Room-temperature control and electrical readout of individual nitrogen-vacancy nuclear spins
Michal Gulka, Daniel Wirtitsch, Viktor Ivády, Jelle Vodnik, Jaroslav Hruby, Goele Magchiels, Emilie Bourgeois, Adam Gali, Michael Trupke, Milos Nesladek
Nuclear spins in semiconductors are leading candidates for quantum technologies, including quantum computation, communication, and sensing. Nuclear spins in diamond are particularly attractive due to their extremely long coherence lifetime. With the nitrogen-vacancy (NV) centre, such nuclear qubits benefit from an auxiliary electronic qubit, which has enabled entanglement mediated by photonic links. The transport of quantum information by the electron itself, via controlled transfer to an adjacent centre or via the dipolar interaction, would enable even faster and smaller processors, but optical readout of arrays of such nodes presents daunting challenges due to the required sub-diffraction inter-site distances. Here, we demonstrate the electrical readout of a basic unit of such systems - a single 14N nuclear spin coupled to the NV electron. Our results provide the key ingredients for quantum gate operations and electrical readout of nuclear qubit registers, in a manner compatible with nanoscale electrode structures. This demonstration is therefore a milestone towards large-scale diamond quantum devices with semiconductor scalability.
Nitrogen-vacancy centers in diamond, being a promising candidate for quantum information processing, may also be an ideal platform for simulating many-body physics. However, it is difficult to realize interactions between nitrogen-vacancy centers strong enough to form a macroscopically ordered phase under realistic temperatures. Here we propose a scheme to realize long-range ferromagnetic Ising interactions between distant nitrogen-vacancy centers by using a mechanical resonator as a medium. Since the critical temperature in the long-range Ising model is proportional to the number of spins, a …
The diamond nitrogen-vacancy (NV) center is a leading platform for quantum information science due to its optical addressability and room-temperature spin coherence. However, measurements of the NV center's spin state typically require averaging over many cycles to overcome noise. Here, we review several approaches to improve the readout performance and highlight future avenues of research that could enable single-shot electron-spin readout at room temperature.
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)
We show how nitrogen-vacancy centers can be used to `detect' magnetic fields, that is, to find out whether a magnetic field, about which we may not have complete information, is actually present or not. The solution to this problem comes from quantum state discrimination theory. The effect of decoherence is taken into account to optimize the time over which the nitrogen-vacancy center is allowed to interact with the magnetic field before making a measurement. We also find the optimum measurement that should be performed. We then show how multiple measurements reduce the error in detecting the …
We present a scheme of positioning a single electron spin with sub-nanometer resolution through multiple nitrogen-vacancy centers in diamond. With unwanted noise suppressed by dynamical decoupling, the spin coherence of each center develops characteristic oscillations due to a single electron spin located $4{\sim20}$ nm away from the centers. We can extract the position information from the characteristic electron spin-coherence oscillations of each center. This scheme is useful for high-resolution nanoscale magnetometry and spin-based quantum computing.
We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen vacancy center in the setting of coherent population trapping and by estimating magnetic field from the time series of the observed photon counts, which are correlated with the underlying field. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. By taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detec…
Fast quantum spin manipulation is needed to design spin-based quantum logic gates and other quantum applications. Here, we construct exact evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields and investigate the nonadiabatic geometric phases, both cyclic and non-cyclic, in these fast-manipulated NV spin systems. It is believed that the nonadiabatic geometric phases can be measured in future experiments and these fast quantum manipulations can be useful in designing spin-based quantum applications.
In order to better understand the underlying fundamental physical processes in nitrogen-vacancy centers in diamond, and to realize improvements in the use of this system for technological applications, it is imperative to gain new insight into the origins of the apparent inhomogeneous broadening. In this work we make use of a novel type of spectroscopy developed specifically for this task. The pump-probe spectroscopy closely follows Doppler-free spectroscopy used in atomic vapor. We show that the origin of inhomogeneous broadening comes from local magnetic field variations in the diamond latti…
Applications of negatively charged nitrogen-vacancy center in diamond exploit the center's unique optical and spin properties, which at ambient temperature, are predominately governed by electron-phonon interactions. Here, we investigate these interactions at ambient and elevated temperatures by observing the motional narrowing of the center's excited state spin resonances. We determine that the center's Jahn-Teller dynamics are much slower than currently believed and identify the vital role of symmetric phonon modes. Our results have pronounced implications for center's diverse applications (…
Nitrogen-Vacancy (NV) color centers in diamond have emerged as promising quantum solid-state systems, with applications ranging from quantum information processing to magnetic sensing. One of the most useful properties of NVs is the ability to read their ground-state spin projection optically at room temperature. This work provides a theoretical analysis of Purcell enhanced NV optical coupling, through which we find optimal parameters for maximal Signal to Noise Ratio (SNR) of the optical spin-state readout. We conclude that a combined increase in spontaneous emission (through Purcell enhancem…
We present an experimental and theoretical study of the optically detected magnetic resonance signals for ensembles of negatively charged nitrogen-vacancy (NV) centers in 13C isotopically enriched single-crystal diamond. We observe four broad transition peaks with superimposed sharp features at zero magnetic field and study their dependence on applied magnetic field. A theoretical model that reproduces all qualitative features of these spectra is developed. Understanding the magnetic-resonance spectra of NV centers in isotopically enriched diamond is important for emerging applications in nucl…
We present the development of an optically detected magnetic resonance (ODMR) system, which enables us to perform the ODMR measurements of a single defect in solids at high frequencies and high magnetic fields. Using the high-frequency and high-field ODMR system, we demonstrate 115 GHz continuous-wave and pulsed ODMR measurements of a single nitrogen-vacancy (NV) center in a diamond crystal at the magnetic field of 4.2 Tesla as well as investigation of field dependence ($0-8$ Tesla) of the longitudinal relaxation time ($T_1$) of NV centers in nanodiamonds.
We show that nitrogen-vacancy (NV) centers in diamond interfaced with a suspended carbon nanotube carrying a dc current can facilitate a spin-nanomechanical hybrid device. We demonstrate that strong magnetomechanical interactions between a single NV spin and the vibrational mode of the suspended nanotube can be engineered and dynamically tuned by external control over the system parameters. This spin-nanomechanical setup with strong, \emph{intrinsic} and \emph{tunable} magnetomechanical couplings allows for the construction of hybrid quantum devices with NV centers and carbon-based nanostructu…
The neutral charge state plays an important role in quantum information and sensing applications based on nitrogen-vacancy centers. However, the orbital and spin dynamics remain unexplored. Here, we use resonant excitation of single centers to directly reveal the fine structure, enabling selective addressing of spin-orbit states. Through pump-probe experiments, we find the orbital relaxation time (430ns at 4.7K) and measure its temperature-dependence up to 11.8K. Finally we reveal the spin relaxation time (1.5s), and realize projective high-fidelity single-shot readout of the spin state ($\geq…
We model the decoherence and dephasing of nitrogen vacancy (NV) centers in diamond due to a noisy paramagnetic bath, with and without the presence of a rf field that couples levels of the ground electronic state manifold, using a simple quantum mechanical model that allows for analytical solutions. The model treats the NV three-level ground state system in the presence of fluctuating magnetic fields that arise from the environment, and that result in decoherence, dephasing and dissipation. We show that all 9 eigenmodes of the three-level system are coupled to each other due to interaction with…
Recently we have demonstrated AC magnetic field sensing scheme using a simple continuous-wave optically detected magnetic resonance of nitrogen-vacancy centers in diamond [Appl. Phys. Lett. 113, 082405 (2018)]. This scheme is based on electronic spin double resonance excited by continuous microwaves and radio-frequency (RF) fields. Here we measured and analyzed the double resonance spectra and magnetic field sensitivity for various frequencies of microwaves and RF fields. As a result, we observed a clear anticrossing of RF-dressed electronic spin states in the spectra and estimated the bandwid…
Nitrogen-vacancy ensembles promise an unprecedented combination of sensitivity and resolution for magnetic field sensing under ambient conditions. However, their full sensing potential is limited by the inhomogeneous degradation of their collective coherence, while dynamical-decoupling limits sensing to the detection of AC-fields. Here we propose using the recently demonstrated cavity-protection effect for room-temperature, ensemble-based DC metrology. We identify a parameter space where strong-coupling can persist at room temperature and where the dressed states are limited solely by the deph…
We report on a planar microwave resonator providing arbitrarily polarized oscillating magnetic fields that enable selective excitation of the electronic spins of nitrogen-vacancy (NV) centers in diamond. The polarization plane is parallel to the surface of diamond, which makes the resonator fully compatible with (111)-oriented diamond. The field distribution is spatially uniform in a circular area with a diameter of 4 mm, and a near-perfect circular polarization is achieved. We also demonstrate that the original resonance frequency of 2.8 GHz can be varied in the range of 2-3.2 GHz by introduc…
We demonstrate optomechanical quantum control of the internal electronic states of a diamond nitrogen vacancy (NV) center in the resolved-sideband regime by coupling the NV to both optical fields and surface acoustic waves via a phonon-assisted optical transition and by taking advantage of the strong excited-state electron-phonon coupling of a NV center. Optomechanically-driven Rabi oscillations as well as quantum interferences between the optomechanical sideband and the direct dipole-optical transitions have been realized. These studies open the door to using resolved-sideband optomechanical …
Silicon carbide (SiC) has become a key player in realization of scalable quantum technologies due to its ability to host optically addressable spin qubits and wafer-size samples. Here, we have demonstrated optically detected magnetic resonance (ODMR) with resonant excitation, and clearly identified the ground state energy levels of the NV centers in 4H-SiC. Coherent manipulation of NV centers in SiC has been achieved with Rabi and Ramsey oscillations. Finally, we show the successful generation and characterization of single nitrogen vacancy (NV) center in SiC employing ion implantation. Our re…
In this review, we briefly overview recent works on hybrid (nano) opto-mechanical systems that contain both mechanical oscillators and diamond nitrogen-vacancy (NV) centers. We review two different types of mechanical oscillators. The first one is a clamped mechanical oscillator, such as a cantilever, with a fixed frequency. The second one is an optically trapped nano-diamond with a build-in nitrogen-vacancy center. By coupling mechanical resonators with electron spins, we can use the spins to control the motion of mechanical oscillators. For the first setup, we discuss two different coupling …
Nitrogen-Vacancy (NV) centers in diamond have been used in recent years for a wide range of applications, from nano-scale NMR to quantum computation. These applications depend strongly on the efficient readout of the NV center's spin state, which is currently limited. Here we suggest a method of reading the NV center's spin state, using the weak optical transition in the singlet manifold. We numerically calculate the number of photons collected from each spin state using this technique, and show that an order of magnitude enhancement in spin readout signal-to-noise ratio is expected, making si…
Nitrogen-vacancy (NV) centers are defects in diamonds, which, due to their electronic structure, have been extensively studied as magnetic field sensors. Such field detection applications usually employ the NV centers to detect field components aligned with the direction of the internally-defined spin axis of the NV center. In this work we detect magnetic fields which are slightly misaligned with the NV center axis. In particular, we demonstrate that the NV center can measure the square of the angle between the magnetic field and the NV center axis with high sensitivity which diverges as the e…
We investigate the correlation between surface roughness and corresponding $T_2$ times of nearsurface nitrogen-vacancy centers (~7 nm/ 5 keV implantation energy) in diamond. For this purpose we compare five different polishing techniques, including both purely mechanical as well as chemical mechanical approaches, two different substrate sources (Diam2tec and Element Six) and two different surface terminations (O- and H-termination) during nitrogen-vacancy forming. All coherence times are measured and compared before and after an oxygen surface treatment at 520 °C. We find that the coherence ti…
The core of a ferromagnetic vortex domain creates a strong, localized magnetic field which can be manipulated on nanosecond timescales, providing a platform for addressing and controlling individual nitrogen-vacancy center spins in diamond at room temperature, with nanometer-scale resolution. First, we show that the ferromagnetic vortex can be driven into proximity with a nitrogen-vacancy defect using small applied magnetic fields, inducing significant nitrogen-vacancy spin splitting. Second, we find that the magnetic field gradient produced by the vortex is sufficient to address spins separat…
Surface plasmon polaritons (SPPs) are locally excited at silver surfaces using (~100) nm-sized nanodiamonds (NDs) with multiple nitrogen-vacancy (NV) centers (~400). The fluorescence from an externally illuminated (at 532 nm) ND and from nearby NDs, which are not illuminated but produce out-of-plane scattering of SPPs excited by the illuminated ND, exhibit distinctly different wavelength spectra, showing short-wavelength filtering due to the SPP propagation loss. The results indicate that NDs with multiple NV centers can be used as efficient sub-wavelength SPP sources in planar integrated plas…
We demonstrate fully three-dimensional and patterned localization of nitrogen-vacancy (NV) centers in diamond with coherence times in excess of 1 ms. Nitrogen δ-doping during CVD diamond growth vertically confines nitrogen to 4 nm while electron irradiation with a transmission electron microscope (TEM) laterally confines vacancies to less than 1 μm. We characterize the effects of electron energy and dose on NV formation. Importantly, our technique enables the formation of reliably high-quality NV centers inside diamond nanostructures, with applications in quantum information and sensing.
We report a study of high-resolution microwave spectroscopy of nitrogen-vacancy centers in diamond crystals at and around zero magnetic field. We observe characteristic splitting and transition imbalance of the hyperfine transitions, which originate from level anti-crossings in the presence of a transverse effective field. We use pulsed electron spin resonance spectroscopy to measure the zero-field spectral features of single nitrogen-vacancy centers for clearly resolving such level anti-crossings. To quantitatively analyze the magnetic resonance behavior of the hyperfine spin transitions in t…
We present systematic measurements of longitudinal relaxation rates ($1/T_1$) of spin polarization in the ground state of the nitrogen-vacancy (NV$^-$) color center in synthetic diamond as a function of NV$^-$ concentration and magnetic field $B$. NV$^-$ centers were created by irradiating a Type 1b single-crystal diamond along the [100] axis with 200 keV electrons from a transmission electron microscope with varying doses to achieve spots of different NV$^-$ center concentrations. Values of ($1/T_1$) were measured for each spot as a function of $B$.
Nitrogen-vacancy centers in diamond allow for coherent spin state manipulation at room temperature, which could bring dramatic advances to nanoscale sensing and quantum information technology. We introduce a novel method for the optical measurement of the spin contrast in dense nitrogen-vacancy (NV) ensembles. This method brings a new insight into the interplay between the spin contrast and fluorescence lifetime. We show that for improving the spin readout sensitivity in NV ensembles, one should aim at modifying the far field radiation pattern rather than enhancing the emission rate.
Ensembles of nitrogen-vacancy centers in diamond are a highly promising platform for high-sensitivity magnetometry, whose efficacy is often based on efficiently generating and monitoring magnetic-field dependent infrared fluorescence. Here we report on an increased sensing efficiency with the use of a 532-nm resonant confocal cavity and a microwave resonator antenna for measuring the local magnetic noise density using the intrinsic nitrogen-vacancy concentration of a chemical-vapor deposited single-crystal diamond. We measure a near-shot-noise-limited magnetic noise floor of 200 pT/$\sqrt{\tex…
We study the longitudinal relaxation of a nitrogen-vacancy (NV) center surrounded by a $^{13}$C nuclear spin bath in diamond. By means of cluster-correlation expansion (CCE), we numerically demonstrate the decay process of electronic state induced by cross relaxation at low temperature. It is shown that the CCE method is not only capable of describing pure-dephasing effect at large-detuning regime, but it can also simulate the quantum dynamics of populations in the nearly resonant regime. We present a proposal to slow down the decay of NV center via implementing quantum Zeno effect (QZE). The …
The nuclear spin in the vicinity of a nitrogen-vacancy (NV) center possesses of long coherence time and convenient manipulation assisted by the strong hyperfine interaction with the NV center. It is suggested for the subsequent quantum information storage and processing after appropriate initialization. However, current experimental schemes are either sensitive to the inclination and magnitude of the magnetic field or require thousands of repetitions to achieve successful realization. Here, we propose polarizing a 13C nuclear spin in the vicinity of an NV center via a dark state. We demonstrat…
Individual, luminescent point defects in solids so called color centers are atomic-sized quantum systems enabling sensing and imaging with nanoscale spatial resolution. In this overview, we introduce nanoscale sensing based on individual nitrogen vacancy (NV) centers in diamond. We discuss two central challenges of the field: First, the creation of highly-coherent, shallow NV centers less than 10 nm below the surface of single-crystal diamond. Second, the fabrication of tip-like photonic nanostructures that enable efficient fluorescence collection and can be used for scanning probe imaging bas…
We demonstrate a robust, scale-factor-free vector magnetometer, which uses a closed-loop frequency-locking scheme to simultaneously track Zeeman-split resonance pairs of nitrogen-vacancy (NV) centers in diamond. Compared with open-loop methodologies, this technique is robust against fluctuations in temperature, resonance linewidth, and contrast; offers a three-order-of-magnitude increase in dynamic range; and allows for simultaneous interrogation of multiple transition frequencies. By directly detecting the resonance frequencies of NV centers aligned along each of the diamond's four tetrahedra…
We show that electric field noise from surface charge fluctuations can be a significant source of spin decoherence for near-surface nitrogen-vacancy (NV) centers in diamond. This conclusion is based on the increase in spin coherence observed when the diamond surface is covered with high-dielectric-constant liquids, such as glycerol. Double resonance experiments show that improved coherence occurs even though the coupling to nearby electron spins is unchanged when the liquid is applied. Multipulse spin echo experiments reveal the effect of glycerol on the spectrum of NV frequency noise.
In this paper, starting from a quantum master equation, we discuss the interaction between two negatively charged Nitrogen-vacancy color centers in diamond via exciton-polaritons propagating in a two-dimensional transition metal dichalcogenide layer in close proximity to a diamond crystal. We focus on the optical 1.945 eV transition and model the Nitrogen-vacancy color centers as two-level (artificial) atoms. We find that the interaction parameters and the energy levels renormalization constants are extremely sensitive to the distance of the Nitrogen-vacancy centers to the transition metal dic…
We present an experimental study of the longitudinal electron-spin relaxation of ensembles of negatively charged nitrogen-vacancy (NV ) centers in diamond. The measurements were performed with samples having different NV- concentrations and at different temperatures and magnetic fields. We found that the relaxation rate T1-1 increases when transition frequencies in NV- centers with different orientations become degenerate and interpret this as cross-relaxation caused by dipole-dipole interaction.
We show that nitrogen-vacancy (NV) centers in diamond can produce a novel quantum hyperbolic metamaterial. We demonstrate that a hyperbolic dispersion relation in diamond with NV centers can be engineered and dynamically tuned by applying a magnetic field. This quantum hyperbolic metamaterial with a tunable window for the negative refraction allows for the construction of a superlens beyond the diffraction limit. In addition to subwavelength imaging, this NV-metamaterial can be used in spontaneous emission enhancement, heat transport and acoustics, analogue cosmology, and lifetime engineering.…
We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a $T_{1}$ relaxation time that helps resolve the $T_{2} \leq 2T_{1}$ coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates $T_{1}$ of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate $1/f^α$ spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at materi…
