# Robust single divacancy defects near stacking faults in 4H-SiC under
resonant excitation

Zhen-Xuan He  CAS Key Laboratory of Quantum Information, University of Science
and Technology of China, Hefei, Anhui 230026, China  CAS Center For Excellence
in Quantum Information and Quantum Physics, University of Science and
Technology of China, Hefei, Anhui 230026, China  Hefei National Laboratory,
University of Science and Technology of China, Hefei, Anhui 230088, China  Ji-
Yang Zhou  CAS Key Laboratory of Quantum Information, University of Science
and Technology of China, Hefei, Anhui 230026, China  CAS Center For Excellence
in Quantum Information and Quantum Physics, University of Science and
Technology of China, Hefei, Anhui 230026, China  Wu-Xi Lin  CAS Key Laboratory
of Quantum Information, University of Science and Technology of China, Hefei,
Anhui 230026, China  CAS Center For Excellence in Quantum Information and
Quantum Physics, University of Science and Technology of China, Hefei, Anhui
230026, China  Hefei National Laboratory, University of Science and Technology
of China, Hefei, Anhui 230088, China  Qiang Li  Institute of Advanced
Semiconductors and Zhejiang Provincial Key Laboratory of Power Semiconductor
Materials and Devices, ZJU-Hangzhou Global Scientific and Technological
Innovation Center, Hangzhou, Zhejiang 311200, China  State Key Laboratory of
Silicon Materials and Advanced Semiconductors and School of Materials Science
and Engineering, Zhejiang University, Hangzhou 310027, China  Rui-Jian Liang
CAS Key Laboratory of Quantum Information, University of Science and
Technology of China, Hefei, Anhui 230026, China  CAS Center For Excellence in
Quantum Information and Quantum Physics, University of Science and Technology
of China, Hefei, Anhui 230026, China  Jun-Feng Wang  College of Physics,
Sichuan University, Chengdu, Sichuan 610065, China  Xiao-Lei Wen  Center for
Micro and Nanoscale Research and Fabrication, University of Science and
Technology of China, Hefei, Anhui 230026, People’s Republic of China  Zhi-He
Hao  CAS Key Laboratory of Quantum Information, University of Science and
Technology of China, Hefei, Anhui 230026, China  CAS Center For Excellence in
Quantum Information and Quantum Physics, University of Science and Technology
of China, Hefei, Anhui 230026, China  Wei Liu  CAS Key Laboratory of Quantum
Information, University of Science and Technology of China, Hefei, Anhui
230026, China  CAS Center For Excellence in Quantum Information and Quantum
Physics, University of Science and Technology of China, Hefei, Anhui 230026,
China  Shuo Ren  CAS Key Laboratory of Quantum Information, University of
Science and Technology of China, Hefei, Anhui 230026, China  CAS Center For
Excellence in Quantum Information and Quantum Physics, University of Science
and Technology of China, Hefei, Anhui 230026, China  Hao Li  State Key
Laboratory of Functional Materials for Informatics, Shanghai Institute of
Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai
200050, China  Li-Xing You  State Key Laboratory of Functional Materials for
Informatics, Shanghai Institute of Microsystem and Information Technology,
Chinese Academy of Sciences, Shanghai 200050, China  Jian-Shun Tang  CAS Key
Laboratory of Quantum Information, University of Science and Technology of
China, Hefei, Anhui 230026, China  CAS Center For Excellence in Quantum
Information and Quantum Physics, University of Science and Technology of
China, Hefei, Anhui 230026, China  Hefei National Laboratory, University of
Science and Technology of China, Hefei, Anhui 230088, China  Jin-Shi Xu
Email<EMAIL_ADDRESS>CAS Key Laboratory of Quantum Information, University
of Science and Technology of China, Hefei, Anhui 230026, China  CAS Center For
Excellence in Quantum Information and Quantum Physics, University of Science
and Technology of China, Hefei, Anhui 230026, China  Hefei National
Laboratory, University of Science and Technology of China, Hefei, Anhui
230088, China  Chuan-Feng Li  Email<EMAIL_ADDRESS>CAS Key Laboratory of
Quantum Information, University of Science and Technology of China, Hefei,
Anhui 230026, China  CAS Center For Excellence in Quantum Information and
Quantum Physics, University of Science and Technology of China, Hefei, Anhui
230026, China  Hefei National Laboratory, University of Science and Technology
of China, Hefei, Anhui 230088, China  Guang-Can Guo  CAS Key Laboratory of
Quantum Information, University of Science and Technology of China, Hefei,
Anhui 230026, China  CAS Center For Excellence in Quantum Information and
Quantum Physics, University of Science and Technology of China, Hefei, Anhui
230026, China  Hefei National Laboratory, University of Science and Technology
of China, Hefei, Anhui 230088, China

###### Abstract

Color centers in silicon carbide (SiC) have demonstrated significant promise
for quantum information processing. However, the undesirable ionization
process that occurs during optical manipulation frequently causes fluctuations
in the charge state and performance of these defects, thereby restricting the
effectiveness of spin-photon interfaces. Recent predictions indicate that
divacancy defects near stacking faults possess the capability to stabilize
their neutral charge states, thereby providing robustness against
photoionization effects. In this work, we present a comprehensive protocol for
the scalable and targeted fabrication of single divacancy arrays in 4H-SiC
using a high-resolution focused helium ion beam. Through photoluminescence
emission (PLE) experiments, we demonstrate long-term emission stability with
minimal linewidth shift ($\sim$ 50 MHz over 3 hours) for the single c-axis
divacancies within stacking faults. By measuring the ionization rate for
different polytypes of divacancies, we found that the divacancies within
stacking faults are more robust against resonant excitation. Additionally,
angle-resolved PLE spectra reveal their two resonant-transition lines with
mutually orthogonal polarizations. Notably, the PLE linewidths are
approximately 7 times narrower and the spin-coherent times are 6 times longer
compared to divacancies generated via carbon-ion implantation. These findings
highlight the immense potential of SiC divacancies for on-chip quantum
photonics and the construction of efficient spin-to-photon interfaces,
indicating a significant step forward in the development of quantum
technologies.

## Introduction

Silicon carbide (SiC) is a prominent example of third-generation
semiconductors. It is renowned for its well-established inch-scale production,
mature controlled-doping techniques, high-quality nanofabrication
capabilities, and compatibility with CMOS-friendly processes. Similar to the
nitrogen-vacancy (NV) centers in diamond, SiC also possesses a range of color
centers, including silicon vacancies ($V_{Si}$) [1, 2, 3, 4, 5, 6],
divacancies (DVs) [7, 8, 9, 10, 11, 14], NV centers [15, 16, 17], and
substitutional transition metal ions [18, 19, 20]. In comparison to NV centers
in diamond that emit visible light, SiC color centers exhibit near-infrared
photon luminescence (PL) with lower attenuation in fiber transitions.
Moreover, the inherent response of SiC color centers to external fields makes
them excellent platforms for magnetic, electric, thermal, and extreme-
condition quantum sensing [21, 22, 23, 24, 25, 26, 27, 28, 29]. Leveraging
well-established semiconductor integration technology, color centers can be
manipulated within P-I-N junctions to achieve stark detuning [30, 31], control
charge states [32], and generate electrically-driven single photon sources
[33, 34]. Additionally, SiC color centers exhibit long spin-coherent times at
both room and low temperatures [1, 6, 7, 9, 10, 13], as well as spin-selective
optical transitions under resonant optical excitation [10, 30, 31, 2, 3, 4],
making them promising candidates for creating spin-to-photon interfaces.

Figure 1: FHIB-generated DV arrays in 4H-SiC and characterization of
individual DVs. (a) Schematic illustration depicting the fabrication of DV
arrays in 4H-SiC utilizing FHIB. (b) Confocal scanning image displaying the DV
arrays generated using a dose of 300 ions/spot. (c) Low-temperature ODMR
spectrum obtained from the single white-circled PL6 (upper panel) and yellow-
circled PL4 (lower panel) in (b). (d) As-measured second-order autocorrelation
function for a single PL6. (e) As-measured second-order autocorrelation
function for a single PL4.(f) The excited-state lifetimes for a single PL6
(black) and a single PL4 (blue).

However, the charge-state instabilities of color centers under optical
excitation have proven to be an important unresolved problem. Previous
theoretical works have predicted that the quantum well structures in SiC, like
stacking faults, which are of an extended defect, can stabilize the charge
state of a point defect [11]. Experimental works have also observed the stable
photoemission under optical illumination of stacking-fault DVs in 4H-SiC (PL5
and PL6) ensembles [43]. Thus, stacking-faults DVs in 4H-SiC are potential
high-optical-quality platforms for the quantum information process.

In this work, we investigated the application of a high-precise focused helium
ion beam (FHIB) to create individual DV arrays in 4H-SiC. Through
photoluminescence emission (PLE) experiments, we examined the optical
properties under resonant excitation of the c-axis DV near stacking fault
(PL6) and basal DV (PL4) in 4H-SiC. We found that the individual PL6
divacancies showed long-term emission stability for over 3 hours. Notably, by
measuring the photoionization rates for PL4 and PL6, we found that stacking-
fault-protected PL6 exhibits better resistance against resonant excitation-
induced ionization. Additionally, we performed excitation angle-resolved PLE
spectra measurements and observed two resonant-transition lines with mutually
orthogonal polarizations, making them ideal for constructing spin-to-photon
interfaces. Moreover, our results showed a significant improvement in optical
and spin properties for the helium ion implanted samples, with the PLE
linewidths being 7 times narrower and the spin-coherent times being 6 times
longer compared to divacancies generated via carbon-ion ($C^{+}$)
implantation. Overall, our findings contribute to developing SiC-based quantum
networking [44], showing the potential of stacking-fault DV in this field.

## Results

###  .1 The FHIB-fabricated divacancy arrays

We utilized a helium ion microscope (HIM, ZEISS Orien NanoFab) to employ the
FHIB technique for fabricating DV ensembles and arrays. The helium ion beam,
with an incident energy of 30 keV, was accelerated and focused to achieve a
spot size of approximately 0.5 nm. The implantation depth was simulated to be
about 170 nm (see Supplementary Materials (SM) Fig. S1). The specific
locations for each spot were determined based on a pre-designed layout. Fig.
1(a) illustrates the schematic diagram of the FHIB implantation process. DV
ensembles were fabricated using the raster scanning mode with a dose of
$1\times 10^{15}$ ions/$cm^{2}$, while the arrays were created using the spot
mode with varying doses (see Materials and Methods and SM Section S1).
Subsequently, the sample was annealed at 500 oC for 2 hours, followed by a
post-annealing at 900 oC for 1 hour to facilitate DV formation.

Fig. 1(b) displays the confocal scanning image of the generated DV arrays with
an incident dose of 300 ions/spot, where a distance of 3 µm separated each
spot. To investigate the polytypes of DVs within the array, we conducted
measurements of the low-temperature (L-T) photoluminescence (PL) spectra and
continuous-microwave (MW) optically-detected-magnetic-resonance (ODMR) spectra
of both the ensembles and arrays at 4.5 K. (The L-T optical and spin-
properties characterization are observable in Figs. S3 and S4 in SM) Within
the array, we identified single PL6 defects. We have highlighted one
representative PL6 and PL4 with a white and a yellow circle in Fig. 1(b),
respectively. The L-T ODMR spectra for the circled PL6 (upper panel) and PL4
(lower panel) under a zero magnetic field ($B\approx 0$ G) are shown in Fig.
1(c). For the c-axis PL6, a single dip was observed at $\sim$ 1365 MHz,
exhibiting an ODMR contrast of $\sim$ -0.16. This dip corresponds to the spin
transition from the ground state $\ket{0}$ with the magnetic quantum number
$m_{s}=0$ to the degenerate states $\ket{\pm 1}$ with $m_{s}=\pm 1$ when
$B\approx 0$ G [7]. By contrast, the basal PL4 exhibited one peak at $\sim$
1316 MHz and one dip at $\sim$ 1353 MHz, representing the transitions from
$\ket{0}$ to $\ket{-}$ ($=\frac{1}{\sqrt{2}}(\ket{1}-\ket{-1})$) and $\ket{+}$
($=\frac{1}{\sqrt{2}}(\ket{1}+\ket{-1})$) in the ground state [7, 30]. To
confirm the single-photon emission properties of the defects, we conducted
Hanbury Brown-Twiss (HBT) interference measurements. Figs. 1(d) and (e)
illustrate the as-measured second-order autocorrelation functions
$g^{2}(\tau)$ for PL6 and PL4 without background extraction. The fitted
$g^{2}(0)$ values were 0.15 $\pm$ 0.01, and 0.35 $\pm$ 0.05, respectively,
which are all far below 0.5, indicating single photon emission properties.
Furthermore, we measured the PL spectrum to further confirm the polytype (see
Fig. S4 in SM). The measured zero-phonon line (ZPL) positions were $\sim$ 1038
nm and $\sim$ 1078 nm, which were consistent with previous studies [7, 12, 14,
30]. We also measured the excited-state lifetime of the single PL6 and the
single PL4, obtaining fitted values of $\tau=15.06\pm 0.14$ ns and
$\tau=11.97\pm 0.12$ ns, as shown in Fig. 1(f).

In addition, we also observed spots with ZPL emission and ODMR signals for PL4
with adjacent PL2. TABLE S3 and Fig. S4(d) in SM summarize the polytype of DVs
for each spot within the 10 × 10 arrays shown in Fig. 1(b). The ODMR and PL
signals were detected in 98 spots, with 82 spots exhibiting PL4, 11 spots
showing PL4 with adjacent PL2 (denoted as PL2&4), and 5 spots indicating PL6.
Notably, the proportion of PL4 was the highest, consistent with the PL
spectrum of the DV ensembles (see Fig. S2 in SM), where PL4 exhibited the
strongest ZPL emissions compared to the other polytypes. The likelihood of
finding DVs was significantly higher compared to electron-irradiated spots
[10]. While the PL5 spectrum was detected in the DV ensembles, no PL5 defects
were encountered in the scanned 10$\times$10 array, suggesting a relatively
limited efficiency in the preparation of PL5 defects.

###  .2 Robust resonant excitation properties of PL6

The PLE experiments are important for investigating the spin-to-photon
interface of solid-state color centers [40, 4, 3, 10]. We conducted PLE
experiments on single PL6 and PL4 defects. We used a 914 nm off-resonant laser
to initialize the spin state to $\ket{0}$ and perform deionization, followed
by closing the off-resonant laser using a shutter. We then resonantly excited
the DVs by scanning the wavelength of a tunable laser diode (ranging from 1030
nm to 1080 nm, encompassing the ZPLs of PL6 and PL4). We collected the PL
intensity of phonon sideband (PSB) emission photons synchronously at each
excitation wavelength, allowing us to obtain the responses to the varying
excitation wavelengths.

Figure 2: Different resonant excitation properties for PL6 and PL4. (a) PLE
spectrum of a single PL6. The red line represents the Lorentz fitting. (b)
Time-resolved PLE spectra of a single PL6 over 3 hours. (c) PLE spectrum of a
single PL4. The red line represents the Lorentz fitting. (d) Fluorescence
decay of a single PL6 (blue dots) and a single PL4 (red dots) due to resonant
excitation. The solid lines represent the exponential fittings. The upper
panel presents the sequences to measure the data. (e) The ionization rates
against resonant laser power for 3 single PL6 and 3 single PL4, showed good
linear dependence. The ionization rate for PL4 is approximately 2.6 times
higher than those of PL6.

The PL6 defect has been previously identified as a c-axis defect [7, 8, 52].
In the case of a single PL6, we observed two resonant-transition lines
originating from the ground state $\ket{0}$ to the excited states energy
levels (ESELs). Fig. 2(a) displays the PLE spectrum of a single PL6, where the
two branches correspond to the $E_{x}$ and $E_{y}$ transitions. The linewidths
for the two branches were 721.22 $\pm$ 27.8 MHz and 820.03 $\pm$ 29.3 MHz,
respectively. The zero laser detuning frequency is approximately 288.794 THz,
which is about 1037.78 nm, in good agreement with the result of the PL
spectrum. The linewidths observed in our measurements were approximately one
order of magnitude larger than those obtained from the Fourier transformation
of the measured lifetime. This phenomenon has been previously observed in
similar studies of electron-irradiated DV defects [10], and it can be
attributed to the interaction of lattice phonons induced by nitrogen
impurities present in the commercial sample. Additionally, the insufficient
implantation depth ($\sim$ 170 nm) could contribute to the broader line widths
observed in our measurements. In comparison to electron-irradiated DV defects,
which have an embedded depth of several micrometers, the FHIB-induced DV
defects are slightly influenced by surface charge and electrical environments.
By integrating the DV into a P-I-N junction, combined with charge depletion,
it is possible to achieve a linewidth of approximately 20 MHz, approaching the
lifetime limit [31, 30]. Furthermore, the linewidths were comparable to those
of the substitutional Vandanium ions in 4H-SiC [19] and electron-irradiated
DVs in NIN-type SiC [35], being only around 4 to 8 times wider than the
linewidths of electron-irradiated DVs (with a typical linewidth of 100 $\sim$
200 MHz) in a commercial sample without charge depletion [10, 31].

To test the stability of resonant excitation, we conducted a 3-hour analysis
of the PLE spectra from a single PL6 defect. The time-resolved PLE spectra,
shown in Fig. 2(b), exhibited remarkable stability in the positions of the two
$E_{x}$ and $E_{y}$ transition lines during long-term monitoring. We performed
double-peak Lorentz fittings for the acquired PLE spectra within the 3 hours
and compared the fitted frequencies for both $E_{x}$ and $E_{y}$ with the
central frequencies (see Fig. S5 in SM). The calculated average frequencies
shift for $E_{x}$ and $E_{y}$ are $\pm$ 50.2 MHz and $\pm$ 51.3 MHz,
comparable to the electron-irradiated DVs, whose long-term frequency shift is
around 25 MHz [31]. Such phenomena may originate from the protection of
stacking-fault structures of PL6, which acts as a quantum well shelving.

We proceeded with further characterization of the resonant excitation
properties of the single PL4 defect. Fig 2(c) displays the PLE spectra for an
individual PL4 defect, excited from the spin state $\ket{0}$ in the ground
state, with a zero laser detuning frequency of approximately 278.105 THz. The
ESELs associated with PL4 belong to the $C_{1h}$ point group, the excited
states $A_{0}^{{}^{\prime}}$ and $A_{0}^{"}$ are correlated with the ground
$\ket{0}$ state [30]. However, due to fast relaxation caused by the internal
conversion from $A_{0}^{"}$ to $A_{0}^{{}^{\prime}}$, only the
$A_{0}^{{}^{\prime}}$ state is observable in the experiment, which aligns with
previous findings [30]. The fitted linewidth was 863.4 $\pm$ 36.6 MHz, which
was of the same magnitude as that of PL6.

The applied optical illumination drives undesired ionization processes that
degrade the defects desired properties and functionality. For example, the
fluorescence of color centers undergoes decay due to photoionization resulting
from continuous resonant excitation. Therefore, it is crucial to identify
color centers with robust emission properties that are resistant to
ionization. To investigate the ionization process of the fabricated DVs, we
employed a 10 µs off-resonant laser to initialize the DVs to the spin-0 ground
state. Subsequently, a 30 ms continuous resonant laser pulse was applied, as
depicted in the upper part of Fig. 2(d). The PL intensity during resonant
excitation was synchronously collected and recorded using a counter.

Figure 3: The optical polarization properties for $E_{x}$ and $E_{y}$
transitions (a) Upper: the schematic diagram for the strain-split resonant
excitation directions for the c-axis stacking-fault PL6. Lower: The schematic
diagram illustrating the transitions of PL6 from the ground state (GS)
$\ket{0}$ to the excited states (ES) $\ket{E_{x}}$ and $\ket{E_{y}}$. (b)
Resonant-laser-power-resolved PLE spectra for a single PL6. (c) The PL
intensity for the $E_{x}$ (blue dots, upper panel) and $E_{y}$ (red dots,
lower panel) transitions against resonant laser power. The dash lines are the
fitting. (d) The linewidths for $E_{x}$ (blue dots) and $E_{y}$ (red dots) of
a single PL6 defect against resonant laser power. (e) Excitation angle-
resolved PLE spectra. (f) Extracted data (blue dots for $E_{x}$ and red dots
for $E_{y}$) from (e) with the corresponding cosine fitting.

Fig. 2(d) demonstrates the exponential decay of PL for both PL6 and PL4 under
the same resonant excitation laser power ($P=18.75$ µW). Notably, the PL
intensity of a single PL4 decreases more rapidly than that of a single PL6,
indicating a higher ionization rate $\Gamma$ for PL4 compared to PL6. The
ionization rate $\Gamma$ was determined from the exponential fitting
$I(t)=I_{0}\exp(-\Gamma t)$, where $I(t)$ represents the time-resolved PL
intensity under resonant excitation. To further verify this, we measured the
ionization rates for three individual PL6 and three individual PL4 defects at
different resonant laser powers ranging from approximately 12.5 µW to 37.5 µW,
as shown in Fig. 2(e). Under a high resonant laser power of 37.5 µW, the
ionization rates for both PL4 and PL6 were below 1 kHz. In contrast, for NV
centers in diamond, the rate reaches 1 kHz at 10 µW [46], confirming the
greater resilience of DVs in 4H-SiC against photoionization. For each DV, the
ionization rates exhibited a linear increase with the resonant driving power,
with average linear parameters of 6.5 MHz/W for PL6 and 17.2 MHz/W for PL4,
respectively. A previous experiment has reported a similar parameter of 10.2
MHz/W for c-axis DVs in 4H-SiC [45]. Notably, under the same resonant
excitation laser power, the ionization rate for PL4 was approximately 2.6
times higher than that for PL6, confirming the superior resistance of PL6
defects to photoionization. These properties can be attributed to the quantum
well effect arising from stacking faults. Previous works have predicted that a
quantum well can lower the ionization energy of a point defect’s dark state so
that the excitation laser will preferentially repopulate the point defect’s
bright state [11]. Another study has also demonstrated the robustness of
stacking-fault DVs, as the PL intensity of PL6 remained stable under UV
illumination [43]. This experiment provides direct evidence supporting the
emission stability of single stacking-fault DVs under resonant excitation
[43].

###  .3 Optical polarization properties for PL6 under resonant excitation

Alongside the robust optical properties under resonant excitation, we also
observed distinguish polarization properties for PL6. From the group theory
analysis, the ESELs of the c-axis DVs belong to a highly symmetrical $C_{3v}$
group due to the special lattice structure. The $E_{x}$ and $E_{y}$
transitions are split by a local strain ($E_{x(y)}$ is a direct product of
$\ket{0}$ and X (Y) polarized photons, which are denoted as $\ket{X(Y)}$). The
excitation main axes for $E_{x}$ and $E_{y}$ exhibit mutual orthogonality,
which are approximately parallel to the surface and perpendicular to the
c-axis, as illustrated in Fig. 3(a).

Firstly, we investigated the influence of resonant excitation laser power on
both $E_{x}$ and $E_{y}$ transitions. Fig. 3(b) presents the power-resolved
PLE spectra, demonstrating that the positions of $E_{x}$ and $E_{y}$ remained
stable even as the laser power increased. The PL intensity against resonant
laser power for $E_{x}$ and $E_{y}$ are observable in Fig. 3(c), both fitted
by $I=I_{s}/(1+P/P_{s})$ (dash lines), where $P_{s}$ represents the saturation
resonant laser power. The fitted saturation powers are 370 $\pm$ 63 nW for
$E_{x}$ and 481 $\pm$ 87 nW for $E_{y}$. Additionally, we performed linewidth
fitting for PL6 under different excitation powers, as shown in Fig. 3(d). We
didn’t observe significant power-induced linewidth broadening.

To confirm the polarization properties, we measured the excitation angle-
resolved PLE spectra of the single PL6, which are presented in Fig. 3(e). By
rotating the polarization angle of the resonant laser, the PL intensity of
$E_{x}$ and $E_{y}$ varied, displaying a cosine relationship with the angle.
The angles corresponding to maximum emission for $E_{x}$ and $E_{y}$ exhibited
an offset of approximately 90 degrees, as depicted in Fig. 3(f) (data
extracted from Fig. 3(e)). The results are in good agreement with group theory
analysis, and a previous work observing strain-split two ZPL emission branches
with mutually orthogonal polarization in c-axis DVs [52]. These properties of
PL6 resemble those of color centers with $C_{3v}$ symmetry, such as NV centers
in diamond [50, 51], PL1 and PL2 in 4H-SiC, and DVs in 3C-SiC [31, 10, 52],
indicating their potential for constructing spin-photon entanglement through
time-to-polarization conversion [53].

Figure 4: Comparision between FHIB-fabricated PL6 and $C^{+}$-implanted PL6.
(a) PLE spectra of 5 FHIB-fabricated individual PL6 defects. (b) PLE spectrum
of a single PL6 generated by carbon-implantation. (c) The Hahn-echo
measurement of for a single PL6 defect fabricated by FHIB. (d) Ramsey
interference between the $\ket{0}$ and $\ket{-1}$ states for a single PL6
defect fabricated by FHIB.

###  .4 Comparison between DVs fabricated by FHIB and $C^{+}$-implantation

Furthermore, we conducted measurements of the PLE spectra (Fig. 4(a)) for
another 5 single PL6 defects, labeled PL6-A to PL6-E. The linewidth values are
summarized in Supplementary Material Table S4, and the average linewidths are
approximately 879.3 MHz, consistent with the PL6 defect presented in Fig. 2.
The time-resolved PLE spectra for these 5 defects, consisting of 80 cycles,
can be found in Fig. S6, while the lifetime measurement results are shown in
Fig. S7 in SM. For comparison, we also measured the PLE spectrum of a single
PL6 defect generated through $C^{+}$ implantation (refer to Materials and
Methods) [14], as depicted in Fig. 4(b). The linewidths for the $E_{x}$ and
$E_{y}$ transitions were 6.77 $\pm$ 0.12 GHz and 5.70 $\pm$ 0.08 GHz,
respectively. In contrast, the linewidths of the DVs generated by FHIB were 7
to 8 times narrower compared to those generated by $C^{+}$ implantation. The
observed linewidth broadening in carbon-implanted PL6 defects may be
attributed to the shallower implantation depth in comparison to helium ion
implantation (refer to Fig. S1 in SM), which exposes them to an unstable
surface electrical environment during excitation, as well as the significant
lattice damage caused by heavy ion implantation. Additionally, we compared the
PLE linewidth between PL4 fabricated by FHIB and $C^{+}$-implantation (see
Fig. S10 in SM), and the results were similar to those obtained for PL6.

We further conducted spin-coherent manipulations on the single PL6 defect
illustrated in Fig. 2 at room temperature ($\sim$ 300 K). A c-axis magnetic
field of approximately $190$ G was applied to separate the $\ket{\pm 1}$
states in the ground states (refer to Fig. S8). We performed spin-coherent
control between $\ket{0}$ and $\ket{-1}$. The Ramsey interference measurement
was carried out with a microwave frequency detuning of $\Delta f=6$ MHz, as
shown in Fig. 4(d), resulting in a spin-coherent time of $T_{2}^{*}=2.84\pm
0.09$ $\mu$s. This value is comparable to electron-irradiated DVs in
commercial 4H-SiC [9] and approximately 6 times longer than that of
$C^{+}$-implanted PL6 defects at room temperature, with $T_{2}^{*}\approx 450$
ns [14]. Fig. 4(c) illustrates the Hahn-echo measurements, exhibiting
electron-spin-echo-envelope-modulation (ESEEM), with a fitted spin-coherent
time of $T_{2}=55.6\pm 5.8$ $\mu$s. This value is 2.5 times longer than that
of $C^{+}$-implanted PL6 defects ($\sim$ 22 $\mu$s) [14]. We also examined the
spin-coherent properties of two additional PL6 defects under the same
experimental conditions, and their spin-coherent times were nearly identical
(refer to Fig. S9 in SM). Furthermore, we performed spin-coherent control
experiments on PL4 (refer to Fig. S11 in SM), and the coherent times were of a
similar magnitude.

The observed longer spin-coherent times can be attributed to the deeper helium
ion implantation mentioned earlier, which protects against surface noise for
the spin states. Similar properties have been reported for nitrogen-vacancy
(NV) centers in diamonds, emphasizing the significance of deep implantation in
preserving spin properties [47, 49]. Furthermore, the reduced lattice damage
resulting from helium ion implantation may also contribute to the preservation
of spin properties, as discussed in previous studies [48].

## Discussion and conclusion

In this study, we have investigated the feasibility of generating arrays of
single divacancies using focused helium ion beam techniques. FHIB has shown
great promise for precisely integrating color centers into nanophotonic
structures, thanks to its high image resolution and generation efficiency.
Moreover, the high-precision implantation provided by FHIB significantly
enhances the coupling efficiency of defects compared to randomly distributed
defects induced by electron irradiation. By studying the resonant excitation
properties, we have observed that the stacking-fault DV PL6 exhibits long-term
emission stability for over 3 hours. In comparison to the basal DV PL4, the
photoionization rates for PL6 are 2.6 times lower, highlighting the
significant role of stacking-fault protection. We have also discovered two
mutually perpendicular resonant transition branches in PL6, similar to the NV
centers in diamond. Furthermore, we have found that FHIB-induced DVs exhibit
about 7 times narrower photoluminescence emission (PLE) linewidths and 6 times
longer spin-coherent times compared to DVs generated by $C^{+}$ implantation.
With its favorable spin-coherent properties, robust PLE emission with quantum-
well protection, unique electron-spin-echo envelope modulation structures, and
photon emission properties similar to NV centers in diamond, PL6 represents a
promising candidate for constructing spin-photon entanglement networks based
on time-to-polarization conversion and spin-photon entanglement states in
ESELs [51, 53]. In conclusion, our findings highlight the potential of FHIB
techniques and the unique properties of PL6 divacancies in silicon carbide for
advancing the field of quantum information processing and constructing
efficient spin-photon interfaces.

## Materials and Methods

Sample Fabrication: We utilized a 4H-SiC sample with a 10 µm epitaxy layer.
The helium ion microscope (HIM, Zeiss Orion NanoFab) with an imaging
resolution of 0.5 nm and an incident energy of 30 keV was employed to implant
the DV ensembles in scanning mode, with a dose of 1$\times$1015 ions/cm2. The
DV arrays were fabricated using the spot mode with three different doses (400,
300, and 200 ions/spot). The sample was annealed at 500 ∘C for 2 hours,
followed by a post-annealing step at 900 ∘C for 1 hour. The heating ramps for
both annealing steps were set to 5 ∘C/min.

We further prepared a $C^{+}$-implanted sample. This sample was derived from
the same wafer as the FHIB-fabricated sample. The array of single DVs and
ensembles was generated by a 30-keV $C^{+}$ implantation using a pre-designed
PMMA mask, followed by a 900 ∘C annealing for 1 hour. The heating ramp during
annealing was set to 5 ∘C/min.

Room-temperature and Low-temperature Optical Setup: For the room-temperature
experiment, we employed a custom-built confocal laser scanning setup equipped
with a piezo nanopositioner (E-727, PI). In the low-temperature experiment, a
cryostat (Cryostation s200, Montana) fitted with an L-T piezo nanopositioner
(ANC350, Attocube) was utilized to manipulate the sample position. To adjust
the excitation laser trajectory and the photoluminescence (PL) of DVs, a fast
steering mirror (Galvo, Thorlabs) was employed. The PL signal was collected
through a single-mode fiber and detected by a superconducting nanowire single-
photon detector (SNSPD, PHOTEC) with an approximate efficiency of 90%.

Spin Control: The microwave sequences were generated using a synthesized
signal generator (MiniCircuits, SSG-6000 RC) and controlled by a switch (Mini-
Circuits, ZASWA-2-50DR+). After amplification (Mini-Circuits, ZHL-25W-272+),
the microwave signals were transmitted to a 50-$\mu$m-wide copper wire
positioned above the surface of the 4H-SiC sample, within a distance of 80
$\mu$m from the DV arrays under investigation. The 914-nm continuous wave (CW)
laser used for excitation was modulated using an acousto-optic modulator. The
timing sequence of the electrical signals, which controlled and synchronized
the laser, microwave, and counter, was generated by a pulse generator
(SpinCore, PBESRPRO500).

PLE Experiment: We employed an arbitrary function generator (AFG31252,
Tektronix) to generate scanning voltages for the tunable laser diode (DL Pro,
Toptica). The synchronization of the off-resonant laser, resonant laser,
shutter, arbitrary function generator, and the counter was also controlled by
a pulse generator (SpinCore, PBESRPRO500).

Antibunching Experiment: The coincidence correlation with variable delay times
was measured using a time-to-digital converter (IDQ, ID800-TDC) with a
resolution of 81 ps.

## Supplementary Materials

This part contains sections S1 to S5, figures S1 to S11, and tables S1 to S5.

## Author contributions

J.-S.X. and Z.-X.H. conceived the experiments. Z.-X.H. built the experiment
set-up and performed the measurements with the help of J.-Y.Z., W.-X.L., Q.L.,
J.-F.W., Z.-H.H., W.L., R.S., R.-J.L., H.L., L.-X.Y. J.-S.T., and fabricated
the sample with the help of Q.L. and X.L.W. Z.X.H.and J.-S.X. performed the
data analysis and wrote the manuscript with contributions from all co-authors.
J.-S.X., C.-F.L., and G.-C.G. supervised the project. All authors contributed
to the discussion of the results.

## Acknowledgement

We thank Prof. Stefania Castelletto at the Royal Melbourne Institute of
Technology for the helpful discussion. This work was supported by the
Innovation Program for Quantum Science and Technology (Grants No.
2021ZD0301400), the National Natural Science Foundation of China (Grants No.
U19A2075, No. 92365205, No. 11774335, No. 11821404 and No. 61725504), the
Anhui Initiative in Quantum Information Technologies (Grant No. AHY060300).
This work was partially performed at the University of Science and Technology
of China Center for Micro and Nanoscale Research and Fabrication.

## Competing interests

There are no conflicts to declare.

## Data and materials availability

All data are available in the main text or the supplementary materials.

## References

  * [1] Widmann, Matthias and Lee, Sang-Yun and Rendler, Torsten and Son, Nguyen Tien and Fedder, Helmut and Paik, Seoyoung and Yang, Li-Ping and Zhao, Nan and Yang, Sen and Booker, Ian and others, Coherent control of single spins in silicon carbide at room temperature, _Nat. Mater._ , 2015, 14, 164-168.
  * [2] Nagy, Roland and Widmann, Matthias and Niethammer, Matthias and Dasari, Durga BR and Gerhardt, Ilja and Soykal, Öney O and Radulaski, Marina and Ohshima, Takeshi and Vučković, Jelena and Son, Nguyen Tien and others, Quantum properties of dichroic silicon vacancies in silicon carbide, _Phys. Rev. Appl._ , 2018, 9, 034022.
  * [3] Nagy, Roland and Niethammer, Matthias and Widmann, Matthias and Chen, Yu-Chen and Udvarhelyi, Péter and Bonato, Cristian and Hassan, Jawad Ul and Karhu, Robin and Ivanov, Ivan G and Son, Nguyen Tien and others, High-fidelity spin and optical control of single silicon-vacancy centres in silicon carbide, _Nat. Commun._ , 2019, 1, 1-8.
  * [4] Naoya Morioka and Di Liu and Öney O. Soykal and Izel Gediz and Charles Babin and Rainer J. Stöhr and Takeshi Ohshima and Nguyen Tien Son and Jawad Ul-Hassan and Florian Kaiser and Jörg Wrachtrup, Spin-Optical Dynamics and Quantum Efficiency of a Single V1 Center in Silicon Carbide, _Phys. Rev. Appl._ , 2022, 17, 054005.
  * [5] Fuchs, F and Stender, B and Trupke, M and Simin, D and Pflaum, J and Dyakonov, V and Astakhov, GV, Engineering near-infrared single-photon emitters with optically active spins in ultrapure silicon carbide, _Nat. Commun._ , 2015, 6, 1-7.
  * [6] Simin, D and Kraus, H and Sperlich, A and Ohshima, T and Astakhov, GV and Dyakonov, V, Locking of electron spin coherence above 20 ms in natural silicon carbide, _Phys. Rev. B_ , 2017, 95, 161201.
  * [7] Koehl, William F and Buckley, Bob B and Heremans, F Joseph and Calusine, Greg and Awschalom, David D, Room temperature coherent control of defect spin qubits in silicon carbide, _Nature_ , 2011, 479, 84-87.
  * [8] Falk, Abram L and Buckley, Bob B and Calusine, Greg and Koehl, William F and Dobrovitski, Viatcheslav V and Politi, Alberto and Zorman, Christian A and Feng, Philip X-L and Awschalom, David D, Polytype control of spin qubits in silicon carbide, _Nat. Commun._ , 2013, 4, 1-7.
  * [9] Christle, David J and Falk, Abram L and Andrich, Paolo and Klimov, Paul V and Hassan, Jawad Ul and Son, Nguyen T and Janzén, Erik and Ohshima, Takeshi and Awschalom, David D, Isolated electron spins in silicon carbide with millisecond coherence times, _Nat. Mater._ , 2015,14, 160-163.
  * [10] Christle, David J and Klimov, Paul V and Charles, F and Szász, Krisztián and Ivády, Viktor and Jokubavicius, Valdas and Hassan, Jawad Ul and Syväjärvi, Mikael and Koehl, William F and Ohshima, Takeshi and others, Isolated spin qubits in SiC with a high-fidelity infrared spin-to-photon interface, _Phys. Rev. X_ , 2017, 7, 021046.
  * [11] Viktor Iv’ady and Joel Davidsson and Abram L. Falk and Paul V. Klimov and Nguyen Tien Son and David D. Awschalom and Igor A. Abrikosov and Ádám Gali, Enhanced stability of defect-based qubits in quantum wells, _Nat. Commun._ , 2019, 10, 5607.
  * [12] Björn Magnusson and Nguyen Tien Son and Andr’as Cs’or’e and Andreas Gallstrom and Takeshi Ohshima and Ádám Gali and Ivan G. Ivanov, Excitation properties of the divacancy in 4H -SiC, _Phys. Rev. B_ , 2018, 98, 195202.
  * [13] Alexandre Bourassa and Christopher P. Anderson and Kevin C. Miao and Mykyta Onizhuk and He Ma and Alexander L. Crook and Hiroshi Abe and Jawad Ul-Hassan and Takeshi Ohshima and Nguyen Tien Son and Giulia Galli and David D. Awschalom, Entanglement and control of single nuclear spins in isotopically engineered silicon carbide, _Nat. Mater._ , 2020, 19, 1319-1325.
  * [14] Qiang Li and Jun-Feng Wang and Fei-Fei Yan and Ji-Yang Zhou and Hanlin Wang and He Liu and Liping Guo and Xiong Zhou and Ádám Gali and Zhenghao Liu and Zuming Wang and Kai Sun and Guoping Guo and Jian-Shun Tang and Jin-Shi Xu and Chuan‐Feng Li and Guangcan Guo, Room-temperature coherent manipulation of single-spin qubits in silicon carbide with a high readout contrast, _Natl. Sci. Rev._ , 2022, 9, nwab122.
  * [15] Hans Jurgen von Bardeleben and Jean Louis Cantin and András Csóré and Ádám Gali and Eva Rauls and Uwe Gerstmann, NV centers in 3 C ,4 H , and 6 H silicon carbide: A variable platform for solid-state qubits and nanosensors, _Phys. Rev. B_ , 2016, 94, 121202.
  * [16] Wang, Jun-Feng and Yan, Fei-Fei and Li, Qiang and Liu, Zheng-Hao and Liu, He and Guo, Guo-Ping and Guo, Li-Ping and Zhou, Xiong and Cui, Jin-Ming and Wang, Jian and others, Coherent control of nitrogen-vacancy center spins in silicon carbide at room temperature, _=_ Phys. Rev. Lett., 2020, _124_ , 223601.
  * [17] Mu, Zhao and Zargaleh, Soroush Abbasi and von Bardeleben, Hans Jurgen and Froöch, Johannes E and Nonahal, Milad and Cai, Hongbing and Yang, Xinge and Yang, Jianqun and Li, Xingji and Aharonovich, Igor and others, Coherent manipulation with resonant excitation and single emitter creation of nitrogen vacancy centers in 4H silicon carbide, _Nano Lett._ , 2020, 20, 6142-6147.
  * [18] Berk Diler and Samuel J. Whiteley and Christopher P. Anderson and Gary Wolfowicz and Gary Wolfowicz and Marie E. Wesson and Edward S. Bielejec and Joseph P. Heremans and Joseph P. Heremans and David D. Awschalom and David D. Awschalom, Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide, _npj Quantum Infor._ , 2019, 6, 1-6.
  * [19] Gary Wolfowicz and Christopher P. Anderson and Berk Diler and Oleg G. Poluektov and F. Joseph Heremans and David D. Awschalom, Vanadium spin qubits as telecom quantum emitters in silicon carbide, _Sci. Adv._ , 2019,6, eaaz1192.
  * [20] Cilibrizzi, Pasquale and Arshad, Muhammad Junaid and Tissot, Benedikt and Son, Nguyen Tien and Ivanov, Ivan G and Astner, Thomas and Koller, Philipp and Ghezellou, Misagh and Ul-Hassan, Jawad and White, Daniel and others, Ultra-narrow inhomogeneous spectral distribution of telecom-wavelength vanadium centres in isotopically-enriched silicon carbide, arXiv:2305.01757
  * [21] Kraus, H and Soltamov, VA and Fuchs, F and Simin, D and Sperlich, A and Baranov, PG and Astakhov, GV and Dyakonov, Vladimir, Magnetic field and temperature sensing with atomic-scale spin defects in silicon carbide, _Sci. Rep._ , 2014, 4, 1-8.
  * [22] Simin, D and Fuchs, F and Kraus, H and Sperlich, A and Baranov, PG and Astakhov, GV and Dyakonov, V, High-precision angle-resolved magnetometry with uniaxial quantum centers in silicon carbide, _Phys. Rev. Appl._ , 2015, 4, 014009.
  * [23] Niethammer, Matthias and Widmann, Matthias and Lee, Sang-Yun and Stenberg, Pontus and Kordina, Olof and Ohshima, Takeshi and Son, Nguyen Tien and Janzén, Erik and Wrachtrup, Jörg, Vector Magnetometry Using Silicon Vacancies in 4 H-SiC Under Ambient Conditions, _Phys. Rev. Appl._ , 2016, 6, 034001.
  * [24] Yan, Fei-Fei and Wang, Jun-Feng and Li, Qiang and Cheng, Ze-Di and Cui, Jin-Ming and Liu, Wen-Zheng and Xu, Jin-Shi and Li, Chuan-Feng and Guo, Guang-Can, Coherent control of defect spins in silicon carbide above 550 K, _Phys. Rev. Appl._ , 2018, 10, 044042.
  * [25] Zhou, Yu and Wang, Junfeng and Zhang, Xiaoming and Li, Ke and Cai, Jianming and Gao, Weibo, Self-protected thermometry with infrared photons and defect spins in silicon carbide, _Phys. Rev. Appl._ , 2017, 8, 044015.
  * [26] Jun-Feng Wang and Lin Liu and Xiao-Di Liu and Qiang Li and Jinming Cui and Dingbang Zhou and Ji-Yang Zhou and Yu Wei and Haiman Xu and Wan Xu and Wu-Xi Lin and Jingyang Yan and Zhenhui He and Zhenghao Liu and Zhichao Hao and Haiou Li and Wen Liu and Jin-Shi Xu and Eugene Gregoryanz and Chuan Li and Guangcan Guo, Magnetic detection under high pressures using designed silicon vacancy centres in silicon carbide, _Nat. Mater._ , 2022, 22, 489-494.
  * [27] Lin Liu and Jun-Feng Wang and Xiao-Di Liu and Hai-An Xu and Jinming Cui and Qiang Li and Ji-Yang Zhou and Wu-Xi Lin and Zhen-Xuan He and Wan Xu and Yu Wei and Zheng-Hao Liu and Pu Wang and Zhi-He Hao and J. F. Ding and Haiou Li and Wen Liu and Hao Li and Lixing You and Jin-Shi Xu and Eugene Gregoryanz and Chuan‐Feng Li and Guang-Can Guo, Coherent Control and Magnetic Detection of Divacancy Spins in Silicon Carbide at High Pressures, _Nano Lett._ , 2022, 22, 9943-9950.
  * [28] Castelletto, Stefania and Lew, Christopher and Lin, Wu-Xi and Xu, Jin-Shi, Quantum systems in silicon carbide for sensing applications, _Rep. Prog. Phys_ , 2024, 87, 014501.
  * [29] Luo, Qin-Yue and Li, Qiang and Wang, Jun-Feng and Guo, Pei-Jie and Lin, Wu-Xi and Zhao, Shuang and Hu, Qi-Cheng and Zhu, Zi-Qi and Xu, Jin-Shi and Li, Chuan-Feng and others, Fabrication and quantum sensing of spin defects in silicon carbide, _Frontiers in Physics_ , 2023, 11, 1270602.
  * [30] Miao, Kevin C and Bourassa, Alexandre and Anderson, Christopher P and Whiteley, Samuel J and Crook, Alexander L and Bayliss, Sam L and Wolfowicz, Gary and Thiering, Gergő and Udvarhelyi, Péter and Ivády, Viktor and others, Electrically driven optical interferometry with spins in silicon carbide, _Sci. Adv._ , 2019, 5, eaay0527.
  * [31] Christopher P. Anderson and Alexandre Bourassa and Kevin C. Miao and Gary Wolfowicz and Peter J. Mintun and Alexander L. Crook and Hiroshi Abe and Jawad Ul Hassan and Nguyen Tien Son and Takeshi Ohshima and David D. Awschalom, Electrical and optical control of single spins integrated in scalable semiconductor devices, _Science_ , 2019, 366, 1225-1230.
  * [32] Widmann, Matthias and Niethammer, Matthias and Fedyanin, Dmitry Yu and Khramtsov, Igor A and Rendler, Torsten and Booker, Ian D and Ul Hassan, Jawad and Morioka, Naoya and Chen, Yu-Chen and Ivanov, Ivan G and others, Electrical charge state manipulation of single silicon vacancies in a silicon carbide quantum optoelectronic device, _Nano Lett._ , 2019, 19, 7173-7180.
  * [33] Lohrmann, Alexander and Iwamoto, N and Bodrog, Zoltan and Castelletto, Stefania and Ohshima, T and Karle, TJ and Gali, Adam and Prawer, Steven and McCallum, JC and Johnson, BC, Single-photon emitting diode in silicon carbide, _Nat. Commun._ , 2015, 6, 7783.
  * [34] Shin‐ichiro Sato and Tomoya Honda and Takahiro Makino and Yasuto Hijikata and Sang-Yun Lee and Takeshi Ohshima, Room Temperature Electrical Control of Single Photon Sources at 4H-SiC Surface, _ACS Photon._ , 2018, 5, 3159-3165.
  * [35] Crook, Alexander L and Anderson, Christopher P and Miao, Kevin C and Bourassa, Alexandre and Lee, Hope and Bayliss, Sam L and Bracher, David O and Zhang, Xingyu and Abe, Hiroshi and Ohshima, Takeshi and others, Purcell enhancement of a single silicon carbide color center with coherent spin control, _Nano Lett._ , 2020, 5, 3427-3434.
  * [36] G. Calusine and Alberto Politi and David D. Awschalom, Cavity-enhanced measurements of defect spins in silicon carbide, _Phys. Rev. Appl._ , 2015,6, 014019.
  * [37] G. Calusine and Alberto Politi and David D. Awschalom, Silicon carbide photonic crystal cavities with integrated color centers, _Appl. Phys. Lett._ , 2014, 105, 011123.
  * [38] David O. Bracher and Evelyn L. Hu, Fabrication of High-Q Nanobeam Photonic Crystals in Epitaxially Grown 4H-SiC, _Nano Lett._ , 2015, 15, 6202.
  * [39] Aaron M. Day and Jonathan R. Dietz and Madison Sutula and Matthew Yeh and Evelyn L. Hu, Laser writing of spin defects in nanophotonic cavities, _Nat. Mater._ , 2023, 22, 696-702.
  * [40] Charles Babin and Rainer Stöhr and Naoya Morioka and Tobias Linkewitz and Timo Steidl and Raphael Wörnle and Di Liu and Erik Hesselmeier and Vadim Vorobyov and Andrej Denisenko and Mario Hentschel and Christian Gobert and Patrick Berwian and Georgy V. Astakhov and Wolfgang Knolle and Sridhar Majety and Pranta Saha and Marina Radulaski and Nguyen Tien Son and Jawad Ul-Hassan and Florian Kaiser and Jörg Wrachtrup, Fabrication and nanophotonic waveguide integration of silicon carbide colour centres with preserved spin-optical coherence, _Nat. Mater._ , 2021, 21, 67-73.
  * [41] Radulaski, Marina and Widmann, Matthias and Niethammer, Matthias and Zhang, Jingyuan Linda and Lee, Sang-Yun and Rendler, Torsten and Lagoudakis, Konstantinos G and Son, Nguyen Tien and Janzen, Erik and Ohshima, Takeshi and others, Scalable quantum photonics with single color centers in silicon carbide, _Nano Lett._ , 2017, 17, 1782-1786.
  * [42] Fiammetta Sardi and Thomas Kornher and Matthias Widmann and Roman L. Kolesov and Friedrich Schiller and Thomas Reindl and Marion Hagel and Jörg Wrachtrup, Scalable production of solid-immersion lenses for quantum emitters in silicon carbide, _Appl. Phys. Lett._ , 2020, 117, 022105.
  * [43] Wolfowicz, Gary and Anderson, Christopher P and Yeats, Andrew L and Whiteley, Samuel J and Niklas, Jens and Poluektov, Oleg G and Heremans, F Joseph and Awschalom, David D, Optical charge state control of spin defects in 4H-SiC, _Nat. Commun._ , 2017, 8, 1876.
  * [44] Jin-Shi Xu, Chuan-Feng Li, and Guang-Can Guo, Silicon carbide based quantum networking, _Fund. Res._ , 2021, 1, 220.
  * [45] Anderson, Christopher P and Glen, Elena O and Zeledon, Cyrus and Bourassa, Alexandre and Jin, Yu and Zhu, Yizhi and Vorwerk, Christian and Crook, Alexander L and Abe, Hiroshi and Ul-Hassan, Jawad and others, Five-second coherence of a single spin with single-shot readout in silicon carbide, _Sci. Adv._ , 2022, 8, eabm5912.
  * [46] Robledo, Lucio and Bernien, Hannes and Van Weperen, Ilse and Hanson, Ronald, Control and coherence of the optical transition of single nitrogen vacancy centers in diamond, _Phys. Rev. Lett._ , 2010, 105, 177403.
  * [47] Myers, Bryan A and Das, A and Dartiailh, MC and Ohno, K and Awschalom, David D and Jayich, AC Bleszynski, Probing surface noise with depth-calibrated spins in diamond, _Phys. Rev. Lett._ , 2014, 113, 027602.
  * [48] Fávaro de Oliveira, Felipe and Antonov, Denis and Wang, Ya and Neumann, Philipp and Momenzadeh, Seyed Ali and Häußermann, Timo and Pasquarelli, Alberto and Denisenko, Andrej and Wrachtrup, Jörg, Tailoring spin defects in diamond by lattice charging, _Nat. Commun._ , 2017, 1, 15409.
  * [49] Sangtawesin, Sorawis and Dwyer, Bo L and Srinivasan, Srikanth and Allred, James J and Rodgers, Lila VH and De Greve, Kristiaan and Stacey, Alastair and Dontschuk, Nikolai and O’Donnell, Kane M and Hu, Di and others, Origins of diamond surface noise probed by correlating single-spin measurements with surface spectroscopy, _Phys. Rev. X_ , 2019, 9, 031052.
  * [50] Kaiser, F and Jacques, V and Batalov, A and Siyushev, P and Jelezko, F and Wrachtrup, J, Polarization properties of single photons emitted by nitrogen-vacancy defect in diamond at low temperature, arXiv:09063426.
  * [51] Togan, Emre and Chu, Yiwen and Trifonov, Alexei S and Jiang, Liang and Maze, Jeronimo and Childress, Lilian and Dutt, MV Gurudev and Sørensen, Anders Søndberg and Hemmer, Phillip R and Zibrov, Alexander S and others, Quantum entanglement between an optical photon and a solid-state spin qubit, _Nature_ , 2010, 466, 730-734.
  * [52] Falk, Abram L and Klimov, Paul V and Buckley, Bob B and Ivády, Viktor and Abrikosov, Igor A and Calusine, Greg and Koehl, William F and Gali, Ádám and Awschalom, David D, Electrically and mechanically tunable electron spins in silicon carbide color centers, _Phys. Rev. Lett._ , 2014, 112, 187601.
  * [53] Vasconcelos, Rui and Reisenbauer, Sarah and Salter, Cameron and Wachter, Georg and Wirtitsch, Daniel and Schmiedmayer, Jörg and Walther, Philip and Trupke, Michael, Scalable spin–photon entanglement by time-to-polarization conversion, _npj Quantum Infor._ , 2020, 1, 9.
  * [54] Klimov, Paul V and Falk, Abram L and Christle, David J and Dobrovitski, Viatcheslav V and Awschalom, David D, Quantum entanglement at ambient conditions in a macroscopic solid-state spin ensemble, _Sci. Adv._ , 2015, 1, e1501015.