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We present a sensitive diamond quantum sensor with a magnetic field sensitivity of $9.4 \pm 0.1~\mathrm{pT/\sqrt{Hz}}$ in a near-dc frequency range of 5 to 100~Hz. This sensor is based on the continuous-wave optically detected magnetic resonance of an ensemble of nitrogen-vacancy centers along the [111] direction in a diamond (111) single crystal. The long $T_{2}^{\ast} \sim 2~\mathrm{\mu s}$ in our diamond and the reduced intensity noise in laser-induced fluorescence result in remarkable sensitivity among diamond quantum sensors. Based on an Allan deviation analysis, we demonstrate that a sub-picotesla field of 0.3~pT is detectable by interrogating the magnetic field for a few thousand seconds. The sensor head is compatible with various practical applications and allows a minimum measurement distance of about 1~mm from the sensing region. The proposed sensor facilitates the practical application of diamond quantum sensors., Comment: 8 pages, 5 figures

The use of diamond color centers such as the nitrogen-vacancy (NV) center is increasingly enabling quantum sensing and computing applications. Novel concepts like cavity coupling and readout, laser threshold magnetometry and multi-pass geometries allow significantly improved sensitivity and performance via increased signals and strong light fields. Enabling material properties for these techniques and their further improvements are low optical material losses via optical absorption of signal light and low birefringence. Here we study systematically the behavior of absorption around 700 nm and birefringence with increasing nitrogen- and NV-doping, as well as their behavior during NV creation via diamond growth, electron beam irradiation and annealing treatments. Absorption correlates with increased nitrogen-doping yet substitutional nitrogen does not seem to be the direct absorber. Birefringence reduces with increasing nitrogen doping. We identify multiple crystal defect concentrations via absorption spectroscopy and their changes during the material processing steps and thus identify potential causes of absorption and birefringence as well as strategies to fabricate CVD diamonds with high NV density yet low absorption and low birefringence., Comment: Accepted by Philosophical Transactions A (DOI: 10.1098/rsta.2022.0314)

Magnetic imaging with nitrogen-vacancy centers in diamond, also known as quantum diamond microscopy, has emerged as a useful technique for the spatial mapping of charge currents in solid-state devices. In this work, we investigate an application to photovoltaic (PV) devices, where the currents are induced by light. We develop a widefield nitrogen-vacancy microscope that allows independent stimulus and measurement of the PV device, and test our system on a range of prototype crystalline silicon PV devices. We first demonstrate micrometer-scale vector magnetic field imaging of custom PV devices illuminated by a focused laser spot, revealing the internal current paths in both short-circuit and open-circuit conditions. We then demonstrate time-resolved imaging of photocurrents in an interdigitated back-contact solar cell, detecting current build-up and subsequent decay near the illumination point with microsecond resolution. This work presents a versatile and accessible analysis platform that may find distinct application in research on emerging PV technologies., Comment: 14 pages, 9 figures

The nitrogen-vacancy (NV) center in diamond is a promising quantum system for magnetometry applications exhibiting optical readout of minute energy shifts in its spin sub-levels. Key material requirements for NV ensembles are a high NV$^-$ concentration, a long spin coherence time and a stable charge state. However, these are interdependent and can be difficult to optimize during diamond growth and subsequent NV creation. In this work, we systematically investigate the NV center formation and properties in chemical vapor deposition (CVD) diamond. The nitrogen flow during growth is varied by over 4 orders of magnitude, resulting in a broad range of single substitutional nitrogen concentrations of 0.2-20 parts per million. For a fixed nitrogen concentration, we optimize electron-irradiation fluences with two different accelerated electron energies, and we study defect formation via optical characterizations. We discuss a general approach to determine the optimal irradiation conditions, for which an enhanced NV concentration and an optimum of NV charge states can both be satisfied. We achieve spin-spin coherence times T$_2$ ranging from 45.5 to 549 $\mu$s for CVD diamonds containing 168 to 1 parts per billion NV$^-$ centers, respectively. This study shows a pathway to engineer properties of NV-doped CVD diamonds for improved sensitivity., Comment: 14 pages, 9 figures

Negatively charged nitrogen-vacancy centres in diamond are promising quantum magnetic field sensors. Laser threshold magnetometry has been a theoretical approach for the improvement of NV-centre ensemble sensitivity via increased signal strength and magnetic field contrast. In this work we experimentally demonstrate laser threshold magnetometry. We use a macroscopic high-finesse laser cavity containing a highly NV-doped and low absorbing diamond gain medium that is pumped at 532nm and resonantly seeded at 710nm. This enables amplification of the signal power by stimulated emission of 64%. We show the magnetic-field dependency of the amplification and thus, demonstrate magnetic-field dependent stimulated emission from an NV-centre ensemble. This emission shows a record contrast of 33% and a maximum output power in the mW regime. These advantages of coherent read-out of NV-centres pave the way for novel cavity and laser applications of quantum defects as well as diamond NV magnetic field sensors with significantly improved sensitivity for the health, research and mining sectors.

We demonstrate a simple, robust and contactless method for non-destructive testing of magnetic materials such as steel. This uses a fiber-coupled magnetic sensor based on nitrogen vacancy centers (NVC) in diamond without magnetic shielding. Previous NVC magnetometry has sought a homogeneous bias magnetic field, but in our design we deliberately applied an inhomogeneous magnetic field. As a consequence of our experimental set-up we achieve a high spatial resolution: 1~mm in the plane parallel and 0.1~mm in the plane perpendicular to the surface of the steel. Structural damage in the steel distorts this inhomogeneous magnetic field and by detecting this distortion we reconstruct the damage profile through quantifying the shifts in the NVC Zeeman splitting. This works even when the steel is covered by a non-magnetic material. The lift-off distance of our sensor head from the surface of 316 stainless steel is up to 3~mm.

This article reviews efforts to build a new type of quantum device, which combines an ensemble of electronic spins with long coherence times, and a small-scale superconducting quantum processor. The goal is to store over long times arbitrary qubit states in orthogonal collective modes of the spin-ensemble, and to retrieve them on-demand. We first present the protocol devised for such a multi-mode quantum memory. We then describe a series of experimental results using NV center spins in diamond, which demonstrate its main building blocks: the transfer of arbitrary quantum states from a qubit into the spin ensemble, and the multi-mode retrieval of classical microwave pulses down to the single-photon level with a Hahn-echo like sequence. A reset of the spin memory is implemented in-between two successive sequences using optical repumping of the spins., Comment: 27 pages, 7 figures

A hidden order that emerges in the frustrated pyrochlore Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ with $T_{\text{c}}=0.53$ K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semi-quantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb$_2$Ti$_2$O$_7$ is most likely a U(1) quantum spin-liquid state., Comment: 5 pages, 5 figures, including Supplemental Material

We report the storage of microwave pulses at the single-photon level in a spin-ensemble memory consisting of $10^{10}$ NV centers in a diamond crystal coupled to a superconducting LC resonator. The energy of the signal, retrieved $100\, \mu \mathrm{s}$ later by spin-echo techniques, reaches $0.3\%$ of the energy absorbed by the spins, and this storage efficiency is quantitatively accounted for by simulations. This figure of merit is sufficient to envision first implementations of a quantum memory for superconducting qubits., Comment: 6 pages

Nitrogen impurities help to stabilize the negatively-charged-state of NV$^-$ in diamond, whereas magnetic fluctuations from nitrogen spins lead to decoherence of NV$^-$ qubits. It is not known what donor concentration optimizes these conflicting requirements. Here we used 10-MeV $^{15}$N$^{3+}$ ion implantation to create NV$^-$ in ultrapure diamond. Optically detected magnetic resonance of single centers revealed a high creation yield of $40\pm3$% from $^{15}$N$^{3+}$ ions and an additional yield of $56\pm3$% from $^{14}$N impurities. High-temperature anneal was used to reduce residual defects, and charge stable NV$^-$, even in a dilute $^{14}$N impurity concentration of 0.06 ppb were created with long coherence times.

A quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above one second. Benefiting from these long coherence times requires to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy (NV) centres in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the NV spins into their ground state by optical pumping and their refocusing by Hahn echo sequences. This enables the storage of multiple microwave pulses at the picoWatt level and their retrieval after up to $35 \mu$s, a three orders of magnitude improvement compared to previous experiments., Comment: 8 pages, 5 figures + Supplementary information (text and 6 figures)

Spins of negatively charged nitrogen-vacancy (NV$^-$) defects in diamond are among the most promising candidates for solid-state qubits. The fabrication of quantum devices containing these spin-carrying defects requires position-controlled introduction of NV$^-$ defects having excellent properties such as spectral stability, long spin coherence time, and stable negative charge state. Nitrogen ion implantation and annealing enable the positioning of NV$^-$ spin qubits with high precision, but to date, the coherence times of qubits produced this way are short, presumably because of the presence of residual radiation damage. In the present work, we demonstrate that a high temperature annealing at 1000$^\circ$C allows 2 millisecond coherence times to be achieved at room temperature. These results were obtained for implantation-produced NV$^-$ defects in a high-purity, 99.99% $^{12}$C enriched single crystal chemical vapor deposited diamond. We discuss these remarkably long coherence times in the context of the thermal behavior of residual defect spins. [Published in Physical Review B {\bf{88}}, 075206 (2013)]

Pulsed excitation of broad spectra requires very high field strengths if monochromatic pulses are used. If the corresponding high power is not available or not desirable, the pulses can be replaced by suitable low-power pulses that distribute the power over a wider bandwidth. As a simple case, we use microwave pulses with a linear frequency chirp. We use these pulses to excite spectra of single NV-centers in a Ramsey experiment. Compared to the conventional Ramsey experiment, our approach increases the bandwidth by at least an order of magnitude. Compared to the conventional ODMR experiment, the chirped Ramsey experiment does not suffer from power broadening and increases the resolution by at least an order of magnitude. As an additional benefit, the chirped Ramsey spectrum contains not only `allowed' single quantum transitions, but also `forbidden' zero- and double quantum transitions, which can be distinguished from the single quantum transitions by phase-shifting the readout pulse with respect to the excitation pulse or by variation of the external magnetic field strength., Comment: 13 pages, 7 figures

Quantum adiabatic passages can be greatly accelerated by a suitable control field, called a counter-diabatic field, which varies during the scan through resonance. Here, we implement this technique on the electron spin of a single nitrogen-vacancy center in diamond. We demonstrate two versions of this scheme. The first follows closely the procedure originally proposed by Demirplak and Rice (J. Phys. Chem. A 107, 9937 (2003)). In the second scheme, we use a control field whose amplitude is constant, but its phase varies with time. This version, which we call the rapid-scan approach, allows an even faster passage through resonance and therefore makes it applicable also for systems with shorter decoherence times.

A new method for detecting the magnetic resonance of electronic spins at low temperature is demonstrated. It consists in measuring the signal emitted by the spins with a superconducting qubit that acts as a single-microwave-photon detector, resulting in an enhanced sensitivity. We implement this new type of electron-spin resonance spectroscopy using a hybrid quantum circuit in which a transmon qubit is coupled to a spin ensemble consisting of NV centers in diamond. With this setup we measure the NV center absorption spectrum at 30mK at an excitation level of \thicksim15\,\mu_{B} out of an ensemble of 10^{11} spins., Comment: 6 pages, 4 figures, submitted to PRX

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. These results constitute a first proof of concept of spin-ensemble based quantum memory for superconducting qubits., Comment: 13 pages, 4 figures, plus supplementary information

We uncover a strong anisotropy in both the anomalous Hall effect (AHE) and the magnetoresistance of the chiral spin states of Pr$_2$Ir$_2$O$_7$. The AHE appearing below 1.5 K at zero magnetic field shows hysteresis which is most pronounced for fields cycled along the [111] direction. This hysteresis is compatible with the field-induced growth of domains composed by the 3-in 1-out spin states which remain coexisting with the 2-in 2-out spin ice manifold once the field is removed. Only for fields applied along the [111] direction, we observe a large positive magnetoresistance and Shubnikov de Haas oscillations above a metamagnetic critical field. These observations suggest the reconstruction of the electronic structure of the conduction electrons by the field-induced spin-texture., Comment: 7 pages and 5 figures (including Supplementary Material), Accepted in Physical Review Letters

We developed a gauge-covariant formulation of the non-equilibrium Green function method for the dynamical and/or non-uniform electromagnetic field by means of the deformational quantization method. Such a formulation is realized by replacing the Moyal product in the so-called Wigner space by the star product, and facilitates the order-by-order calculation of a gauge-invariant observable in terms of the electromagnetic field. An application of this formalism to the linear response theory is discussed.

Anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in a variety of ferromagnetic metals including pure metals, oxides, and chalcogenides, are studied to obtain unified understandings of their origins. We show a universal scaling behavior of anomalous Hall conductivity $\sigma_{xy}$ as a function of longitudinal conductivity $\sigma_{xx}$ over five orders of magnitude, which is well explained by a recent theory of the AHE taking into account both the intrinsic and extrinsic contributions. ANE is closely related with AHE and provides us with further information about the low-temperature electronic state of itinerant ferromagnets. Temperature dependence of transverse Peltier coefficient $\alpha_{xy}$ shows an almost similar behavior among various ferromagnets, and this behavior is in good agreement quantitatively with that expected from the Mott rule., Comment: 4pages, 4figures, 1table

We report on the in-plane anisotropy of the electronic response in the spin/charge/orbital ordered phase of a half-doped layered-structure manganite. The optical conductivity spectra for a single domain of Eu$_{1/2}$% Ca$_{3/2}$MnO$_{4}$ unambiguously show the anisotropic charge dynamics which well corresponds to the theoretical calculation: the optical conductivity with the polarization along the zigzag ferromagnetic chain direction exhibits a smaller gap and a larger intensity at lower energies than that of the perpendicular polarization mostly due to the charge/orbital ordering and the associated quantum interference effect., Comment: 4 pages, 3 figures

It is demonstrated both theoretically and experimentally that the spin chirality associated with a noncoplanar spin configuration produces a magneto-optical effect. Numerical study of the two-band Hubbard model on a triangle cluster shows that the optical Hall conductivity $\sigma_{xy}(\omega)$ is proportional to the spin chirality. The detailed comparative experiments on pyrochlore-type molybdates $R_2$Mo$_2$O$_7$ with $R=$Nd (Ising-like moments) and $R=$Gd (Heisenberg-like ones) clearly distinguishes the two mechanisms, i.e., spin chirality and spin-orbit interactions. It is concluded that for $R$=Nd, $\sigma_{xy}(\omega)$ is dominated by the spin chirality for the dc ($\omega=0$) and the $d \to d$ incoherent intraband optical transitions between Mo atoms., Comment: 4 pages, 5 figures. submitted to Phys. Rev. B