Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide

## Abstract

Transition metal ions provide a rich set of optically active defect spins in wide bandgap semiconductors. Chromium (Cr4+) in silicon-carbide (SiC) produces a spin-1 ground state with a narrow, spectrally isolated, spin-selective, near-telecom optical interface. However, previous studies were hindered by material quality resulting in limited coherent control. In this work, we implant Cr into commercial 4H-SiC and show optimal defect activation after annealing above 1600 °C. We measure an ensemble optical hole linewidth of 31 MHz, an order of magnitude improvement compared to as-grown samples. An in-depth exploration of optical and spin dynamics reveals efficient spin polarization, coherent control, and readout with high fidelity (79%). We report T1 times greater than 1 s at cryogenic temperatures (15 K) with a T2* = 317 ns and a T2 = 81 μs, where spin dephasing times are currently limited by spin–spin interactions within the defect ensemble. Our results demonstrate the potential of Cr4+ in SiC as an extrinsic, optically active spin qubit.

## Introduction

Optically active defect spins in wide bandgap semiconductors have attracted much attention as candidate qubits for quantum information.1,2 These defects hold promise due to their long lived, highly localized ground state spin states. They can be manipulated using a number of quantum control mechanisms3 and interfaced with optics through atom-like spin-selective transitions for long-distance quantum communication and entanglement.4 The wide range of available point defects, including complexes and vacancies in diamond4,5,6 and silicon-carbide (SiC)7,8,9,10 as well as rare-earth ions in oxides,11 offer many possible electronic, spin, and optical properties depending on their host materials. As each host provides different benefits, it is desirable to decouple the defect properties from their hosts for reliable defect qubit integration into semiconducting devices.

The prototypical host-independent optically active defects are rare-earth ions, since the transitions within their partially filled f-orbitals are shielded by their outer electronic shells.12 However, their magnetic fine structure within the orbitals due to the crystal field is highly host dependent and is difficult to predict.13 Furthermore, the weak dipole moment of these orbitals result in millisecond long excited state lifetimes which makes optical spin polarization and detecting a single emitter challenging without integrated nanophotonics.14,15,16

Transition metal ions have shown to be host-independent by preserving the physics of the defect center across multiple platforms.10 This is enabled by the similar defect d-orbital electronic structures between various hosts that share lattice symmetry and have similar bond strength.17 Transition metal systems in SiC have already attracted attention as optically active spin qubits such as V4+ 18,19 and Mo5+.20 Both defects possess only one electron in their d-orbitals, resulting in a 3d1 and 4d1 configuration, respectively, with a spin-½ ground and excited states. Under the SiC ligand symmetry the ground state is expected to be comprised of multiple close orbitals which could result in short spin-lattice relaxation (T1) times.19,21

By contrast, chromium defects in SiC in the 4+ charge state (Cr4+) are in the 3d2 electronic configuration, forming a 3A2, orbital singlet spin triplet ground state and a 1E spin singlet orbital doublet excited state. The non-degenerate nature of the ground state orbital yields long spin T1 times while the low nuclear spin density of the SiC host should enable long spin coherence times (T2). Even though the optical transition between 1E and 3A2 states is spin forbidden, resulting in a long decay time (146 μs), both states are formed by the different electron configuration of the same orbitals, creating a weak Jahn-Teller coupling22 which leads to a very high Debye-Waller factor of at least 75%.10 This well-isolated transition lies in the near-telecom range (1070 nm), making Cr4+ particularly interesting for in-fiber long distance quantum communication with integrated spins. However, the previous transition metal ion studies in SiC including Cr4+ have been mostly conducted on as-grown samples10,18,20 and their coherent ground state spin characterization is yet to be demonstrated.

In this work, we study the creation of Cr4+ defect spins in commercial SiC through implantation and annealing, a critical step towards accurate three-dimensional localization of spin defects for device integration.23 Since the optical transition is rather insensitive to environmental perturbations like strain, the fine structure of an ensemble of Cr4+ can be resolved under resonant excitation. This property combined with the Λ-like configuration of the spin forbidden optical transitions makes ensemble spin polarization and readout possible. We therefore demonstrate high fidelity coherent control of the Cr4+ ensemble by Rabi oscillations with contrast exceeding 79%. We then characterize the ground state spin coherence times of Cr4+ in SiC and find long longitudinal spin relaxation times (T1) at cryogenic temperatures and spin-dephasing relaxation time (T2) over 80 μs, similar to other spin defects in SiC with comparable ensemble densities.24 The transportable nature of the electronic configuration and the lattice insensitive narrow optical transitions combined with long spin coherence times that can be read out with high fidelity, makes Cr4+ in SiC and more generally, the d2 configuration in strong tetrahedral ligand field, a promising optically active, transportable and localizable spin qubit.

## Results

Creation and activation of Cr4+ in commercial SiC is a critical step for devices with integrated, optically accessible spins. To this end we introduce isotopically pure, nuclear spin-free 52Cr atoms into commercially purchased 4H-SiC substrates through implantation at elevated temperatures up to 700 °C. We believe that the implanted chromium atoms sit mainly in interstitial sites of the SiC lattice. During the subsequent annealing, Cr atoms move to the silicon (Si) site and form bonds with the surrounding carbon atoms (Fig. 1a). This generates the Cr4+ level structure shown in Fig. 1b (defect activation). The two different Si lattice sites in 4H-SiC result in two distinct Cr4+ species: CrA (quasi-cubic k-site) and CrC (quasi-hexagonal h-site).22 To investigate the electrical activation of the defect ensembles, we anneal different samples from the same implanted substrate between 800 and 1800 °C and then measure the zero-phonon line (ZPL) intensities of CrA and CrC (Fig. 1c). Cr4+ activation, not observable when the samples are not annealed, increases monotonically as a function of annealing temperature until 1600 °C where it saturates.

For coherent characterization of the defect, we create Cr4+ in a wider range of depth in SiC by combining multiple high energy ion implantations (see Methods) followed by 1800 °C annealing to reduce the overall Cr4+ density while maximizing its signal. Off-resonant photoluminescence (PL) at 30 K demonstrates successful activation of Cr4+ in this sample (Fig. 1d). The weak spin-forbidden transition of Cr4+ under resonant excitation is challenging to detect in the presence of other four orders of magnitude brighter optically active residual defects (such as the divacancy8) created during substrate growth and ion implantation. However, the long-lived excited state of Cr4+ enables temporal separation of the relevant PL from the background (see SI) by only integrating over the transient signal. We measure the photoluminescence excitation (PLE) spectrum by resonantly exciting Cr4+ ZPL and collecting the transient phonon sideband (Fig. 1e) at 30 K. A fit to two Gaussian functions for the ms= 0 and ms = ± 1 sublevels with a known ground state crystal field splitting (D) for CrA (1063 MHz) yields an average PLE linewidth of 5.1(4) GHz with the ms= 0 linewidth roughly two times larger than the ms = ± 1 linewidth. The origin of this behavior is unknown and may be a result of mass related shift due to 13C, 29Si, and 30Si isotopes.19,25,26 We observe a similar trend for CrC (see SI) where the individual PLE lines are more resolved due to a larger D. The overall sharper inhomogeneous linewidth of the implanted sample compared to the as-grown sample10 allows for better spin sublevel resolution and is likely due to an improved spatial strain profile.

We then characterize the ground state spins of Cr4+ in SiC through resonant hole burning and hole recovery at 15 K where the spin T1 is longer than the optical lifetime. The population of a spin sub-ensemble excited by the narrow line resonant laser will be redistributed among the other ground state spin sublevels after spontaneous emission, leading to hole burning and spin polarization. Since the polarized sub-population is off-resonant relative to the probe laser, the defect goes dark resulting in a spin selective optical contrast. We can recover the hole by reintroducing the polarized population into the optical cycle in two ways, either by using a second laser color to probe the polarized sublevels or by driving ground state spins with microwaves. A second laser tone generated by a phase modulator recovers the CrA hole at a D of 1062.7(4) MHz (Fig. 2a). A Lorentzian fit to the data extracts a 31(2) MHz ensemble hole linewidth, which is more than an order of magnitude narrower than the as grown samples,10 demonstrating the superior material quality of the implanted and annealed sample. However, the sharp hole linewidth is also two orders of magnitude narrower than the inhomogeneous optical linewidth, indicating only 1% of the created CrA defects are accessed under resonant excitation. One could increase the net ensemble polarization by further reducing the inhomogeneous linewidth through material improvements. The hole can also be recovered by microwave mixing of the ground state spin sublevels, enabling optical detection of magnetic resonance (ODMR) (Fig. 2b). Stray magnetic fields Zeeman split the ms = ±1 ODMR by ~5 MHz centered around D = 1063.11(1) MHz (Fig. 2b). A Lorentzian fit to the non-power broadened ODMR reveals a linewidth of 1.32(2) MHz. Because the 31 MHz optical hole linewidth is not confined by the ODMR linewidth, the optical coherence is likely excited-state limited. The four orders of magnitude difference between the measured and lifetime limited hole linewidth (~2 kHz) may be a result of decoherence induced by the degenerate excited state orbital doublet structure that can be lifted by applying high magnetic fields22 or spectral diffusion due to charge fluctuations that can be addressed by creating charge depletion zones;27 the exact mechanism and its solution would require further investigation.

A c-axis magnetic field lifts the optical degeneracy of the ms = ±1 sublevels by Zeeman splitting while the S = 0 excited state remains unaffected (Fig. 1b). It is worth noting that the population can become trapped in the unprobed third level after using either the optical sideband probe or the microwave mixing, as these techniques can only address one sub-level at a time. By applying both an optical sideband probe and a microwave tone together, all states can be addressed simultaneously resulting in hole recovery (Fig. 2c). Using a second laser to trap the population into the third sublevel provides a path for efficient spin polarization under a magnetic field.

For coherent control and readout of Cr4+, we polarize a subpopulation into the ms = +1 sublevel by tuning the primary laser color to be resonant with ms = 0 state and adding a sideband tone to optically excite the ms = −1 sublevel (see SI). Once polarized, we coherently control the subpopulation using resonant microwave rotations within the ms = 0, +1 manifold and read out the ms = 0 population with a short (50 μs) primary laser excitation (Fig. 3a). We measure Rabi rotations at B = 158 G by varying the microwave excitation length and obtain a contrast of 63(1)% with an envelope decay time of 4.76(7) μs (Fig. 3b).

To characterize the ground state spin coherence times, we perform Ramsey interferometry and Hahn echo measurements. For the Ramsey measurement, we detune the resonant microwave frequency by 5 MHz and delay the time between two πx/2 pulses. The characteristic oscillations at the detuning frequency have an envelope with a decay time of T2* = 307(17) ns (Fig. 3c), in agreement with the ODMR linewidth measurements in Fig. 2b. We measure the T2 coherence time by (±πx/2 − tfree/2 − πytfree/2 − πx/2) echo-pulse sequence. We fit the data to an electron spin echo envelope modulation function where nuclear Larmor precessions are enveloped by a decay function of $$e^{ - \left( t/T_2 \right)^n}{\prod} {\left( {1 - K_{\mathrm{a}}{\mathrm{sin}}^2\left( {\pi \omega _a\tau } \right)} \right)}$$, with the precession amplitudes (Ka), frequencies (ωa) and decay power (n) and time (T2) as free fit parameters.28 We recover the characteristic oscillations at the current B field for 13C (87.5(3) kHz) and 29Si (68.0(1) kHz) as well as T2 = 81(2) μs with a decay power dependence of n = 1.9(1) (Fig. 3d). The average defect density in our sample is roughly 3 × 1016 atoms/cm3 (see SI) and the measured T2 time is in line with similarly dense divacancy ensembles in SiC.24 This indicates that the observed coherence times are likely limited by electron spin–spin interactions between defects, and further reduction of the Cr4+ and background defect densities could result in millisecond long coherence times.28

Finally, we report that by sacrificing overall signal and reducing the probe time from 50 to 1 μs we increase the Rabi contrast to 79(2)% contrast (Fig. 3f). This places a lower bound on the ensemble polarization of at least 77%. The contrast, however, is lower than our estimate (see SI) and we believe a spin-reset mechanism induced by the probe itself could be responsible, therefore, further exploration of this effect could increase the readout fidelity.

The spin characterization measurements reported above are enabled by the careful study of the rates responsible for the Cr4+ population dynamics. One such rate is the excited state lifetime (Topt) under resonant excitation which we measure at 30 K by histogramming the transient PLE to find Topt = 156.3(5) μs (Fig. 4a). This is in agreement with the off-resonant excited state lifetime10 (see SI). Based on this measurement, our integration window for the collected photons in the transient readout is 155 μs long.

To understand the ground state spin dynamics, we measure the spin T1 time at B = 0 G by population inversion relaxation using a microwave π-pulse. By repeating this measurement for temperatures between 15 and 30 K and fitting each data set to an exponential decay function, we extract T1 times and use this dataset to distinguish between Orbach and Raman processes29 (Fig. 4b). For the Orbach process, we use $$\frac{1}{{T_1}} = A\,e^{ - \frac{E}{{k_{\mathrm{B}}T}}}$$ as our fit function where A and E, the energy difference to a low-lying excited state, are fit parameters. For the Raman process we use $$\frac{1}{{T_1}} = A\,\left( {T - \Delta T} \right)^n$$ where A and ΔT, a constant temperature offset of the sample, are fit parameters for various fixed odd integers n. The Orbach model fits the data poorly and returns an energy gap of E = 20(1) meV which is a factor of 50 lower from the first excited state energy and a factor of 4 lower than the closest phonon line energy,22 indicating that Orbach process is not the likely explanation for T1 decay mechanism. Out of the Raman processes, the most likely explanation is the n = 9 process (see SI), indicating that the T1 is spin-orbit interaction limited. The longest measured spin T1 time is 1.6(3) s long at T = 15 K, long enough to not limit the spin dephasing times and to offer a very long window for high fidelity spin initialization.

Finally, we time resolve the polarization dynamics of Cr4+ to investigate defect initialization. We sweep the resonant excitation time using the same parameters in Fig. 3b–d and measure the populations of the ms = 0 and the ms = +1 spin sublevels (Fig. 4c). When the resonant excitation time of the ms = 0 is less than the optical lifetime of 155 μs, the population in the excited state transferred from the ms = 0 increases. Past that point in time, the ms = 0 population depletes as the sub-ensemble polarizes into the ms = +1. Using a π-pulse to coherently swap the populations between the ms = 0 and the ms = +1 states, we measure the polarized population within the ms = +1 sublevel which increases monotonically with the laser excitation time. The difference of the two traces is the optical contrast shown in Fig. 4d. An exponential fit to the data yields a rise time of 1.27(3) ms, corresponding to polarization within ~10 optical lifetimes with maximum contrast at 64(2)%. In order to achieve the reported 63% contrast for a 50 μs probe time, we polarized the defect for 5 ms. Reducing the optical lifetime through Purcell enhancement in an optical cavity would significantly decrease this initialization time.

## Discussion

In summary, we have demonstrated successful creation and activation of Cr4+ ions with exceptional optical and spin properties in commercial semi-insulating SiC substrates. This method could be used to introduce other transition metal ions such as V18,19 and Mo20 into SiC and GaN.10 The reported defect creation technique can also be extended to three-dimensional localization of single transition metal ions in SiC for device integration through nano-implantation.30,31 For example, a single Cr4+ can be detected by placing it into a photonic cavity to reduce the excited state lifetime by Purcell enhancement.15 Within such a device, the already large fraction of indistinguishable photons in the near-telecom ZPL would be further enhanced.4 A dense ensemble of Cr4+ ions within a cavity may achieve population inversion through the second-excited state to realize a laser.32 This ensemble can also be used to realize an optical memory where the optical qubit is stored within the collective ground state spin wave, limited by the T2.33 All these possible photonics applications readily come with integrated spins that can be initialized and read out with a high fidelity of at least 79%. Furthermore, the measured ensemble spin coherence time T2 of 81 μs is spin–spin limited, showing that the potential of an isolated Cr4+ in SiC as spin qubits.28

Finally, our results can be generalized to a broader set of transition metal ions in d2 electronic configuration in a host that provides a strong tetrahedral ligand field. The 31 MHz ensemble optical linewidth and the 79% readout fidelity combined with T1 time greater than 1 s makes these class of transition metal electronic structures a promising set of transportable optically active spin qubits.

## Methods

### Sample preparation

In Fig. 1c the substrates were high purity semi-insulating, on-axis 4H-SiC sourced by Norstel AB. The SiC samples were co-implanted with 52Cr at 190 keV energy with a dose of 5 × 1011 cm−2, and 12C at 100 keV energy with a dose of 5 × 1011 cm−2 by CuttingEdge Ions, LLC. Both ions were hot implanted with a 7° tilt at a temperature of 600 °C. Chromium atoms are calculated to have an average depth of 110 nm and a 30 nm straggle using the program Stopping Range of Ions in Matter (SRIM). All samples were subsequently cleaned with organic solvents. A photoresist layer (AZ1518) is spun ~2 µm thick, baked at 95 °C for 1 minute then 350 °C for 30 min, as a protective surface coating by forming a graphite cap during the high temperature annealing. The samples are annealed in a tube furnace with high purity Ar at 800–1400 °C for 15 min with ramp rates of 100 °C per hour. The annealing of the samples at 1500–1800 °C was performed by Fraunhofer IISB in an Ar environment for 15 min with ramp rates of 900 °C per hour. The graphite cap was removed by heating the sample to 750 °C for 30 min in air.

The box profile implanted sample in Figs. 1b, c, 24 used an epitaxial, undoped (intrinsic), 20 µm thick 4H-SiC layer that was grown on a 4° off-axis semi-insulating SiC substrate sourced by Norstel AB. The 4H-SiC sample was implanted with 52Cr ions in four steps with energies of 10, 5, 2, 1 MeV and doses of (3, 3, 2, 1.5) × 1012 cm−2, respectively, at a sample temperature of approximately 690 °C at Sandia National Laboratories. After 52Cr implantation the sample was cleaned, photoresist capped, and annealed at 1800 °C for 15 minutes using the same procedures detailed above.

### Optical and spin characterization experiments

A closed cycle cryostat (Montana Instruments Nanoscale Workstation), with microwave and optical access is used to cool the sample. A NIR 50× objective (Olympus) is mounted to a heated and isolated shroud within the cryostat. Three in-cryo piezo stages (Attocube), each with a 4 mm range enabled switching between samples and locating microwave striplines.

A Thorlabs TO can 730 nm laser is used for off-resonant excitation. Resonant excitation is achieved by a fiber-coupled, external-cavity diode laser with a tuning range of 1035–1075 nm and a linewidth <200 kHz integrated over 50 ms with 18 mW maximum output power (Newfocus Velocity 6700). An electro-optical modulator (iXBlue) with a 12 GHz bandwidth that generates optical side-bands is used for the experiments that needed two colors. A fiber coupled acousto-optical modulator (Aaoptoelectronic) is used to rapidly turn the laser on and off, a second one is added for the T1 data in Fig. 4b to improve the extinction ratio over long wait times.

A vector signal generator (Stanford Research Instruments SG396) with a 30 W 0.6–2.7 GHz amplifier (Minicircuits) is used for microwave excitation. It is fed to a shorted coplanar wave guide patterned on a custom-made printed circuit board situated behind the sample within the cryostat.

For spectrally resolved measurements a liquid nitrogen cooled InGaAs NIR camera with a spectrometer (Princeton Instruments) is used. For resonant measurements, a superconducting nanowire single photon detector that is optimized for 1.0–1.2 μm regime coupled to a 25 μm multimode fiber (Quantum-Opus LLC) is used. The average dark count resulting from thermal photons slowly varying between 6 and 9 k counts/s were measured before an experiment and subtracted from the data. The detection signal is gated using a microwave switch (Minicurcuits) and counted using a data acquisition system (National Instruments).

An arbitrary waveform generator (Swabian Instruments) is used to synchronize timings of the laser excitation, probe generation, microwave excitation with IQ control, collection, and counter gating.

## Data availability

All the data that support the findings of this study are available from the corresponding author upon reasonable request.

## References

1. 1.

Awschalom, D. D., Hanson, R., Wrachtrup, J. & Zhou, B. B. Quantum technologies with optically interfaced solid-state spins. Nat. Photonics 12, 516–527 (2018).

2. 2.

Atatüre, M., Englund, D., Vamivakas, N., Lee, S.-Y. & Wrachtrup, J. Material platforms for spin-based photonic quantum technologies. Nat. Rev. Mater. 3, 38–51 (2018).

3. 3.

Heremans, F. J., Yale, C. G. & Awschalom, D. D. Control of spin defects in wide-bandgap semiconductors for quantum technologies. Proc. IEEE 104, 2009–2023 (2016).

4. 4.

Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

5. 5.

Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013).

6. 6.

Bradac, C., Gao, W., Forneris, J., Trusheim, M. E., & Aharonovich, I. Quantum nanophotonics with group IV defects in diamond. Nat. Commun. 10, 5625 (2019). https://doi.org/10.1038/s41467-019-13332-w.

7. 7.

Koehl, W. F., Buckley, B. B., Heremans, F. J., Calusine, G. & Awschalom, D. D. Room temperature coherent control of defect spin qubits in silicon carbide. Nature 479, 84–87 (2011).

8. 8.

Christle, D. J. et al. Isolated spin qubits in SiC with a high-fidelity infrared spin-to-photon interface. Phys. Rev. X 7, 021046 (2017).

9. 9.

Nagy, R. et al. High-fidelity spin and optical control of single silicon-vacancy centres in silicon carbide. Nat. Commun. 10, 1954 (2019).

10. 10.

Koehl, W. F. et al. Resonant optical spectroscopy and coherent control of Cr4+ spin ensembles in SiC and GaN. Phys. Rev. B 95, 035207 (2017).

11. 11.

Kunkel, N. & Goldner, P. Recent advances in rare earth doped inorganic crystalline materials for quantum information processing. Z. Anorg. Allg. Chem. 644, 66–76 (2018).

12. 12.

Dieke, G. H., Crosswhite, H. M. & Dunn, B. Emission spectra of the doubly and triply ionized rare earths. J. Opt. Soc. Am. 51, 820 (1961).

13. 13.

Abragam, A. & Bleaney, B. (Brebis). in Electron Paramagnetic Resonance of Transition Ions 277–345 (Oxford University Press, 2012).

14. 14.

Zhong, T. et al. Nanophotonic rare-earth quantum memory with optically controlled retrieval. Science 357, 1392–1395 (2017).

15. 15.

Dibos, A. M., Raha, M., Phenicie, C. M. & Thompson, J. D. Atomic source of single photons in the telecom band. Phys. Rev. Lett. 120, 243601 (2018).

16. 16.

Raha, M. et al. Optical quantum nondemolition measurement of a solid-state spin without a cycling transition. Preprint at arXiv:1907.09992 (2019).

17. 17.

Figgis, B. N. & Hitchman, M. A. Ligand Field Theory and Its Applications (Special Topics in Inorganic Chemistry) (Wiley, 1999).

18. 18.

Spindlberger, L. et al. Optical properties of vanadium in 4H silicon carbide for quantum technology. Phys. Rev. Appl. 12, 014015 (2019).

19. 19.

Wolfowicz, G. et al. Vanadium spin qubits as telecom quantum emitters in silicon carbide. Preprint at arXiv:1908.09817 (2019).

20. 20.

Bosma, T. et al. Identification and tunable optical coherent control of transition-metal spins in silicon carbide. npj Quantum Inf. 4, 48 (2018).

21. 21.

Pingault, B. et al. Coherent control of the silicon-vacancy spin in diamond. Nat. Commun. 8, 15579 (2017).

22. 22.

Son, N. T. et al. Photoluminescence and Zeeman effect in chromium-doped 4H and 6H SiC. J. Appl. Phys. 86, 4348–4353 (1999).

23. 23.

Ohno, K. et al. Three-dimensional localization of spins in diamond using 12C implantation. Appl. Phys. Lett. 105, 052406 (2014).

24. 24.

Falk, A. L. et al. Polytype control of spin qubits in silicon carbide. Nat. Commun. 4, 1819 (2013).

25. 25.

Cardona, M. & Thewalt, M. L. W. Isotope effects on the optical spectra of semiconductors. Rev. Modern Phys. 77, 1173 (2005).

26. 26.

Imbusch, G. F., Yen, W. M., Schawlow, A. L., Devlin, G. E. & Remeika, J. P. Isotope shift in the R lines of chromium in ruby and MgO. Phys. Rev. 136, A481–A486 (1964).

27. 27.

Anderson, C. P. et al. Electrical and optical control of single spins integrated in scalable semiconductor devices. Science 366, 1225–1230 (2019).

28. 28.

Christle, D. J. et al. Isolated electron spins in silicon carbide with millisecond coherence times. Nat. Mater. 14, 160–163 (2015).

29. 29.

Castner, T. G. Jr. Raman spin-lattice relaxation of shallow donors in silicon. Phys. Rev. 491, 58–75 (1963).

30. 30.

Jamieson, D. N. et al. Deterministic doping. Mater. Sci. Semicond. Process. 62, 23–30 (2017).

31. 31.

Pacheco, J. L. et al. Ion implantation for deterministic single atom devices. Rev. Sci. Instrum. 88, 123301 (2017).

32. 32.

Kück, S. Laser-related spectroscopy of ion-doped crystals for tunable solid-state lasers. Appl. Phys. B Lasers Opt. 72, 515–562 (2001).

33. 33.

Afzelius, M., Simon, C., de Riedmatten, H. & Gisin, N. Multimode quantum memory based on atomic frequency combs. Phys. Rev. A 79, 052329 (2009).

34. 34.

Ferro, G. & Chaussende, D. A new model for in situ nitrogen incorporation into 4H-SiC during epitaxy. Sci. Rep. 7, 43069 (2017).

## Acknowledgements

The authors thank S. Bayliss, M. Fataftah, D.W. Laorenza, M.K. Wojnar, T. Fidler, and A. Bauer for useful discussion. This project was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government.

## Author information

Authors

### Contributions

B.D. performed the experiments and analyzed the data. S.J.W. and C.P.A. annealed and cleaned the samples and E.S.B. implanted the box profile implanted sample. M.W. deposited an IR coating to enhance the signal that was used for the initial exploration. G.W. provided experimental guidance. D.D.A. and F.J.H. advised and coordinated all efforts. All authors contributed to the manuscript.

### Corresponding author

Correspondence to David D. Awschalom.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Diler, B., Whiteley, S.J., Anderson, C.P. et al. Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide. npj Quantum Inf 6, 11 (2020). https://doi.org/10.1038/s41534-020-0247-7

• Accepted:

• Published:

• ### Spin–spin interactions in defects in solids from mixed all-electron and pseudopotential first-principles calculations

• Krishnendu Ghosh
• , He Ma
• , Mykyta Onizhuk
• , Vikram Gavini
•  & Giulia Galli

npj Computational Materials (2021)

• ### Entanglement and control of single nuclear spins in isotopically engineered silicon carbide

• Alexandre Bourassa
• , Christopher P. Anderson
• , Kevin C. Miao
• , Mykyta Onizhuk
• , He Ma
• , Alexander L. Crook
• , Hiroshi Abe
• , Takeshi Ohshima
• , Nguyen T. Son
• , Giulia Galli
•  & David D. Awschalom

Nature Materials (2020)

• ### Quantum simulations of materials on near-term quantum computers

• He Ma
• , Marco Govoni
•  & Giulia Galli

npj Computational Materials (2020)