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The neutral divacancy and the negatively charged nitrogen-vacancy defects in 4H-silicon carbide (SiC) are two of the most prominent candidates for functioning as room-temperature quantum bits (qubits) with telecommunication-wavelength emission. Nonetheless, the pivotal role of electron-phonon coupling in the spinpolarization loop is still unrevealed. In this work, we theoretically investigate the microscopic magneto-optical properties and spin-dependent optical loops utilizing the first-principles calculations. First, we quantitatively demonstrate the electronic level structure, assisted by symmetry analysis. Moreover, the fine interactions, including spin-orbit coupling and spin-spin interaction, are fully characterized to provide versatile qubit functional parameters. Subsequently, we explore the electron-phonon coupling, encompassing dynamics- and pseudo-Jahn--Teller effects in the intersystem crossing transition. In addition, we analyze the photoluminescence PL lifetime based on the major transition rates in the optical spinpolarization loop. We compare two promising qubits with similar electronic properties, but their respective rates differ substantially. Finally, we detail the threshold of ODMR contrast for further optimization of the qubit operation. This work not only reveals the mechanism underlying the optical spinpolarization but also proposes productive avenues for optimizing quantum information processing tasks based on the ODMR protocol., Comment: 17 pages, 7 figures, 7 tables

In recent years, the negatively charged group-IV--vacancy defects in diamond, labeled as G4V($-$) or G4V centers, have received a great attention in quantum information processing. In this study, we investigate the magneto-optical properties of the G4V centers under high compressive hydrostatic pressures up to 180~GPa. The spin-orbit splitting for the electronic ground and excited states and the hyperfine tensors are calculated by means of plane wave supercell density functional theory as unique fingerprints of these defects. To this end, we developed a theory for calculating the hyperfine tensors when the electronic states are subject to Jahn--Teller effect. We find that the zero-phonon-line energy increases with adding hydrostatic pressures where the coupling strength increases from SiV($-$) to PbV($-$). On the other hand, the calculated photoionization threshold energies indicate that the operation of PbV($-$) based quantum sensor is limited up to 30~GPa of hydrostatic pressure whereas SnV($-$), GeV($-$) and SiV($-$) remain photostable up to 180~GPa of hydrostatic pressure., Comment: 16 pages, 7 figures, 7 tables

Coherent light sources emitting in the terahertz range are highly sought after for fundamental research and applications. THz lasers rely on achieving population inversion. We demonstrate the generation of THz radiation using nitrogen-vacancy (NV) centers in a diamond single crystal. Population inversion is achieved through the Zeeman splitting of the $S=1$ state in $15\ \text{T}$, resulting in a splitting of $0.42\ \text{THz}$, where the middle $S_z=0$ sublevel is selectively pumped by visible light. To detect the THz radiation, we utilize a phase-sensitive THz setup, optimized for electron spin resonance measurements (ESR). We determine the spin-lattice relaxation time up to $15\ \text{T}$ using the light-induced ESR measurement, which shows the dominance of phonon-mediated relaxation and the high efficacy of the population inversion. The THz radiation is tunable by the magnetic field, thus these findings may lead to the next generation of tunable coherent THz sources., Comment: 45 pages, 14 figures

We apply density functional theory to investigate interactions between electronic and vibrational states in crystal defects with multi-mode dynamical Jahn-Teller (JT) systems. Our focus is on transitions between orbital singlet and degenerate orbital doublet characterized by $E \otimes (e \oplus e \oplus \cdots)$ JT coupling, which frequently occurs in crystal defects that are investigated for applications in quantum information science. We utilize a recently developed methodology to model the photoluminescence (PL) spectrum of the negatively charged split nickel-vacancy center (NiV$^{-}$) in diamond, where JT-active modes significantly influence electron-phonon interactions. Our results validate the effectiveness of the methodology in accurately reproducing the observed 1.4 eV PL lineshape. The strong agreement between our theoretical predictions and experimental observations reinforces the identification of the 1.4 eV PL center with the NiV$^{-}$ complex. This study highlights the critical role of JT-active modes in affecting optical lineshapes and demonstrates the power of advanced techniques for modeling optical properties in complex systems with multiple JT-active frequencies., Comment: 13 pages, 7 figures

Optically accessible solid state defect spins are primary platform for quantum information processing where tight control of the electron spin and ancilla nuclear spins is pivotal for the operation. We demonstrate on the exemplary nitrogen-vacancy (NV) color center in diamond by means of a combined group theory and density functional theory study that spin-phonon relaxation rate of the nitrogen nuclear spin is with several orders of magnitude enhanced by the strong electron-phonon coupling in the optical excited state of the defect. The mechanism is common to other solid state defect spins sharing similar optical excited states with that of the NV center., Comment: 6 pages, 3 figures, 2 tables

The last decade has seen an explosive growth in the use of color centers for metrology applications, the paradigm example arguably being the nitrogen-vacancy (NV) center in diamond. Here, we focus on the regime of cryogenic temperatures and examine the impact of spin-selective, narrow-band laser excitation on NV readout. Specifically, we demonstrate a more than four-fold improvement in sensitivity compared to that possible with non-resonant (green) illumination, largely due to a boost in readout contrast and integrated photon count. We also leverage nuclear spin relaxation under resonant excitation to polarize the 14N host, which we then prove beneficial for spin magnetometry. These results open opportunities in the application of NV sensing to the investigation of condensed matter systems, particularly those exhibiting superconducting, magnetic, or topological phases selectively present at low temperatures.

We analyze the spin-orbit and Jahn-Teller interactions in $T_d$ symmetry that are relevant for substitutional transition metal defects in semiconductors. We apply our theory to the substitutional nickel defect in diamond and compute the appropriate fine-leve structure and magneto-optical parameters by means of hybrid density functional theory. Our calculations confirm the intepretations of previous experimental findings that the 2.56-eV and 2.51-eV optical centres are associated with this defect. Our analysis of the electronic structure unravels possible mechanisms behind the observed optical transitions and the optically detected magnetic resonance signal, too.

Certain intrinsic point defects in silicon carbide are promising quantum systems with efficient spin-photon interface. Despite carbon vacancy in silicon carbide is an elementary and relatively abundant intrinsic defect, no optical signal has been reported associated with it. Here, we revisit the positively charged carbon vacancy defects in the 4H polytype of silicon carbide (4H-SiC) by means of \textit{ab initio} calculations. We find that the excited state is optically active for the so-called h-site configuration of carbon vacancy in 4H-SiC, with zero-phonon line at $0.65~\mathrm{eV}$. We propose this defect as an exotic paramagnetic near-infrared emitter in the IR-B region., Comment: 8 pages, 5 figures

Point defects in diamond may act as quantum bits. Recently, oxygen-vacancy related defects have been proposed to the origin of the so-called ST1 color center in diamond that can realize a long-living solid-state quantum memory. Motivated by this proposal we systematically investigate oxygen-vacancy complexes in diamond by means of first principles density functional theory calculations. We find that all the considered oxygen-vacancy defects have a high-spin ground state in their neutral charge state, which disregards them as an origin for the ST1 color center. We identify a high-spin metastable oxygen-vacancy complex and characterize their magnetooptical properties for identification in future experiments., Comment: 9 pages, 6 figures, 2 tables

Color centers in diamond are promising platforms for quantum technologies. Most color centers in diamond discovered thus far emit in the visible or near-infrared wavelength range, which are incompatible with long-distance fiber communication and unfavorable for imaging in biological tissues. Here, we report the experimental observation of a new color center that emits in the telecom O-band, which we observe in silicon-doped bulk single crystal diamonds and microdiamonds. Combining absorption and photoluminescence measurements, we identify a zero-phonon line at 1221 nm and phonon replicas separated by 42 meV. Using transient absorption spectroscopy, we measure an excited state lifetime of around 270 ps and observe a long-lived baseline that may arise from intersystem crossing to another spin manifold.

We investigate the optical properties of silicon-vacancy (SiV) and germanium-vacancy (GeV) color centers in nanodiamonds under hydrostatic pressure up to 180 GPa. The nanodiamonds were synthetized by Si or Ge-doped plasma assisted chemical vapor deposition and, for our experiment, pressurized in a diamond anvil cell. Under hydrostatic pressure we observe blue-shifts of the SiV and GeV zero-phonon lines by 17 THz (70 meV) and 78 THz (320 meV), respectively. These measured pressure induced shifts are in good agreement with ab initio calculations that take into account the lattice compression based on the equation of state of diamond and that are extended to the case of the tin-vacancy (SnV) center. This work provides guidance on the use of group-IV-vacancy centers as quantum sensors under extreme pressures that will exploit their specific optical and spin properties induced by their intrinsic inversion-symmetric structure., Comment: 7 pages, 4 figures

Point defect qubits in semiconductors have demonstrated their outstanding high spatial resolution sensing capabilities of broad multidisciplinary interest. Two-dimensional (2D) semiconductors hosting such sensors have recently opened up new horizons for sensing in the subnanometer scales in 2D heterostructures. However, controlled creation of quantum sensor in a single layer 2D materials with high sensitivity has been elusive so far. Here, we report on a novel 2D quantum sensor, the VB2 centre in hexagonal boron nitride (hBN), with superior sensing capabilities. The centre's inherently low symmetry configuration gives rise to unique electronic and spin properties that implement a qubit in a 2D material with unprecedented sensitivity. The qubit is decoupled from its dense spin environment at low magnetic fields that gives rise to the reduction of the spin resonance linewidth and elongation of the coherence time. The VB2 centre is also equipped with a classical memory that can be utilized in storing population information. Using scanning transmission electron microscopy imaging, we confirm the presence of the point defect structure in free standing monolayer hBN created by electron beam irradiation. Our results provide a new material solution towards atomic-scale sensing in low dimensions.

Ultraviolet (UV) quantum emitters in hexagonal boron nitride (hBN) have generated considerable interest due to their outstanding optical response. Recent experiments have identified a carbon impurity as a possible source of UV single photon emission. Here, based on the first principles calculations, we systematically evaluate the ability of substitutional carbon defects to develop the UV colour centres in hBN. Of seventeen defect configurations under consideration, we particularly emphasize the carbon ring defect (6C), for which the calculated zero-phonon line (ZPL) agrees well the experimental 4.1-eV emission signal. We also compare the optical properties of 6C with those of other relevant defects, thereby outlining the key differences in the emission mechanism. Our findings provide new insights about the large response from this colour centre to external perturbations and pave the way to a robust identification of the particular carbon substitutional defects by spectroscopic methods., Comment: 4 figures

We identify the exact microscopic structure of the G photoluminescence center in silicon by first principles calculations with including a self-consistent many-body perturbation method, which is a telecommunication wavelength single photon source. The defect constitutes of $\text{C}_\text{s}\text{C}_\text{i}$ carbon impurities in its $\text{C}_\text{s}-\text{Si}_\text{i}-\text{C}_\text{s}$ configuration in the neutral charge state, where $s$ and $i$ stand for the respective substitutional and interstitial positions in the Si lattice. We reveal that the observed fine structure of its optical signals originates from the athermal rotational reorientation of the defect. We attribute the monoclinic symmetry reported in optically detected magnetic resonance measurements to the reduced tunneling rate at very low temperatures. We discuss the thermally activated motional averaging of the defect properties and the nature of the qubit state., Comment: 2 figures

Many quantum emitters have been measured close or near the grain boundaries of the two-dimensional hexagonal boron nitride where various Stone-Wales defects appear. We show by means of first principles density functional theory calculations that the pentagon-heptagon Stone-Wales defect is an ultraviolet emitter and its optical properties closely follow the characteristics of a 4.08-eV quantum emitter often observed in polycrystalline hexagonal boron nitride. We also show that the square-octagon Stone-Wales line defects are optically active in the ultraviolet region with varying gaps depending on their density in hexagonal boron nitride. Our results may introduce a paradigm shift in the identification of fluorescent centres in this material., Comment: 5 figures

Neutral silicon vacancy (SiV0) centers in diamond are promising candidates for quantum networks because of their excellent optical properties and long spin coherence times. However, spin-dependent fluorescence in such defects has been elusive due to poor understanding of the excited state fine structure and limited off-resonant spin polarization. Here we report the realization of optically detected magnetic resonance and coherent control of SiV0 centers at cryogenic temperatures, enabled by efficient optical spin polarization via previously unreported higher-lying excited states. We assign these states as bound exciton states using group theory and density functional theory. These bound exciton states enable new control schemes for SiV0 as well as other emerging defect systems.

Silicon-vacancy qubits in silicon carbide (SiC) are emerging tools in quantum technology applications due to their excellent optical and spin properties. In this paper, we explore the effect of temperature and strain on these properties by focusing on the two silicon-vacancy qubits, V1 and V2, in 4H SiC. We apply density functional theory beyond the Born-Oppenheimer approximation to describe the temperature dependent mixing of electronic excited states assisted by phonons. We obtain polaronic gap around 5 and 22~meV for V1 and V2 centers, respectively, that results in significant difference in the temperature dependent dephasing and zero-field splitting of the excited states, which explains recent experimental findings. We also compute how crystal deformations affect the zero-phonon-line of these emitters. Our predictions are important ingredients in any quantum applications of these qubits sensitive to these effects., Comment: 8 pages, 5 figures

Quantum systems combining indistinguishable photon generation and spin-based quantum information processing are essential for remote quantum applications and networking. However, identification of suitable systems in scalable platforms remains a challenge. Here, we investigate the silicon vacancy centre in silicon carbide and demonstrate controlled emission of indistinguishable and distinguishable photons via coherent spin manipulation. Using strong off-resonant excitation and collecting photons from the ultra-stable zero-phonon line optical transitions, we show a two-photon interference contrast close to 90% in Hong-Ou-Mandel type experiments. Further, we exploit the system's intimate spin-photon relation to spin-control the colour and indistinguishability of consecutively emitted photons. Our results provide a deep insight into the system's spin-phonon-photon physics and underline the potential of the industrially compatible silicon carbide platform for measurement-based entanglement distribution and photonic cluster state generation. Additional coupling to quantum registers based on recently demonstrated coupled individual nuclear spins would further allow for high-level network-relevant quantum information processing, such as error correction and entanglement purification., Comment: Manuscript and Methods: 21 pages, 4 figures Supplementary Information: 18 pages, 6 figures, 1 table

We study the effect of strain on the physical properties of the nitrogen antisite-vacancy pair in hexagonal boron nitride ($h$-BN), a color center that may be employed as a quantum bit in a two-dimensional material. With group theory and ab-initio analysis we show that strong electron-phonon coupling plays a key role in the optical activation of this color center. We find a giant shift on the zero-phonon-line (ZPL) emission of the nitrogen antisite-vacancy pair defect upon applying strain that is typical of $h$-BN samples. Our results provide a plausible explanation for the experimental observation of quantum emitters with similar optical properties but widely scattered ZPL wavelengths and the experimentally observed dependence of the ZPL on the strain., Comment: 7 pages, 3 figures

Highly correlated orbitals coupled with phonons in two-dimension are identified for paramagnetic and optically active boron vacancy in hexagonal boron nitride by first principles methods which are responsible for recently observed optically detected magnetic resonance signal. We report ab initio analysis of the correlated electronic structure of this center by density matrix renormalization group and Kohn-Sham density functional theory methods. By establishing the nature of the bright and dark states as well as the position of the energy levels, we provide a complete description of the magneto-optical properties and corresponding radiative and non-radiative routes which are responsible for the optical spin polarization and spin dependent luminescence of the defect. Our findings pave the way toward advancing the identification and characterization of room temperature quantum bits in two-dimensional solids.

The recently discovered negatively charged tin-vacancy centre in diamond is a promising candidate for applications in quantum information processing (QIP). We here present a detailed spectroscopic study encompassing single photon emission and polarisation properties, the temperature dependence of emission spectra as well as a detailed analysis of the phonon sideband and Debye-Waller factor. Using photoluminescence excitation spectroscopy (PLE) we probe an energetically higher lying excited state and prove fully lifetime limited linewidths of single emitters at cryogenic temperatures. For these emitters we also investigate the stability of the charge state under resonant excitation. These results provide a detailed insight into the spectroscopic properties of the $\text{SnV}^-$ centre and lay the foundation for further studies regarding its suitability in QIP.

Interfacing solid-state defect electron spins to other quantum systems is an ongoing challenge. The ground-state spin's weak coupling to its environment bestows excellent coherence properties, but also limits desired drive fields. The excited-state orbitals of these electrons, however, can exhibit stronger coupling to phononic and electric fields. Here, we demonstrate electrically driven coherent quantum interference in the optical transition of single, basally oriented divacancies in commercially available 4H silicon carbide. By applying microwave frequency electric fields, we coherently drive the divacancy's excited-state orbitals and induce Landau-Zener-Stuckelberg interference fringes in the resonant optical absorption spectrum. Additionally, we find remarkably coherent optical and spin subsystems enabled by the basal divacancy's symmetry. These properties establish divacancies as strong candidates for quantum communication and hybrid system applications, where simultaneous control over optical and spin degrees of freedom is paramount., Comment: 17 pages, 4 figures

The product Jahn-Teller (pJT) effect may occur for such coupled electron-phonon systems in solids where single electrons occupy double degenerate orbitals. We propose that the excited state of the neutral $X$V split-vacancy complex in diamond, where $X$ and V labels a group-IV impurity atom of $X$=Si, Ge, Sn, Pb and the vacancy, respectively, is such a system with $e_g$ and $e_u$ double degenerate orbitals and $E_g$ quasi-localized phonons. We develop and apply \emph{ab initio} theory to quantify the strength of electron-phonon coupling for neutral $X$V complexes in diamond, and find a significant impact on the corresponding optical properties of these centers. Our results show good agreement with recent experimental data on the prospective SiV($0$) quantum bit, and reveals the complex nature of the excited states of neutral $X$V color centers in diamond., Comment: 2 figures, 1 table

Group-IV -- Vacancy color centers in diamond are fast emerging qubits that can be harnessed in quantum communication and sensor applications. There is an immediate quest for understanding their magneto-optical properties, in order to select the appropriate qubits for varying needs of particular quantum applications. Here we present results from cutting edge \emph{ab initio} calculations about the charge state stability, zero-phonon-line energies, spin-orbit and electron-phonon couplings for Group-IV -- Vacancy color centers. Based on the analysis of our results, we develop a novel spin Hamiltonian for these qubits which incorporates the interaction of the electron spin and orbit coupled with phonons beyond perturbation theory. Our results are in good agreement with previous data and predict a new defect for qubit applications with thermally initialized ground state spin and long spin coherence time., Comment: 16 pages, 8 figures, 4 tables

The nitrogen-vacancy (NV) center in diamond is of high importance in quantum information processing applications which relies on the efficient optical polarization of its electron spin. However, the full optical spinpolarization process, in particular, the intersystem crossing between the shelving singlet state and the ground state triplet, is not understood. Here we develop a detailed theory on this process which involves strong electron-phonon couplings and correlation of electronic states that can be described as a combination of pseudo and dynamic Jahn-Teller interactions together with spin-orbit interaction. Our theory provides an explanation for the asymmetry between the observed emission and absorption spectra of the singlet states. We apply density functional theory to calculate the intersystem crossing rates and the optical spectra of the singlets and we obtain good agreement with the experimental data. As NV center serves as a template for other solid-state-defect quantum bit systems, our theory provides a toolkit to study them that might help optimize their quantum bit operation., Comment: 13 pages, 6 figures, 1 table

Color centers in diamond are a promising platform for quantum technologies, and understanding their interactions with the environment is crucial for these applications. We report a study of spin- lattice relaxation (T1) of the neutral charge state of the silicon vacancy center in diamond. Above 20 K, T1 decreases rapidly with a temperature dependence characteristic of an Orbach process, and is strongly anisotropic with respect to magnetic field orientation. As the angle of the magnetic field is rotated relative to the symmetry axis of the defect, T1 is reduced by over three orders of magnitude. The electron spin coherence time (T2) follows the same temperature dependence but is drastically shorter than T1. We propose that these observations result from phonon-mediated transitions to a low lying excited state that are spin conserving when the magnetic field is aligned with the defect axis, and we discuss likely candidates for this excited state.

Point defects in solids may realize solid state quantum bits. The spin-orbit coupling in these point defects plays a key role in the magneto-optical properties that determine the conditions of quantum bit operation. However, experimental data and methods do not directly yield this highly important data, particularly, for such complex systems where dynamic Jahn-Teller (DJT) effect damps the spin-orbit interaction. Here, we show for an exemplary quantum bit, nitrogen-vacancy (NV) center in diamond, that \emph{ab initio} supercell density functional theory provide quantitative prediction for the spin-orbit coupling damped by DJT. We show that DJT is responsible for the multiple intersystem crossing rates of NV center at cryogenic temperatures. Our results pave the way toward optimizing solid state quantum bits for quantum information processing and metrology applications., Comment: 5 pages, 3 figures, 1 table

Color centers in diamond are important quantum emitters for a broad range of applications ranging from quantum sensing to quantum optics. Understanding the internal energy level structure is of fundamental importance for future applications. We experimentally investigate the level structure of an ensemble of few negatively charged silicon-vacancy (SiV$^{-}$) and germanium-vacancy (GeV$^{-}$) centers in bulk diamond at room temperature by photoluminescence (PL) and excitation (PLE) spectroscopy over a broad wavelength range from 460 nm to 650 nm and perform power-dependent saturation measurements. For SiV$^{-}$ our experimental results confirm the presence of a higher energy transition at ~ 2.31 eV. By comparison with detailed theoretical simulations of the imaginary dielectric function we interpret the transition as a dipole-allowed transition from $^{2}E_{g}$-state to $^{2}A_{2u}$-state where the corresponding $a_{2u}$-level lies deeply inside the diamond valence band. Therefore, the transition is broadened by the diamond band. At higher excitation power of 10 mW we indicate signs of a parity-conserving transition at ~2.03 eV supported by saturation measurements. For GeV$^{-}$ we demonstrate that the PLE spectrum is in good agreement with the mirror image of the PL spectrum of the zero-phonon line (ZPL). Experimentally we do not observe a higher lying energy level up to a transition wavelength of 460 nm. The observed PL spectra are identical, independent of excitation wavelength, suggesting a rapid decay to $^{2}E_{u}$ excited state and followed by optical transition to $^{2}E_{g}$ ground state. Our investigations convey important insights for future quantum optics and quantum sensing experiments based on SiV$^{-}$ center and GeV$^{-}$ center in diamond., Comment: 19 pages, 4 figures

$\text{N}_{2}\text{V}$ defect in diamond is characterized by means of \emph{ab initio} methods relying on density functional theory calculated parameters of a Hubbard model Hamiltonian. It is shown that this approach appropriately describes the energy levels of correlated excited states induced by this defect. By determining its critical magneto-optical parameters, we propose to realize a long-living quantum memory by $\text{N}_{2}\text{V}$ defect in diamond., Comment: 4 figures and 5 tables

In recent years, solid-state spin systems have emerged as promising candidates for quantum information processing (QIP). Prominent examples are the Nitrogen-Vacancy (NV) center in diamond, phosphorous dopants in silicon (Si:P), rare-earth ions in solids and V$_{\text{Si}}$-centers in Silicon-carbide (SiC). The Si:P system has demonstrated, that by eliminating the electron spin of the dopant, its nuclear spins can yield exceedingly long spin coherence times. For NV centers, however, a proper charge state for storage of nuclear spin qubit coherence has not been identified yet. Here, we identify and characterize the positively charged NV center as an electron-spin-less and optically inactive state by utilizing the nuclear spin qubit as a probe. We control the electronic charge and spin utilizing nanometer scale gate electrodes. We achieve a lengthening of the nuclear spin coherence times by a factor of 20. Surprisingly, the new charge state allows switching the optical response of single nodes facilitating full individual addressability., Comment: 8 pages, 4 figures, 1 table

Point defects in diamond are of high interest as candidates for realizing solid state quantum bits, bioimaging agents, or ultrasensitive electric or magnetic field sensors. Various artificial diamond synthesis methods should introduce oxygen contamination in diamond, however, the incorporation of oxygen into diamond crystal and the nature of oxygen-related point defects are largely unknown. Oxygen may be potentially interesting as a source of quantum bits or it may interact with other point defects which are well established solid state qubits. Here we employ plane-wave supercell calculations within density functional theory, in order to characterize the electronic and magneto-optical properties of various oxygen-related defects. Beside the trivial single interstitial and substitutional oxygen defects we also consider their complexes with vacancies and hydrogen atoms. We find that oxygen defects are mostly electrically active and introduce highly correlated orbitals that pose a challenge for density functional theory modeling. Nevertheless, we are able to identify the fingerprints of substitutional oxygen defect, the oxygen-vacancy and oxygen-vacancy-hydrogen complexes in the electron paramagnetic resonance spectrum. We demonstrate that first principles calculations can predict the motional averaging of the electron paramagnetic resonance spectrum of defects that are subject to Jahn-Teller distortion. We show that the high-spin neutral oxygen-vacancy defect exhibits very fast non-radiative decay from its optical excited state that might hinder to apply it as a qubit.

Silicon-vacancy (SiV) center in diamond is a photoluminescence (PL) center with a characteristic zero-phonon line energy at 1.681 eV that acts as a solid-state single photon source and, potentially, as a quantum bit. The majority of the luminescence intensity appears in the zero-phonon line; nevertheless, about 30\% of the intensity manifests in the phonon sideband. Since phonons play an essential role in the operation of this system, it is of importance to understand the vibrational properties of the SiV center in detail. To this end, we carry out density functional theory calculations of dilute SiV centers by embedding the defect in supercells of a size of a few thousand atoms. We find that there exist two well-pronounced quasi-local vibrational modes (resonances) with $A_{2u}$ and $E_u$ symmetries, corresponding to the vibration of the Si atom along and perpendicular to the defect symmetry axis, respectively. Isotopic shifts of these modes explain the isotopic shifts of prominent vibronic features in the experimental SiV PL spectrum. Moreover, calculations show that the vibrational frequency of the $A_{2u}$ mode increases by about 30\% in the excited state with respect to the ground state, while the frequency of the $E_u$ mode increases by about 5\%. These changes explain experimentally observed isotopic shifts of the zero-phonon line energy. We also emphasize possible dangers of extracting isotopic shifts of vibrational resonances from finite-size supercell calculations, and instead propose a method to do this correctly., Comment: 9 pages, 6 figures, 2 tables