Nitrogen-vacancy Ensembles Research Articles

Ultralong Dephasing Times in Solid-State Spin Ensembles via Quantum Control

Quantum spin dephasing is caused by inhomogeneous coupling to the environment, with resulting limits to the measurement time and precision of spin-based sensors. The effects of spin dephasing can be especially pernicious for dense ensembles of electronic spins in the solid-state, such as for nitrogen-vacancy (NV) color centers in diamond. We report the use of two complementary techniques, spin bath control and double quantum coherence, to enhance the inhomogeneous spin dephasing time ($T_2^*$) for NV ensembles by more than an order of magnitude. In combination, these quantum control techniques (i) eliminate the effects of the dominant NV spin ensemble dephasing mechanisms, including crystal strain gradients and dipolar interactions with paramagnetic bath spins, and (ii) increase the effective NV gyromagnetic ratio by a factor of two. Applied independently, spin bath control and double quantum coherence elucidate the sources of spin dephasing over a wide range of NV and spin bath concentrations. These results demonstrate the longest reported $T_2^*$ in a solid-state electronic spin ensemble at room temperature, and outline a path towards NV-diamond magnetometers with broadband femtotesla sensitivity.

Coupled charge and spin dynamics in high-density ensembles of nitrogen-vacancy centers in diamond

We studied the spin depolarization of ensembles of nitrogen-vacancy (NV) centers in nitrogen-rich single-crystal diamonds. We found a strong dependence of the evolution of the polarized state in the dark on the concentration of NV centers. At low excitation power, we observed a simple exponential decay profile in the low-density regime and a paradoxical inverted exponential profile in the high-density regime. At higher excitation power, we observed complex behavior, with an initial sharp rise in the luminescence signal after the preparation pulse followed by a slower exponential decay. Magnetic field and excitation laser power-dependent measurements suggest that the rapid initial increase of the luminescence signal is related to recharging of the nitrogen-vacancy centers (from neutral to negatively charged) in the dark. The slow relaxing component corresponds to the longitudinal spin relaxation of the NV ensemble. The shape of the decay profile reflects the interplay between two mechanisms: the NV charge-state conversion in the dark and the longitudinal spin relaxation. These mechanisms, in turn, are influenced by ionization, recharging, and polarization dynamics during excitation. Interestingly, we found that charge dynamics are dominant in NV-dense samples even at very feeble excitation power. These observations may be important for the use of ensembles of NV centers in precession magnetometry and sensing applications.

On the Possibility of Miniature Diamond-Based Magnetometers Using Waveguide Geometries.

We propose the use of a diamond waveguide structure to enhance the sensitivity of magnetometers relying on the detection of the spin state of nitrogen-vacancy ensembles in diamond by infrared optical absorption. An optical waveguide structure allows for enhanced optical path-lengths avoiding the use of optical cavities and complicated setups. The presented design for diamond-based magnetometers enables miniaturization while maintaining high sensitivity and forms the basis for magnetic field sensors applicable in biomedical, industrial and space-related applications.

Circularly polarized zero-phonon transitions of vacancies in diamond at high magnetic fields

We study the circularly polarized photoluminescence of negatively charged (${\mathrm{NV}}^{\ensuremath{-}}$) and neutral (${\mathrm{NV}}^{0}$) nitrogen-vacancy ensembles and neutral vacancies (${\mathrm{V}}^{0}$) in diamond crystals exposed to magnetic fields of up to 10 T. We determine the orbital and spin Zeeman splitting as well as the energetic ordering of their ground and first-excited states. The spin-triplet and -singlet states of the ${\mathrm{NV}}^{\ensuremath{-}}$ are described by an orbital Zeeman splitting of about 9 $\ensuremath{\mu}\mathrm{eV}/\mathrm{T}$, which corresponds to a positive orbital $g$-factor of ${g}_{L}=0.164$ under application of the magnetic field along the (001) and (111) crystallographic directions, respectively. The zero-phonon line (ZPL) of the ${\mathrm{NV}}^{\ensuremath{-}}$ singlet is defined as a transition from the ${}^{1}{E}^{\ensuremath{'}}$ states, which are split by ${g}_{L}{\ensuremath{\mu}}_{\text{B}}B$, to the ${}^{1}{A}_{1}$ state. The energies of the zero-phonon triplet transitions show a quadratic dependence on intermediate magnetic field strengths, which we attribute to a mixing of excited states with nonzero orbital angular momentum. Moreover, we identify slightly different spin Zeeman splittings in the ground (gs) and excited (es) triplet states, which can be expressed by a deviation between their spin $g$-factors: ${g}_{S,\text{es}}={g}_{S,\text{gs}}+\mathrm{\ensuremath{\Delta}}g$ with values of $\mathrm{\ensuremath{\Delta}}g=0.014$ and 0.029 in the (001) and (111) geometries, respectively. The degree of circular polarization of the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs depends significantly on the temperature, which is explained by an efficient spin-orbit coupling of the excited states mediated through acoustic phonons. We further demonstrate that the sign of the circular polarization degree is switched under rotation of the diamond crystal. A weak Zeeman splitting similar to $\mathrm{\ensuremath{\Delta}}g{\ensuremath{\mu}}_{\text{B}}B$ measured for the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs is also obtained for the ${\mathrm{NV}}^{0}$ zero-phonon lines, from which we conclude that the ground state is composed of two optically active states with compensated orbital contributions and opposite spin-1/2 momentum projections. The zero-phonon lines of the ${\mathrm{V}}^{0}$ show Zeeman splittings and degrees of the circular polarization with opposite signs. The magnetophotoluminescence data indicate that the electron transition from the $^{1}T_{2}$ states to the $^{1}A$ ground state defines the zero-phonon emission at 1.674 eV, while the $^{1}T_{2}\ensuremath{\rightarrow}^{1}E$ transition is responsible for the zero-phonon line at 1.666 eV. The $^{1}T_{2}$ ($^{1}E$) states are characterized by an orbital Zeeman splitting with ${g}_{L}=0.071$ (0.128).

Proximity-Induced Artefacts in Magnetic Imaging with Nitrogen-Vacancy Ensembles in Diamond.

Magnetic imaging with ensembles of nitrogen-vacancy (NV) centres in diamond is a recently developed technique that allows for quantitative vector field mapping. Here we uncover a source of artefacts in the measured magnetic field in situations where the magnetic sample is placed in close proximity (a few tens of nm) to the NV sensing layer. Using magnetic nanoparticles as a test sample, we find that the measured field deviates significantly from the calculated field, in shape, amplitude and even in sign. By modelling the full measurement process, we show that these discrepancies are caused by the limited measurement range of NV sensors combined with the finite spatial resolution of the optical readout. We numerically investigate the role of the stand-off distance to identify an artefact-free regime, and discuss an application to ultrathin materials. This work provides a guide to predict and mitigate proximity-induced artefacts that can arise in NV-based wide-field magnetic imaging, and also demonstrates that the sensitivity of these artefacts to the sample can make them a useful tool for magnetic characterisation.

Generating maximally-path-entangled number states in two spin ensembles coupled to a superconducting flux qubit

An ensemble of nitrogen-vacancy (NV) centers coupled to a circuit QED device is shown to enable an efficient, high-fidelity generation of high-N00N states. Instead of first creating entanglement and then increasing the number of entangled particles $N$, our source of high-N00N states first prepares a high-$N$ Fock state in one of the NV ensembles and then entangles it to the rest of the system. With such a strategy, high-$N$ N00N states can be generated in just a few operational steps with an extraordinary fidelity. Once prepared, such a state can be stored over a longer period of time due to the remarkably long coherence time of NV centers.

Nitrogen-vacancy ensemble magnetometry based on pump absorption

We demonstrate magnetic field sensing using an ensemble of nitrogen-vacancy centers by recording the variation in the pump-light absorption due to the spin-polarization dependence of the total ground state population. Using a 532 nm pump laser, we measure the absorption of native nitrogen-vacancy centers in a chemical vapor deposited diamond placed in a resonant optical cavity. For a laser pump power of 0.4 W and a cavity finesse of 45, we obtain a noise floor of $\sim$ 100 nT/$\sqrt{\textrm{Hz}}$ spanning a bandwidth up to 125 Hz. We project a photon shot-noise-limited sensitivity of $\sim$ 1 pT/$\sqrt{\textrm{Hz}}$ by optimizing the nitrogen-vacancy concentration and the detection method.

Quantum interface between a transmon qubit and spins of nitrogen-vacancy centers

Hybrid quantum circuits combining advantages of each individual system have provided a promising platform for quantum information processing. Here we propose an experimental scheme to directly couple a transmon qubit to an individual spin in the nitrogen-vacancy (NV) center, with a coupling strength three orders of magnitude larger than that for a single spin coupled to a microwave cavity. This direct coupling between the transmon and the NV center could be utilized to make a transmon bus, leading to a coherently virtual exchange among different single spins. Furthermore, we demonstrate that, by coupling a transmon to a low-density NV ensemble, a SWAP operation between the transmon and NV ensemble is feasible and a quantum non-demolition measurement on the state of NV ensemble can be realized on the cavity-transmon-NV-ensemble hybrid system. Moreover, on this system, a virtual coupling can be achieved between the cavity and NV ensemble, which is much larger in magnitude than the direct coupling between the cavity and the NV ensemble. The photon state in cavity can be thus stored into NV spins more efficiently through this virtual coupling.

Diamond-Based Magnetic Imaging with Fourier Optical Processing

Diamond-based magnetic field sensors have attracted great interest in recent years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond has been previously demonstrated in condensed matter, biological, and paleomagnetic applications. Vector magnetic imaging with NV ensembles typically requires an applied field (>10 G) to separate the contributions from four crystallographic orientations, hindering studies of magnetic samples that require measurement in low or independently specified bias fields. Here we decompose the NV ensemble magnetic resonance spectrum without such a bias field by modulating the collected light at the microscope's Fourier plane. In addition to enabling vector magnetic imaging at arbitrarily low fields, our method can be used to extend the dynamic range at a given bias field. As demonstrated here, optically-detected diamond magnetometry stands to benefit from Fourier optical approaches, which have already found widespread utility in other branches of photonics.

Highly photostable NV centre ensembles in CVD diamond produced by using N2O as the doping gas

High density Nitrogen-Vacancy (NV) centre ensembles incorporated in plasma assisted chemical vapour deposition (CVD) diamond are crucial to the development of more efficient sensing devices that use the properties of luminescent defects. Achieving high NV doping with N2 as the dopant gas source during diamond growth is, however, plagued by the formation of macroscopic and point defects that quench luminescence. Moreover, such NVs are found to exhibit poor photostability under high laser powers. Although this effect can be harnessed to locally and durably switch off NV luminescence for data storage, it is usually undesirable for most applications. In this work, the use of N2O as an alternative doping source is proposed. Much higher amounts of the doping gas can be added without significantly generating defects, which allows the incorporation of perfectly photostable and higher density NV ensembles. This effect is believed to be related to the lower dissociation energy of the N2O molecule together with the beneficial effect of the presence of a low and controlled amount of oxygen near the growing surface.

Enhanced concentrations of nitrogen-vacancy centers in diamond through TEM irradiation

The studies of many-body dynamics of interacting spin ensembles, as well as quantum sensing in solid state systems, are often limited by the need for high spin concentrations, along with efficient decoupling of the spin ensemble from its environment. In particular, for an ensemble of nitrogen-vacancy (NV) centers in diamond, high conversion efficiencies between nitrogen (P1) defects and NV centers are essential while maintaining long coherence times of an NV ensemble. In this work, we study the effect of electron irradiation on the conversion efficiency and the coherence time of various types of diamond samples with different initial nitrogen concentrations. The samples were irradiated using a 200 keV transmission electron microscope. Our study reveals that the efficiency of NV creation strongly depends on the initial conversion efficiency and on the initial nitrogen concentration. The irradiation of the examined samples exhibits an order of magnitude improvement in the NV concentration (up to ∼1011 NV/cm2), without degradation in their coherence time of ∼180 μs. We address the potential of this technique toward the study of many-body physics of NV ensembles and the creation of non-classical spin states for quantum sensing.

Electron spin contrast of Purcell-enhanced nitrogen-vacancy ensembles in nanodiamonds

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.

Perfectly aligned shallow ensemble nitrogen-vacancy centers in (111) diamond

We report the formation of perfectly aligned, high-density, shallow nitrogen vacancy (NV) centers on the (111) surface of a diamond. The study involved step-flow growth with a high flux of nitrogen during chemical vapor deposition (CVD) growth, which resulted in the formation of a highly concentrated (>1019 cm−3) nitrogen layer approximately 10 nm away from the substrate surface. Photon counts obtained from the NV centers indicated the presence of 6.1 × 1015–3.1 × 1016 cm−3 NV centers, which suggested the formation of an ensemble of NV centers. The optically detected magnetic resonance (ODMR) spectrum confirmed perfect alignment (more than 99%) for all the samples fabricated by step-flow growth via CVD. Perfectly aligned shallow ensemble NV centers indicated a high Rabi contrast of approximately 30% which is comparable to the values reported for a single NV center. Nanoscale nuclear magnetic resonance demonstrated surface-sensitive nuclear spin detection and provided a confirmation of the NV centers' depth. Single NV center approximation indicated that the depth of the NV centers was approximately 9–10.7 nm from the surface with error of less than ±0.8 nm. Thus, a route for material control of shallow NV centers has been developed by step-flow growth using a CVD system. Our finding pioneers on the atomic level control of NV center alignment for large area quantum magnetometry.

Optimised frequency modulation for continuous-wave optical magnetic resonance sensing using nitrogen-vacancy ensembles

Magnetometers based on ensembles of nitrogen-vacancy centres are a promising platform for continuously sensing static and low-frequency magnetic fields. Their combination with phase-sensitive (lock-in) detection creates a highly versatile sensor with a sensitivity that is proportional to the derivative of the optical magnetic resonance lock-in spectrum, which is in turn dependant on the lock-in modulation parameters. Here we study the dependence of the lock-in spectral slope on the modulation of the spin-driving microwave field. Given the presence of the intrinsic nitrogen hyperfine spin transitions, we experimentally show that when the ratio between the hyperfine linewidth and their separation is ≳ 1/4, square-wave based frequency modulation generates the steepest slope at modulation depths exceeding the separation of the hyperfine lines, compared to sine-wave based modulation. We formulate a model for calculating lock-in spectra which shows excellent agreement with our experiments, and which shows that an optimum slope is achieved when the linewidth/separation ratio is ≲ 1/4 and the modulation depth is less then the resonance linewidth, irrespective of the modulation function used.

Formation of perfectly aligned nitrogen-vacancy-center ensembles in chemical-vapor-deposition-grown diamond (111)

Selectively aligning a nitrogen-vacancy (NV) ensemble in diamond is an important technique for obtaining a high-sensitivity magnetic sensor. Nitrogen-doped diamonds were grown on (111) substrates by microwave plasma chemical vapor deposition to perform the selective alignment of high-density NV ensembles, yielding perfectly aligned NV ensembles along the [111] direction with a density greater than 1016 cm−3 and a spin relaxation time of 2 µs. Such alignment results in a high signal contrast with an optical magnetic resonance close to the typical value reported with an isolated NV center. These results indicate the possibility of achieving a high sensitivity through the selective alignment of NV ensembles.

Frequency modulation technique for wide-field imaging of magnetic field with nitrogen-vacancy ensembles

We report on the application of a frequency modulation technique to wide-field magnetic field imaging of nitrogen-vacancy centers in diamond at room temperature. We use a scientific CMOS (sCMOS) camera to collect photoluminescence images from a large number of nitrogen-vacancy center ensembles in parallel. This technique allows a significant reduction in the measurement time required to obtain a magnetic field image compared with a scanning probe approach at a comparable magnetic field sensitivity.

Microwave Magnetic Field Coupling with Nitrogen-Vacancy Center Ensembles in Diamond with High Homogeneity

Electron spin resonance measurements with nitrogen-vacancy (NV) center ensembles in diamond are strongly dependent on a uniform microwave magnetic field. Three different types of microwave resonators are used and are well coupled with the spin ensembles at 2.87 GHz for zero-field splitting of the NV centers. The magnitude and the uniformity of both the horizontal and vertical magnetic fields are extracted and analyzed within a $$1\times 1\times 0.5$$ mm3 volume on a diamond sample surface, and the results indicate that the field homogeneity is up to 200 times better than that of the traditional copper wire microwave delivery model. The horizontal magnetic field magnitude homogeneity is better than 5 % over an area of 1 mm2 on the thin film diamond sample with NV ensembles. The average Rabi oscillation frequency is estimated to be 2.3 MHz per 1 W of microwave input power upon strong coherent coupling between the resonators and the spin ensembles. The effect of the nonuniform microwave magnetic field on the spin signal is also discussed. The approach used here will find widespread application in microwave coupling with spin ensembles in thin films.

Long-distance quantum information transfer with strong coupling hybrid solid system.

In this paper, we demonstrate how information can be transferred among the long-distance memory units in a hybrid solid architecture, which consists the nitrogen-vacancy (NV) ensemble acting as the memory unit, the LC circuit acting as the transmitter (receiver), and the flux qubit acting as the interface. Numerical simulation demonstrates that the high-fidelity quantum information transfer between memory unit and transmitter (receiver) can be implemented, and this process is robust to both the LC circuit decay and NV ensemble spontaneous emission.

Quantifying selective alignment of ensemble nitrogen-vacancy centers in (111) diamond

Selective alignment of nitrogen-vacancy (NV) centers in diamond is an important technique towards its applications. Quantification of the alignment ratio is necessary to design the optimized diamond samples. However, this is not a straightforward problem for dense ensemble of the NV centers. We estimate the alignment ratio of ensemble NV centers along the [111] direction in (111) diamond by optically detected magnetic resonance measurements. Diamond films deposited by N2 doped chemical vapor deposition have NV center densities over 1 × 1015 cm−3 and alignment ratios over 75%. Although spin coherence time (T2) is limited to a few μs by electron spins of nitrogen impurities, the combination of the selective alignment and the high density can be a possible way to optimize NV-containing diamond samples for the sensing applications.

Quantum-information processing on nitrogen-vacancy ensembles with the local resonance assisted by circuit QED

With the local resonant interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting coplanar resonator, and the single-qubit operation, we propose two protocols for the state transfer between two remote NVEs and for fast controlled-phase (c-phase) on these NVEs, respectively. This hybrid quantum system is composed of two distant NVEs coupled to separated high-Q transmission line resonators (TLRs), which are interconnected by a current-biased Josephsonjunction superconducting phase qubit. The fidelity of our state-transfer protocol is about 99.65% within the operation time of 70.60 ns. The fidelity of our c-phase gate is about 98.23% within the operation time of 93.87 ns. Furthermore, using the c-phase gate, we construct a two-dimensional cluster state on NVEs in n*n square grid based on the hybrid quantum system for the one-way quantum computation. Our protocol may be more robust, compared with the one based on the superconducting resonators, due to the long coherence time of NVEs at room temperature.