds at room temperature, nuclear spins hosted by a nitrogen-vacancy center in diamond are thus intriguing systems to observe how classical physical rotation at quantum timescales affects a quantum system. Unlocking this potential is hampe…
One of the most remarkable properties of the nitrogen-vacancy (NV) center in diamond is that optical illumination initializes its electronic spin almost completely, a feature that can be exploited to polarize other spin species in their proximity. Here we use field-cycled nuclear magnetic resonance (NMR) to investigate the mechanisms of spin polarization transfer from NVs to 13C spins in diamond at room temperature. We focus on the dynamics near 51 mT, where a fortuitous combination of energy matching conditions between electron and nuclear spin levels gives rise to alternative polarization tr…
Nuclear spins nearby nitrogen-vacancy (NV) centers in diamond are excellent quantum memory for quantum computing and quantum sensing, but are difficult to be initialized due to their weak interactions with the environment. Here we propose and demonstrate a magnetic-field-independent, deterministic and highly efficient polarization scheme by introducing chopped laser pulses into the double-resonance initialization method. With this method, we demonstrate initialization of single-nuclear-spin approaching $98.1\%$ and a $^{14}N$-$^{13}C$ double-nuclear-spin system approaching $96.8\%$ at room tem…
We report sensitive detection of the nuclear quadrupolar interaction of the 14N nuclear spin of the nitrogen-vacancy (NV) center using the electron spin echo envelope modulation technique. We applied a weak transverse magnetic field to the spin system so that certain forbidden transitions became weakly allowed due to second-order effects involving the nonsecular terms of the hyperfine interaction. The weak transitions cause modulation of the electron spin-echo signal, and a theoretical analysis suggests that the modulation frequency is primarily determined by the nuclear quadrupolar frequency;…
Hybrid quantum registers consisting of different types of qubits offer a range of advantages as well as challenges. The main challenge is that some types of qubits react only slowly to external control fields, thus considerably slowing down the information processing operations. One promising approach that has been tested in a number of cases is to use indirect control, where external fields are applied only to qubits that interact strongly with resonant excitation pulses. Here we use this approach to indirectly control the nuclear spins of an NV center, using microwave pulses to drive the ele…
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)
Most of dynamic nuclear polarization (DNP) has been requiring helium cryogenics and strong magnetic fields for a high degree of polarization. In this work, we instead demonstrate an optical hyperpolarization of naturally abundant $^{13}$C nuclei in a diamond crystal at a low magnetic field and an ambient temperature. It exploits continuous irradiations of pump laser for polarizing electron spins of nitrogen vacancy centers and microwave for transferring the induced polarization to $^{13}$C nuclear spins. Triplet structures corresponding to $^{14}$N hyperfine splitting were clearly observed in …
Quantum memories provide intermediate storage of quantum information until it is needed for the next step of a quantum algorithm or a quantum communication process. Relevant figures of merit are therefore the fidelity with which the information can be written and retrieved, the storage time, and also the speed of the read-write process. Here, we present experimental data on a quantum memory consisting of a single $^{13}$C nuclear spin that is strongly coupled to the electron spin of a nitrogen-vacancy (NV) center in diamond. The strong hyperfine interaction of the nearest-neighbor carbon resul…
We probe dephasing mechanisms within a quantum network node consisting of a single nitrogen-vacancy centre electron spin that is hyperfine coupled to surrounding $^{13} \text{C}$ nuclear-spin quantum memories. Previous studies have analysed memory dephasing caused by the stochastic electron-spin reset process, which is a component of optical internode entangling protocols. Here, we find, by using dynamical decoupling techniques and exploiting phase matching conditions in the electron-nuclear dynamics, that control infidelities and quasi-static noise are the major contributors to memory dephasi…
We studied the dynamic nuclear spin polarization of nitrogen in negatively charged nitrogen-vacancy (NV) centers in diamond both experimentally and theoretically over a wide range of magnetic fields from 0 to 1100 G covering both the excited-state level anti-crossing and the ground-state level anti-crossing magnetic field regions. Special attention was paid to the less studied ground-state level anti-crossing region. The nuclear spin polarization was inferred from measurements of the optically detected magnetic resonance signal. These measurements show that a very large (up to $96 \pm 2\%$) nu…
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 ~…
A hybrid quantum register consisting of nuclear spins in a solid-state platform coupled to a central electron spin is expected to combine the advantages of its elements. However, the potential to exploit long nuclear spin coherence times is severely limited by magnetic noise from the central electron spin during external interrogation. We overcome this obstacle and present protocols for addressing a decoherence-free nuclear spin subspace, which was not accessible by previously existing methods. We demonstrate the efficacy of our protocols using detailed numerical simulations of a nitrogen-vaca…
We use the electronic spin of a single Nitrogen-Vacancy (NV) defect in diamond to observe the real-time evolution of neighboring single nuclear spins under ambient conditions. Using a diamond sample with a natural abundance of $^{13}$C isotopes, we first demonstrate high fidelity initialization and single-shot readout of an individual $^{13}$C nuclear spin. By including the intrinsic $^{14}$N nuclear spin of the NV defect in the quantum register, we then report the simultaneous observation of quantum jumps linked to both nuclear spin species, providing an efficient initialization of the two qu…
The integration of NMR and high pressure technique brings unique opportunities to study electronic, structural and dynamical properties under extreme conditions. Despite a great degree of success has been achieved using coil-based schemes, the contradictory requirement on sample volume of these two techniques remains an outstanding challenge. In this letter, we introduce diamond nitrogen-vacancy (NV) centers, as the source and probe of in-situ nuclear spin polarization, to address the sample volume issue. We demonstrate hyperpolarization and coherent control of $^{14}$N nuclear spins under hig…
We demonstrate electrical detection of the $^{14}$N nuclear spin coherence of NV centers at room temperature. Nuclear spins are candidates for quantum memories in quantum-information devices and quantum sensors, and hence the electrical detection of nuclear spin coherence is essential to develop and integrate such quantum devices. In the present study, we used a pulsed electrically detected electron-nuclear double resonance technique to measure the Rabi oscillations and coherence time ($T_2$) of $^{14}$N nuclear spins in NV centers at room temperature. We observed $T_2 \approx$ 0.9 ms at room …
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 …
Zero-field identification and control of hydrogen-related electron-nuclear spin registers in diamond
Massachusetts Institute of Technology（麻省理工学院）；Quantum Innovation Centre, Agency for Science, Technology and Research（科学技术研究局量子创新中心）；University of Waterloo（滑铁卢大学）
Low thermal polarization of nuclear spins is a primary sensitivity limitation for nuclear magnetic resonance. Here we demonstrate optically pumped (microwave-free) nuclear spin polarization of $^{13}\mathrm{C}$ and $^{15}\mathrm{N}$ in $^{15}\mathrm{N}$-doped diamond. $^{15}\mathrm{N}$ polarization enhancements up to $-2000$ above thermal equilibrium are observed in the paramagnetic system $\mathrm{N_s}^{0}$. Nuclear spin polarization is shown to diffuse to bulk $^{13}\mathrm{C}$ with NMR enhancements of $-200$ at room temperature and $-500$ at $\mathrm{240~K}$, enabling a route to microwave-f…
The sensitivity of Magnetic Resonance Imaging (MRI) depends strongly on nuclear spin polarisation and, motivated by this observation, dynamical nuclear spin polarisation has recently been applied to enhance MRI protocols (Kurhanewicz, J., et al., Neoplasia 13, 81 (2011)). Nuclear spins associated with the 13 C carbon isotope (nuclear spin I = 1/2) in diamond possess uniquely long spin lattice relaxation times (Reynhardt, E.C. and G.L. High, Prog. in Nuc. Mag. Res. Sp. 38, 37 (2011)) If they are present in diamond nanocrystals, especially when strongly polarised, they form a promising contrast …
We introduce an alternate route to dynamically polarize the nuclear spin host of nitrogen-vacancy (NV) centers in diamond. Our approach articulates optical, microwave and radio-frequency pulses to recursively transfer spin polarization from the NV electronic spin. Using two complementary variants of the same underlying principle, we demonstrate nitrogen nuclear spin initialization approaching 80% at room temperature both in ensemble and single NV centers. Unlike existing schemes, our approach does not rely on level anti-crossings and is thus applicable at arbitrary magnetic fields. This versat…
A collapse and revival shape of Rabi oscillations of a single Nitrogen-Vacancy (NV) center electron spin has been observed in diamond at room temperature. Because of hyperfine interaction between the host 14N nuclear spin and NV center electron spin, different orientation of the 14N nuclear spin leads to a triplet splitting of the transition between the ground ms=0 and excited states ms=1. Microwave can excite the three transitions equally to induce three independent nutations and the shape of Rabi oscillations is a combination of the three nutations. This result provides an innovative view of…
Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this p…
Solid-state quantum registers are exceptional for storing quantum information at room temperature with long coherence time. Nevertheless, practical applications toward quantum supremacy require even longer coherence time to allow for more complex algorithms. In this work we propose a quantum register that lies in a decoherence-free subspace to be implemented with color centers in diamond. The quantum information is encoded in two logical states composed of two nearby nuclear spins, while an electron spin is used as ancilla for initialization and control. Moreover, by tuning an off-axis magneti…
