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We present a theoretical study of vibrational and vibronic properties of a point defect in the dilute limit by means of first-principles density functional theory calculations. As an exemplar we choose the negatively charged nitrogen-vacancy center, a solid-state system that has served as a testbed for many protocols of quantum technology. We achieve low effective concentrations of defects by constructing dynamical matrices of large supercells containing tens of thousands of atoms. The main goal of the paper is to calculate luminescence and absorption lineshapes due to coupling to vibrational degrees of freedom. The coupling to symmetric $a_1$ modes is computed via the Huang-Rhys theory. Importantly, to include a nontrivial contribution of $e$ modes we develop an effective methodology to solve the multi-mode $E \otimes e$ Jahn-Teller problem. Our results show that for NV centers in diamond a proper treatment of $e$ modes is particularly important for absorption. We obtain good agreement with experiment for both luminescence and absorption. Finally, the remaining shortcomings of the theoretical approach are critically reviewed. The presented theoretical approach will benefit identification and future studies of point defects in solids., Comment: 21 pages, 17 figures

We use field-cycling-assisted dynamic nuclear polarization and continuous radio-frequency (RF) driving over a broad spectral range to demonstrate magnetic-field-dependent activation of nuclear spin transport from strongly-hyperfine-coupled 13C sites in diamond. We interpret our observations with the help of a theoretical framework where nuclear spin interactions are mediated by electron spins. In particular, we build on the results from a 4-spin toy model to show how otherwise localized nuclear spins must thermalize as they are brought in contact with a larger ancilla spin network. Further, by probing the system response to a variable driving field amplitude, we witness stark changes in the RF-absorption spectrum, which we interpret as partly due to contributions from heterogeneous multi-spin sets, whose 'zero-quantum' transitions become RF active thanks to the hybrid electron-nuclear nature of the system. These findings could prove relevant in applications to dynamic nuclear polarization, spin-based quantum information processing, and nanoscale sensing.

The ST1 center is a point defect in diamond with bright fluorescence and a mechanism for optical spin initialization and readout. The center has impressive potential for applications in diamond quantum computing as a quantum bus to a register of nuclear spins. This is because it has an exceptionally high readout contrast and, unlike the well-known nitrogen-vacancy center, it does not have a ground state electronic spin that decoheres the nuclear spins. However, its chemical structure is unknown and there are large gaps in our understanding of its properties. We present the discovery of ST1 centers in natural diamond. Our experiments identify interesting power dependence of the center's optical dynamics and reveal new electronic structure. We also present a theory of its electron-phonon interactions, which we combine with previous experiments, to shortlist likely candidates for its chemical structure.

The nitrogen-vacancy color center in diamond has rapidly emerged as an important solid-state system for quantum information processing. While individual spin registers have been used to implement small-scale diamond quantum computing, the realization of a large-scale device requires development of an on-chip quantum bus for transporting information between distant qubits. Here we propose a method for coherent quantum transport of an electron and its spin state between distant NV centers. Transport is achieved by the implementation of spatial stimulated adiabatic Raman passage through the optical control of the NV center charge states and the confined conduction states of a diamond nanostructure. Our models show that for two NV centers in a diamond nanowire, high fidelity transport can be achieved over distances of order hundreds of nanometres in timescales of order hundreds of nanoseconds. Spatial adiabatic passage is therefore a promising option for realizing an on-chip spin quantum bus.

The study establishes that the degree of optically induced spin polarization that can be achieved for NV$^- $in 1b diamond is limited by the concentration of single substitutional nitrogen, N$^0$ . The polarization of the individual NV centres in the diamond is dependent on the separation of the NV$^-$ and the nitrogen donor. When the NV$^-$ - N$^+$ pair separation is large the properties of the pair will be as for single sites and a high degree of spin polarization attainable. When the separation decreases the emission is reduced, the lifetime shortened and the spin polarization downgraded. The deterioration occurs as a consequence of electron tunneling in the excited state from NV$^-$ to N$^+$ and results in an optical cycle that includes NV$^0$. The tunneling process is linear in optical excitation and more prevalent the closer the N$^+$ is to the NV$^-$ centre. However, the separation between the NV$^-$ and its donor N$^+$ can be effected by light through the excitation of NV$^-$ and/or ionization of N$^0$. The optical excitation that creates the spin polarization can also modify the sample properties and during excitation creates charge dynamics. The consequence is that the magnitude of spin polarization, the spin relaxation and coherence times T$_1$ and T$_2$ have a dependence on the nitrogen concentration and on the excitation wavelength. The adjacent N$^+$ gives an electric field that Stark shifts the NV$^-$ transitions and for an ensemble results in line broadening. It is observation of changes of these Stark induced effects that allow the variation in NV$^-$ - N$^+$ separation to be monitored. Spectroscopic measurements including that of the varying line widths are central to the study. They are made at low temperatures and include extensive measurements of the NV$^-$ optical transition at 637 nm, the infrared transition at 1042 nm and ODMR at 2.87 GHz., Comment: 33 Pages, 33 figures

Nanomechanical sensors and quantum nanosensors are two rapidly developing technologies that have diverse interdisciplinary applications in biological and chemical analysis and microscopy. For example, nanomechanical sensors based upon nanoelectromechanical systems (NEMS) have demonstrated chip-scale mass spectrometry capable of detecting single macromolecules, such as proteins. Quantum nanosensors based upon electron spins of negatively-charged nitrogen-vacancy (NV) centers in diamond have demonstrated diverse modes of nanometrology, including single molecule magnetic resonance spectroscopy. Here, we report the first step towards combining these two complementary technologies in the form of diamond nanomechanical structures containing NV centers. We establish the principles for nanomechanical sensing using such nano-spin-mechanical sensors (NSMS) and assess their potential for mass spectrometry and force microscopy. We predict that NSMS are able to provide unprecedented AC force images of cellular biomechanics and to, not only detect the mass of a single macromolecule, but also image its distribution. When combined with the other nanometrology modes of the NV center, NSMS potentially offer unparalleled analytical power at the nanoscale., Comment: Errors in the stress susceptibility parameters present in the original arXiv version have been corrected

The nitrogen-vacancy (NV) centre in diamond is emerging as a promising platform for solid-state quantum information processing and nanoscale metrology. Of interest in these applications is the manipulation of the NV charge, which can be attained by optical excitation. Here we use two-color optical microscopy to investigate the dynamics of NV photo-ionization, charge diffusion, and trapping in type-1b diamond. We combine fixed-point laser excitation and scanning fluorescence imaging to locally alter the concentration of negatively charged NVs, and to subsequently probe the corresponding redistribution of charge. We uncover the formation of spatial patterns of trapped charge, which we qualitatively reproduce via a model of the interplay between photo-excited carriers and atomic defects. Further, by using the NV as a probe, we map the relative fraction of positively charged nitrogen upon localized optical excitation. These observations may prove important to transporting quantum information between NVs or to developing three-dimensional, charge-based memories.

Hybrid quantum systems (HQSs) have attracted several research interests in the last years. In this Letter, we report on the design, fabrication, and characterization of a novel diamond architecture for HQSs that consists of a high quality thin circular diamond membrane with embedded near-surface nitrogen-vacancy centers (NVCs). To demonstrate this architecture, we employed the NVCs by means of their optical and spin interfaces as nanosensors of the motion of the membrane under static pressure and in-resonance vibration, as well as the residual stress of the membrane. Driving the membrane at its fundamental resonance mode, we observed coupling of this vibrational mode to the spin of the NVCs by Hahn echo signal. Our realization of this architecture will enable futuristic HQS-based applications in diamond piezometry and vibrometry, as well as spin-mechanical and mechanically mediated spin-spin coupling in quantum information science., Comment: 6 Pages, 4 Figures

Diamond is a proven solid-state platform for spin-based quantum technology. The nitrogen-vacancy (NV) center in diamond has been used to realize small-scale quantum information processing (QIP) and quantum sensing under ambient conditions. A major barrier in the development of large-scale QIP in diamond is the connection of NV spin registers by a quantum bus at room temperature. Given that diamond is expected to be an ideal spin transport material, the coherent transport of spin directly between the spin registers offers a potential solution. Yet, there has been no demonstration of spin transport in diamond due to difficulties in achieving spin injection and detection via conventional methods. Here, we exploit detailed knowledge of the paramagnetic defects in diamond to identify novel mechanisms to achieve spin injection, transport and detection in diamond at room temperature. Having identified these mechanisms, we explore how they may be combined to realise an on-chip spin quantum bus., Comment: 13 pages, 6 figures

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 (including quantum technology) and for understanding its fundamental properties., Comment: 5 pages, 4 figures

The negatively-charged nitrogen-vacancy (NV) center in diamond is at the frontier of quantum nano-metrology and bio-sensing. Recent attention has focused on the application of high-sensitivity thermometry using the spin resonances of NV centers in nano-diamond to sub-cellular biological and biomedical research. Here, we report a comprehensive investigation of the thermal properties of the center's spin resonances and demonstrate an alternate all-optical NV thermometry technique that exploits the temperature dependence of the center's optical Debye-Waller factor., Comment: 22 pages, 5 figures

We investigate phonon induced electronic dynamics in the ground and excited states of the negatively charged silicon-vacancy ($\mathrm{SiV}^-$) centre in diamond. Optical transition line widths, transition wavelength and excited state lifetimes are measured for the temperature range 4-350 K. The ground state orbital relaxation rates are measured using time-resolved fluorescence techniques. A microscopic model of the thermal broadening in the excited and ground states of the $\mathrm{SiV}^-$ centre is developed. A vibronic process involving single-phonon transitions is found to determine orbital relaxation rates for both the ground and the excited states at cryogenic temperatures. We discuss the implications of our findings for coherence of qubit states in the ground states and propose methods to extend coherence times of $\mathrm{SiV}^-$ qubits., Comment: 19 pages, 6 figures

The characteristic transition of the NV- centre at 637 nm is between ${}^3\mathrm{A}_2$ and ${}^3\mathrm{E}$ triplet states. There are also intermediate ${}^1\mathrm{A}_1$ and ${}^1\mathrm{E}$ singlet states, and the infrared transition at 1042 nm between these singlets is studied here using uniaxial stress. The stress shift and splitting parameters are determined, and the physical interaction giving rise to the parameters is considered within the accepted electronic model of the centre. It is established that this interaction for the infrared transition is due to a modification of electron-electron Coulomb repulsion interaction. This is in contrast to the visible 637 nm transition where shifts and splittings arise from modification to the one-electron Coulomb interaction. It is also established that a dynamic Jahn-Teller interaction is associated with the singlet ${}^1\mathrm{E}$ state, which gives rise to a vibronic level 115 $\mathrm{cm}^{-1}$ above the ${}^1\mathrm{E}$ electronic state. Arguments associated with this level are used to provide experimental confirmation that the ${}^1\mathrm{A}_1$ is the upper singlet level and ${}^1\mathrm{E}$ is the lower singlet level., Comment: 19 pages, 6 figures

The negatively charged nitrogen-vacancy (NV-) centre in diamond has many exciting applications in quantum nano-metrology, including magnetometry, electrometry, thermometry and piezometry. Indeed, it is possible for a single NV- centre to measure the complete three-dimensional vector of the local electric field or the position of a single fundamental charge in ambient conditions. However, in order to achieve such vector measurements, near complete knowledge of the orientation of the centre's defect structure is required. Here, we demonstrate an optically detected magnetic resonance (ODMR) technique employing rotations of static electric and magnetic fields that precisely determines the orientation of the centre's major and minor trigonal symmetry axes. Thus, our technique is an enabler of the centre's existing vector sensing applications and also motivates new applications in multi-axis rotation sensing, NV growth characterization and diamond crystallography., Comment: 20 pages, 10 figures

Synthetic diamond production is key to the development of quantum metrology and quantum information applications of diamond. The major quantum sensor and qubit candidate in diamond is the nitrogen-vacancy (NV) color center. This lattice defect comes in four different crystallographic orientations leading to an intrinsic inhomogeneity among NV centers that is undesirable in some applications. Here, we report a microwave plasma-assisted chemical vapor decomposition (MPCVD) diamond growth technique on (111)-oriented substrates that yields perfect alignment ($94\pm2%$) of as-grown NV centers along a single crystallographic direction. In addition, clear evidence is found that the majority ($74\pm4%$) of the aligned NV centers were formed by the nitrogen being first included in the (111) growth surface and then followed by the formation of a neighboring vacancy on top. The achieved homogeneity of the grown NV centers will tremendously benefit quantum information and metrology applications., Comment: 6 pages, 4 figures, changes to previous version: added acknowledgement

Significant attention has been recently focused on the realization of high precision nano-thermometry using the spin-resonance temperature shift of the negatively charged nitrogen-vacancy (NV-) center in diamond. However, the precise physical origins of the temperature shift is yet to be understood. Here, the shifts of the center's optical and spin resonances are observed and a model is developed that identifies the origin of each shift to be a combination of thermal expansion and electron-phonon interactions. Our results provide new insight into the center's vibronic properties and reveal implications for NV- thermometry., Comment: 6 pages, 3 figures

Single charge detection with nanoscale spatial resolution in ambient conditions is a current frontier in metrology that has diverse interdisciplinary applications. Here, such single charge detection is demonstrated using two nitrogen-vacancy (NV) centers in diamond. One NV center is employed as a sensitive electrometer to detect the change in electric field created by the displacement of a single electron resulting from the optical switching of the other NV center between its neutral (NV$^0$) and negative (NV$^-$) charge states. As a consequence, our measurements also provide direct insight into the charge dynamics inside the material.

The negatively-charged silicon-vacancy (SiV$^-$) center in diamond is a promising single photon source for quantum communications and information processing. However, the center's implementation in such quantum technologies is hindered by contention surrounding its fundamental properties. Here we present optical polarization measurements of single centers in bulk diamond that resolve this state of contention and establish that the center has a $\langle111\rangle$ aligned split-vacancy structure with $D_{3d}$ symmetry. Furthermore, we identify an additional electronic level and evidence for the presence of dynamic Jahn-Teller effects in the center's 738 nm optical resonance., Comment: 8 pages, 8 figures

We describe an experimental technique for associating the satellite lines in a rare earth optical spectrum caused by a defect with the rare earth ions in crystal sites around that defect. This method involves measuring the hyperfine splitting caused by a magnetic dipole-dipole interaction between host ions and a magnetic defect. The method was applied to Ce3+:EuCl3.6H2O to assign 13 of the outermost 22 satellite lines to sites. The assignments show that the optical shift of a satellite line is loosely dependent on the distance to the dopant. The interaction between host and dopant ions is purely dipole-dipole at distances greater than 7 Angstroms, with an additional contribution, likely superexchange, at distances less than 7 Angstroms., Comment: 6 pages, 6 figures

The negatively charged nitrogen-vacancy (NV-) center in diamond has realized new frontiers in quantum technology. Here, the center's optical and spin resonances are observed under hydrostatic pressures up to 60 GPa. Our observations motivate powerful new techniques to measure pressure and image high pressure magnetic and electric phenomena. Our observations further reveal a fundamental inadequacy of the current model of the center and provide new insight into its electronic structure., Comment: 6 pages, 3 figures

Electron and nuclear spins associated with point defects in insulators are promising systems for solid state quantum technology. While the electron spin usually is used for readout and addressing, nuclear spins are exquisite quantum bits and memory systems. With these systems single-shot readout of nearby nuclear spins as well as entanglement aided by the electron spin has been shown. While the electron spin in this example is essential for readout it usually limits nuclear spin coherence. This has set of the quest for defects with spin-free ground states. Here, we isolate a hitherto unidentified defect in diamond and use it at room temperature to demonstrate optical spin polarization and readout with exceptionally high contrast (up to 45%), coherent manipulation of an individual excited triplet state spin, and coherent nuclear spin manipulation using the triplet electron spin as a meta-stable ancilla. By this we demonstrate nuclear magnetic resonance and Rabi oscillations of the uncoupled nuclear spin in the spin-free electronic ground state. Our study demonstrates that nuclei coupled to single metastable electron spins are useful quantum systems with long memory times despite electronic relaxation processes., Comment: 4 pages, 5 figures

The nitrogen-vacancy (NV) colour centre in diamond is an important physical system for emergent quantum technologies, including quantum metrology, information processing and communications, as well as for various nanotechnologies, such as biological and sub-diffraction limit imaging, and for tests of entanglement in quantum mechanics. Given this array of existing and potential applications and the almost 50 years of NV research, one would expect that the physics of the centre is well understood, however, the study of the NV centre has proved challenging, with many early assertions now believed false and many remaining issues yet to be resolved. This review represents the first time that the key empirical and ab initio results have been extracted from the extensive NV literature and assembled into one consistent picture of the current understanding of the centre. As a result, the key unresolved issues concerning the NV centre are identified and the possible avenues for their resolution are examined., Comment: Review article, 101 pages, 31 figures, and 18 tables

We study features in the optically detected magnetic resonance (ODMR) signals associated with negatively charged nitrogen-vacancy (NV) centers coupled to other paramagnetic impurities in diamond. Our results are important for understanding ODMR line shapes and for optimization of devices based on NV centers. We determine the origins of several side features to the unperturbed NV magnetic resonance by studying their magnetic field and microwave power dependences. Side resonances separated by around 130 MHz are due to hyperfine coupling between NV centers and nearest-neighbor C-13 nuclear spins. Side resonances separated by approximately {40, 260, 300} MHz are found to originate from simultaneous spin flipping of NV centers and single substitutional nitrogen atoms. All results are in agreement with the presented theoretical calculations., Comment: 12 pages, new data and discussions in updated version