# Large-scale optical characterization of solid-state quantum emitters

Madison Sutula1<EMAIL_ADDRESS>Ian Christen1 Eric Bersin1,2 Michael P.
Walsh1 Kevin C. Chen1 Justin Mallek2 Alexander Melville2 Michael Titze3 Edward
S. Bielejec3 Scott Hamilton2 Danielle Braje2 P. Benjamin Dixon2 Dirk R.
Englund1 1Research Laboratory of Electronics, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA
2Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA
02421, USA
3Sandia National Laboratories, Albuquerque, NM 87185, USA

###### Abstract

Solid-state quantum emitters have emerged as a leading quantum memory for
quantum networking applications. However, standard optical characterization
techniques are neither efficient nor repeatable at scale. In this work, we
introduce and demonstrate spectroscopic techniques that enable large-scale,
automated characterization of color centers. We first demonstrate the ability
to track color centers by registering them to a fabricated machine-readable
global coordinate system, enabling systematic comparison of the same color
center sites over many experiments. We then implement resonant
photoluminescence excitation in a widefield cryogenic microscope to
parallelize resonant spectroscopy, achieving two orders of magnitude speed-up
over confocal microscopy. Finally, we demonstrate automated chip-scale
characterization of color centers and devices at room temperature, imaging
thousands of microscope fields of view. These tools will enable accelerated
identification of useful quantum emitters at chip-scale, enabling advances in
scaling up color center platforms for quantum information applications,
materials science, and device design and characterization.

color centers, diamond, widefield, large-scale, quantum information

Figure 1: Techniques for chip-scale characterization. a, Standard confocal
microscopy enables spectroscopy on a diffraction-limited volume,
$\text{V}_{\text{confocal}}$. b, Our widefield microscopy technique discussed
in Section II allows for parallelized spectroscopic measurements over many
color centers simultaneously in a larger sample volume,
$\text{V}_{\text{widefield}}$. c, We fabricate QR-style codes onto the surface
of our samples as a spatial reference frame which we decode convolutionally in
real time, enabling us to track and revisit color centers. Together, these
techniques allow us to probe d, the optical transitions of color centers,
including perturbations such as e, local strain environment, which the
silicon-vacancy center in diamond (pictured) is particularly sensitive to, f,
electric fields, which the nitrogen-vacancy center in diamond (pictured) is
particularly sensitive to, and g, the time-varying occupancy of charge traps
in the crystal host, which is thought to cause inhomogeneous line broadening.

Quantum emitters play a central role in quantum information science and
technology Awschalom  _et al._ (2021); Alexeev  _et al._ (2021). Color centers
in solids have emerged as a leading platform for quantum information
processing, with applications in sensing, computation, and communication.
Their electron spin degree of freedom can store quantum states for
milliseconds to seconds Sukachev  _et al._ (2017); Bar-Gill  _et al._ (2013),
and can be efficiently transduced into a flying qubit via a coherent spin-
photon interface. These light-matter interactions can be engineered with
cavity quantum electrodynamics Nemoto  _et al._ (2016); Janitz  _et al._
(2020), accessible through nanofabrication Siyushev  _et al._ (2010); Hadden
_et al._ (2010); Mouradian  _et al._ (2017); Calusine  _et al._ (2014); Nguyen
_et al._ (2019); Rugar  _et al._ (2021) and heterogeneous integration
techniques Bayat  _et al._ (2014); Mouradian  _et al._ (2015); Janitz  _et
al._ (2015); Gould  _et al._ (2016); Wan  _et al._ (2020). Nuclear spin
ancilla qubits provide additional degrees of freedom Ruf  _et al._ (2021),
enabling longer storage times Bradley  _et al._ (2019), local multi-qubit
logic protocols such as error detection and correction Stas  _et al._ (2022);
Waldherr  _et al._ (2014), and potential for more robust computation such as
brokered entanglement Benjamin  _et al._ (2006) or cluster state generation
Choi  _et al._ (2019).

In spite of these promising properties and early demonstrations, most
approaches rely on the integration and control of a single color center at
each node Hermans  _et al._ (2022); Bhaskar  _et al._ (2020); Pompili  _et
al._ (2021). However, quantum information processing nodes will require many
individually-addressable quantum emitters, each with long-lived spin states
and a high-quality photonic interface Lee  _et al._ (2022). A critical
challenge faced by color center qubits, especially when compared to neutral
atom and trapped ion qubit architectures, is spectral inhomogeneity Bersin
_et al._ (2019). Although a number of techniques have been demonstrated to
practically or theoretically overcome this inhomogeneity, including retuning
emitter transitions via Stark Bassett  _et al._ (2011) or strain tuning
Meesala  _et al._ (2018), compensating for differential phase accumulation
Metz and Barrett (2008), and shifting emitted photons by optical frequency
conversion Stolk  _et al._ (2022) or frequency modulation Levonian  _et al._
(2022), each of these solutions relies on pre-characterization of the optical
transitions involved. Additionally, up to now, approaches to understand the
range of color center performance and uniformity have been limited to
ensemble-level statistics, obscuring individual color center properties.
Scaling up the number of solid-state quantum memories accessible in quantum
information processing systems requires large-scale characterization
techniques to identify the most viable qubits for practical use.

Here, we report on a high-throughput approach for spectroscopy and synthesis
of quantum emitters, while retaining single-emitter resolution, on diamond
color centers (Fig. 1). We track color centers by registering them to
fabricated, machine-readable global coordinate system, enabling the systematic
comparison of individual center sites over many experiments that is critical
for understanding the role of materials processing Walsh (2020). We then
implement resonant photoluminescence excitation in a widefield cryogenic
microscope to realize two orders of magnitude speed-up over confocal
microscopy. Finally, we demonstrate automated chip-scale characterization of
color centers and devices at room temperature, imaging thousands of microscope
fields of view (see Extended Data Videos).

With the large datasets accessible through these novel approaches, we identify
a sample with an exceptionally narrow inhomogeneous distribution of silicon-
vacancy centers in diamond (SiVs), and we verify in a sample implanted via
focused ion beam (FIB) that the optical properties of highly strained SiVs do
not degrade. These techniques provide a paradigm in which the optical
properties of individual color centers can be identified, tracked, and
categorized. We anticipate that the reported high-throughput tools will close
the loop between materials processing and spectroscopy, enabling development
of scalable quantum information processors.

## Results

##  I Registering color centers to fabricated markers

Figure 2:  Tracking color centers in a sample with fabricated QR codes. a,
Confocal microscope image of a diamond patterned with QR codes and implanted
with 15N. The full figure shows a confocal scan of the sample under incoherent
illumination. The corners of four QR codes are emphasized with white circles.
The insets show i, fluorescence from part of the full field of view under 515
nm excitation, with single nitrogen-vacancy centers in diamond (NVs), and ii,
an SEM micrograph of a QR code. b, Typical photoluminescence excitation (PLE)
spectrum for an NV center in this sample. c, Histogram of the number of
experiments in which an NV was observed for a sample cooled down four times,
with processing steps in between subsequent experiments. Errors in clustering
sites are indicated in bin 5. d, Visualization of the shift in mean optical
transition frequency
$\Delta\bar{\omega}/2\pi=\bar{\omega}_{i}/2\pi-\bar{\omega}_{j}/2\pi$ of the
two $\text{m}_{\text{s}}=0$ spin transitions between experiments $j=1$ &
$i=2$, which served as a control, and between experiments $j=1$ & $i=3$,
before and after tri-acid cleaning. After tri-acid cleaning, two populations
of $\bar{\omega}/2\pi$ are observed, attributable to polarization due to the
presence of an electric field caused by a change in surface termination. e,
Visualization of the shift in the splitting
$\Delta\delta=\delta_{i}-\delta_{j}$ between the two $\text{m}_{\text{s}}=0$
transitions between experiments $j=1$ & $i=2$, which served as a control, and
between experiments $j=1$ & $i=3$, before and after tri-acid cleaning.

Scanning confocal microscopy is a standard technique used to identify color
centers, revealing bright spots located relative to the coordinates set by the
scanning axes of the microscope. However, returning to a previously-
characterized set of emitters on a chip can be challenging due to the vast
difference between the $\mathcal{O}(100~{}\upmu$m $\times$ 100 $\upmu$m) size
of the field of view and the $\mathcal{O}(5$ mm $\times$ 5 mm) size of the
chip, especially after the frame of reference is lost to sample removal.
Previous work has used bright ‘lodestar’ emitters or image-stitching
techniques to return to a given set of emitters Chakravarthi  _et al._ (2020),
though these techniques are not general, as not all samples possess
sufficiently unique features for each field of view of interest.

We demonstrate the ability to register emitters to a global coordinate system
using a standard home-built cryogenic confocal microscope setup. This
technique enables us to revisit the same set of nitrogen-vacancy centers in
diamond (NVs) over the course of multiple cooling cycles, and therefore to
track emitter properties over time. We first fabricate quick response-style
(QR) codes on the surface of the diamond chip (see Methods Section 6). These
are decoded in real-time with custom image processing tools by establishing a
coordinate transform between the global sample coordinates and the local
microscope coordinates using the region of sample space in view of the
scanning confocal microscope (Fig. 2a).

We use off-resonant scanning fluorescence microscopy under 515 nm excitation
to image a low-density of NV centers on the surface of the chip. To create
these fluorescent centers, the chip was implanted with $1\times
10^{9}/\text{cm}^{2}$ of 15N ions at 185 keV, and subsequently annealed at
1200∘C in ultra-high vacuum, tri-acid cleaned in a 1:1:1 mixture of nitric,
perchloric, and sulfuric acids by boiling for 1 hour Chu  _et al._ (2014), and
finally cleaned in a 3:1 sulfuric acid:hydrogen peroxide piranha solution. We
classify bright, diffraction-limited spots as candidate emitter sites, as
shown in the inset of Fig. 2a. We then determine the spectral positions and
linewidths of the zero-phonon line (ZPL) optical transitions at each candidate
site with photoluminescence excitation (PLE) spectroscopy. To do this, we
measure the fluorescence response of each emitter by scanning a resonant laser
over the ZPL transitions and collecting light emitted into the phonon side-
band (PSB) on an avalanche photodiode. We label the spin conserving
transitions associated with $\text{m}_{\text{s}}=0$ by mean ZPL frequency
$\bar{\omega}=1/2\left(E_{x}+E_{y}\right)$ and splitting
$\delta=|E_{y}-E_{x}|$ Bassett  _et al._ (2011). Further information about the
experimental setup and NV centers is provided in the Supplementary
Information. A typical NV PLE spectrum is shown in Fig. 2b. Details regarding
data analysis and QR encoding are provided in the Methods Sections 2 and 4.

We track NV centers over four experiments by registering emitters to the
sample rather than to the microscope coordinates, in spite of the stochastic
movement of the sample caused by remounting along with warming and cooling the
system between experiments. Experiments 1 and 2 served as a control, as we
thermally cycled and remounted the sample in between, but performed no
additional materials processing. Between experiments 2 and 3, the sample was
tri-acid cleaned in a 1:1:1 mixture of nitric, perchloric, and sulfuric acids
by boiling for 1 hour Chu  _et al._ (2014) and between experiments 3 and 4,
the sample was annealed in an oxygen environment at 450∘C for 4 hours Fu  _et
al._ (2010). In each experiment, NVs and QR codes were registered to the local
microscope coordinate system, and then transformed to the global sample
coordinate system. After registering the locations of NVs in all four
experiments, we identified the NVs in each experiment that belonged to the
same confocal site on the sample using a clustering algorithm constrained by a
diffraction-limited Euclidean threshold distance. The number of experiments in
which a color center was found at the same global sample coordinate site is
provided in Fig. 2c: we observe that some NVs disappear over multiple
experiments.

By tracking individual color centers over multiple cryostat cooling cycles, we
observe that tri-acid cleaning the diamond leads to shifts in the mean
frequency at a given NV site
$\Delta\bar{\omega}/2\pi=\bar{\omega}_{i}/2\pi-\bar{\omega}_{j}/2\pi$ (for
experiments $i,j$) of the $\text{m}_{\text{s}}=0$ optical transitions
exceeding those observed in the control. Conversely, the change in splitting
$\Delta\delta=\delta_{i}-\delta_{j}$ between the two $\text{m}_{\text{s}}=0$
states does not deviate from the control. These observations, as shown in Fig.
2d-e, are consistent with the addition of an electric field normal to the
surface Bassett  _et al._ (2011), attributable to a changed surface
termination Sangtawesin  _et al._ (2019). Notably, the population-level
statistics for $\bar{\omega}/2\pi$ alone do not reveal this phenomenon;
tracking individual emitters uniquely enabled us to observe these minute
spectral shifts.

Figure 3: Widefield photoluminescence excitation of silicon-vacancy centers.
a, Fluorescence image of Sample A reconstructed from widefield PLE as the
resonant laser frequency $\omega/2\pi$ was swept over 10 GHz, using the same
field of view as Christen  _et al._ (2022). b, Strain map indicating the
spatial distribution of the mean zero-phonon line (ZPL) transition
$\bar{\omega}/2\pi$ (a proxy for axial strain) at 584 sites that had one PLE
peak at each of the four SiV transition frequencies. We observe that the SiVs
are split into two classes of axial strain. c, Histograms of the locations of
the four optical transitions for 984 groups of SiV peaks, where each group of
SiV peaks consists of a peak at each of the four SiV transition frequencies.
d, Mean ZPL transition frequency $\bar{\omega}/2\pi$ for 984 groups of SiV
peaks: the split into two classes of axial strain is apparent in the
distribution. Fitting the empirical probability density function ($\sigma=10$
MHz, see Methods Section 1) shown in red reveals a population centered at
406.8141 THz with standard deviation 59 MHz, and a population centered at
406.8136 THz with standard deviation 48 MHz. e, Ground state splitting
($\Delta_{GS}$), and f, Excited state splitting ($\Delta_{ES}$), for 984
groups of SiV peaks. The ground and excited state splittings closely
approximate the splitting due to spin-orbit coupling alone, revealing the low-
strain environment.  Figure 4:  Widefield photoluminescence excitation in a
FIB-implanted sample. a, Fluorescence image of Sample B reconstructed from
widefield PLE as the resonant laser frequency $\omega/2\pi$ was swept over 10
GHz. The grid of focused ion beam implantation sites is clearly visible. b,
Probability density function showing the probability to find a
photoluminescence (PL) peak as a function of wavelength for 11,010 SiVs
measured confocally under 515 nm excitation and collected on a spectrometer.
The inset shows the PL spectrum at one site. c, Typical widefield PLE spectrum
of one SiV transition at one spatial site in the widefield field of view, with
intensity data (blue circles) fit to a pseudo-Voigt function (red line). The
fit center location is 406.0582 THz, and the fit linewidth is 210.6(1) MHz.
Details of the image processing performed to extract widefield PLE spectra can
be found in Methods Section 3. d, Histogram showing inhomogeneous distribution
of SiV PLE measured in widefield as a function of resonant laser frequency,
$\omega/2\pi$. 40,186 peaks with linewidths less than 2 GHz and greater than
the lifetime limit of $(2\pi\times 1.7~{}\text{ns})^{-1}$ are represented. A
kernel estimate of the empirical probability density function (see Methods
Section 1) is shown in red. e, Distribution of linewidths for the 40,186 peaks
shown in d. The mean linewidth of all peaks that line in each 20 GHz bin is
shown as a blue circle. Bins containing fewer than 10 peaks are shown in
yellow, and discarded from analysis. Error bars give the standard deviation of
the mean. Optical linewidths do not significantly increase at lower
frequencies, indicating that the optical properties of highly-strained
emitters do not degrade.  Figure 5: Chip-scale verification of fabricated
devices at room temperature. a, White light image of one QR region. b,
Photoluminescence (PL) from the region shown in a under 532 nm excitation with
a longpass filter to block the excitation laser. c, PL from the region shown
in a under 532 nm excitation with a bandpass filter to highlight SiV PL. A
video demonstrating the automated imaging process in action over many QR
regions is provided as Extended Data Video 2. d, Following chip scale
characterization, promising regions are investigated at cryogenic
temperatures. Here, a confocal image of the region shown in a (rotated 30
degrees counter-clockwise) is overlaid with green circles to show pillars that
contained SiVs, and blue circles to show pillars that did not contain SiVs. e,
Example PL spectrum at cryogenic temperatures from the pillar circled in
yellow in d. f, Probability density function showing the probability to find a
PL peak as a function of wavelength for all pillars with SiVs shown in d.

##  II Parallelized photoluminescence excitation via cryogenic widefield
microscopy

Although the ability to register the positions of single emitters to the
surface of a sample enables individual color centers to be tracked and
compared over time, the characterization rate for the previous experiments is
limited by the time to obtain one resonant PLE scan, as each site must be
measured sequentially. To overcome this bottleneck, we modify our standard
confocal microscope setup to excite an entire field of view with a tunable
resonant laser in widefield mode (see Supplementary Information), and thus
parallelize PLE measurements to realize a dramatic speed-up. This is made
possible by the introduction of an electron-multiplying charge coupled device
(EMCCD) camera in the imaging path, which enables us to resolve individual
diffraction-limited color centers via image processing, as detailed in Methods
Section 3. The largest speedup that can be achieved with this techniques is
set by the number of diffraction-limited emitter sites in a given field of
view; we provide a detailed discussion of the regimes in which our widefield
technique is faster than confocal microscopy in Methods Section 5. We
demonstrate widefield PLE for two systems containing silicon-vacancy centers
in diamond (SiVs): one with an exceptionally narrow inhomogeneous distribution
of optical transitions (Sample A), and one with a broad distribution (Sample
B).

For Sample A, SiVs were incorporated in-situ during chemical vapor deposition
(CVD) overgrowth on a low-strain substrate. The sample was subsequently tri-
acid cleaned and annealed at 1200∘C in ultra-high vacuum. Fig. 3a shows a
fluorescence map reconstructed from widefield PLE measurements over the SiV
zero-phonon line (ZPL) (specifically using the ground spin-orbit conserving C
transition). By measuring PLE over all four SiV ZPL transitions (see Extended
Data Video 1), we can determine the strain environment in the overgrown layer
throughout the entire field of view, revealing two classes as shown in Fig.
3b-d. We ascribe this to two populations of strain along the axis of the SiV.
We generate an empirical probability distribution (PDF) function ($\sigma=$ 10
MHz, see Methods Section 1) to determine the inhomogeneous distribution. A
Gaussian fit to the empirical PDF representing $\bar{\omega}/2\pi$ reveals a
population centered at 406.8141 THz with standard deviation 59 MHz, and a
population centered at 406.8136 THz with standard deviation 48 MHz. Previous
work has demonstrated that CVD growth is a promising path towards generating a
narrow inhomogeneous distribution of SiVs Rogers  _et al._ (2014), but to our
knowledge, our measurement represents the largest number of SiVs with center
frequencies that lie within the bandwidth given by the lifetime-limited
linewidth, enabling work requiring high spectral homogeneity Christen  _et
al._ (2022). In a single field of view, we measure 257 SiV sites with ground
spin-orbit C-transition within $(2\pi\times 1.7~{}\text{ns})^{-1}$ from
406.7080 THz, and 613 SiV sites with ground spin-orbit C-transition within
$(2\pi\times 1.7~{}\text{ns})^{-1}$ from 406.7085 THz. The low-transverse-
strain environment is evident in the ground state ($\Delta_{GS}$) and excited
state ($\Delta_{ES}$) splittings, which closely approximate the splittings due
to spin-orbit coupling Meesala  _et al._ (2018) (Fig. 3e-f). Further
information about the relationship between SiV optical transitions and strain
environment can be found in the Supplementary Information. Given the emitter
density and inhomogeneous distribution in this field of view, our widefield
technique yields data on the strain environment $>700$ times faster than
standard confocal microscopy (see Methods Section 5), saturating the limit of
achievable speed-ups given the emitter density in the sample.

Having demonstrated the potential for widefield PLE to generate comprehensive
datasets more quickly than is possible with standard confocal PLE, we then
perform widefield PLE on Sample B, where SiVs were incorporated by focused-ion
beam (FIB) implantation of 29Si and subsequent high-temperature annealing (see
Methods Section 7). Individual FIB sites are visible in a reconstructed PLE
fluorescence map covering a fraction of the $>$1 THz inhomogeneous
distribution of all ZPL transitions, as shown in Fig. 4a.

A typical widefield PLE spectrum at one site is shown in Fig. 4c. After
fitting the widefield PLE spectra at all candidate sites, we extract the
locations of 40,186 widefield PLE peaks, as shown in Fig. 4d, as well as the
linewidths. We measure widefield PLE over the entire inhomogeneous
distribution, illuminating a long tail of highly-strained 29Si present in the
FIB-implanted sites. We validate the presence of the long tail of highly
strained SiVs using off-resonant PL under 515 nm illumination, as shown in
Fig. 4b. To better understand the role that strain plays in SiV optical
linewidths, we section the data into 20 GHz bins, and generate an empirical
probability density function (see Methods Section 1) of the optical linewidths
of all peaks in each bin. We fit this data to a Gaussian distribution, and
plot the mean linewidth in each frequency bin in Fig. 4e. The error bars
represent one standard deviation from the mean. We find that optical
linewidths do not significantly degrade at low optical frequencies, which is
an important validation for high-temperature operation of SiV quantum memories
using highly-strained emitters Stas  _et al._ (2022).

Widefield PLE enables us to collect data for every diffraction-limited site
within the field of view of our camera and within the range of our spectral
scan, reducing pre-selection bias. This permits a more honest and
comprehensive view into color center performance, rather than measuring color
centers serially until an emitter with the requisite optical properties for a
given application is found. Beyond gaining statistics on the likelihood of
finding a high quality quantum emitter, this technique enables large-scale
characterization of materials properties in the environment surrounding color
centers, for example as demonstrated here by measuring strain.

##  III Chip-scale verification of fabricated devices at room temperature

In addition to measuring quantum emitter properties, it is also critical to be
able to characterize color center generation. Further, thousands of photonic
devices can be fabricated on a single chip; characterizing the properties and
promise of each of these devices is time-consuming and tedious. We automate
widefield imaging and spectroscopy across a $2\times 2$ mm region of a diamond
chip, stepping serially between QR regions and using fluorescence to
qualitatively observe color centers in nanopillar devices within each field of
view (see Extended Data Video 2). A room-temperature setup with a motorized
sample stage and home-built imaging processing software enables us to move
from region to region, using real-time convolutional QR code detection as
feedback to bring the sample into focus and compensate for variations in the
sample stage motion (see Methods Section 4). Importantly, this process, and
our QR detection technique, is robust against the presence of dirt or complex
fabricated structures (see Extended Data Videos 3 and 4). Fig. 5 shows a
single QR region under incoherent reflection imaging for focusing and
registration, as well as under fluorescence imaging with a 532 nm excitation
laser. This set of nanopillars was identified to have bright pillars at room
temperature. To confirm this technique enables identification of color centers
that have been successfully incorporated into nanostructures, we verify that
the pillars contain SiVs by measuring confocal PL under 515 nm excitation at 4
K.

We regularly gather datasets over samples with
$\mathcal{O}(10~{}\text{mm}^{2})$ area, corresponding to $\mathcal{O}(10^{8})$
diffraction-limited spots. Moreover, the addition of an automated filter wheel
allows us to coarsely measure the spectral content of each field of view:
Extended Data Video 5 displays data acquired with 10 nm bandpass filters
around 737 nm, 620 nm, and 600 nm targeting silicon-, tin-, and germanium-
vacancy color centers on red, green, and blue color channels, respectively.
This imaging enables chip-scale characterization and classification to
identify promising devices and color centers in a time-efficient and automated
manner.

## Discussion

Large-scale characterization of color centers and photonic devices is
necessary to scale solid-state devices from proof-of-principle demonstrations
to useful technological applications. As the number of devices on chip
increases to thousands or more, manual point-by-point characterization becomes
intractable; our suite of automated tools performs spectroscopic measurements
hundreds of times faster than traditional cryogenic confocal microscopy,
opening up a new regime of system scaling. Individual color center tracking
reveals materials-level insight into device performance which can be used to
inform and revise qubit fabrication and processing. The resultant feedback
loop between design, fabrication, and characterization offers a pathway to
improved yields and device performance.

Furthermore, characterization of completed devices is critical in assessing
device properties and performance before integration into larger systems, a
process realized at chip-scale by our system. We emphasize that these
techniques are readily extensible to other materials platforms and quantum
emitters Viitaniemi  _et al._ (2022); Higginbottom  _et al._ (2022); Lukin
_et al._ (2020); Dietz  _et al._ (2022); Babin  _et al._ (2022); Hu  _et al._
(2020); Trusheim  _et al._ (2020); Davidsson  _et al._ (2022), providing a
basis for broad implementation.

## Methods

###  1 Empirical determination of probability density functions

We estimate empirical probability density functions using the kernel
distribution given by

$f_{k}(\lambda)=\frac{1}{n}\sum_{i=1}^{n}K\left(\frac{\lambda-\lambda_{i}}{h}\right)$
(1)

where $n$ is the number of samples, $\lambda_{i}$ are the sample values, $K$
is the smoothing function, and $h$ is the smoothing bandwidth. We used a
Gaussian smoothing function with bandwidth $\sigma$:

$K(\lambda)=\text{exp}\left(\frac{\left(\lambda-\lambda_{c}\right)^{2}}{2\sigma^{2}}\right)$
(2)

Unless otherwise noted, the bandwidth $\sigma$ is given by our spectrometer
limited bandwidth of 0.05 nm (for photoluminescence) or the appropriate
lifetime limited linewidth (for photoluminescence excitation), and
$\lambda_{c}$ for each candidate site was set to be the center of the fit
spectra at each candidate site.

###  2 Confocal data analysis

To identify and characterize color centers, we first measure a galvanometer
scan of photoluminescence excited with a strong 515 nm excitation laser (Fig.
S1a). We collect fluorescence on an avalanche photodiode in our cryogenic
confocal microscope, which is described in detail in the Supplementary
Information. We identify candidate sites by first applying a Gaussian bandpass
filter to the aggregate image $A(x,y)$, and then fit 2D Gaussians to the
resulting image. First, we convolve the aggregate image with a 2D Gaussian
with the lowpass standard deviation $\sigma_{LP}$:

$f_{LP}(x,y)=e^{-\frac{\left(x^{2}+y^{2}\right)}{2\sigma_{LP}^{2}}}$ (3)

We then discretize and convolve this kernel with the aggregate image $I(x,y)$
via discrete 2-dimensional convolution to yield an intermediate filtered image
$R(x,y)$:

$R(x,y)=\sum_{i}\sum_{j}I(i,j)f_{LP}(x-i+1,y-j+1)$ (4)

We high-pass filter the resulting image $R(x,y)$ by convolution with a 2D
Gaussian with high pass standard deviation $\sigma_{HP}$:

$f_{HP}(x,y)=e^{-\frac{\left(x^{2}+y^{2}\right)}{2\sigma_{HP}^{2}}}$ (5)

Finally, we discretize and convolve this kernel with the intermediate image
$R(x,y)$ via discrete 2-dimensional convolution to yield a bandpass-filtered
image $F(x,y)$:

$F(x,y)=R(x,y)-\sum_{i}\sum_{j}R(i,j)f_{HP}(x-i+1,y-j+1)$ (6)

We use this Gaussian bandpass filtering process to identify bright spots with
radii between the lowpass and highpass filter standard deviations. By fitting
2D Gaussians to the filtered image, we generate candidate emitter sites, which
are stored as an array of galvanometer coordinates.

We then revisit each candidate site to determine its spectral position: we
collect photoluminescence excited with a strong 515 nm laser onto a
spectrometer, as shown in Fig. S1b. We fit the spectrum taken at each
candidate site and determine the center zero-phonon line (ZPL) frequency up to
the resolution limit of the spectrometer. Once the spatial and coarse spectral
coordinates are identified, we measure an open-loop photoluminescence
excitation spectrum at each candidate site using a Newport Velocity TLB-6704
laser, as shown in Fig. S1c. We repump the emitters in between each frequency
step to initialize the NVs into the ground $\text{m}_{\text{s}}=0$ state,
enabling us to probe the $E_{x}$ and $E_{y}$ spin conserving transitions
associated with $\text{m}_{\text{s}}=0$. The mean frequency of the ZPL
transition $\bar{\nu}=\bar{\omega}/2\pi$ and splitting $\delta$ associated
with the emitter at this site are indicated in Fig. S1c. Finally, we obtain a
closed-loop high resolution scan, in which we feed back on the laser frequency
using a HighFinesse WS7 wavemeter, of each transition at every candidate site,
as shown in Fig. S1d-e.

Figure S1: Experimental stack for confocal spectroscopy. a, Confocal
fluorescence image of nitrogen-vacancy centers in diamond under 515 nm
excitation. b, Confocal photoluminescence spectrum under 515 nm excitation of
the NV site highlighted in red in a. Only one peak is resolvable on the
spectrometer: the center of the fit to this peak is used to center the
resonant laser for resonant spectroscopy. c, Open-loop resonant
photoluminescence excitation spectrum of the NV site, showing the $E_{x}$ and
$E_{y}$ transitions. The center location and $E_{x}$-$E_{y}$ splitting, as
well as the fit used to determine these values, are overlaid. d,-e, Closed-
loop photoluminescence excitation scans of the spectra shown in c, with fits
overlaid.

###  3 Widefield data analysis

To measure widefield PLE in Samples A and B, we swept the frequency of a
ti:sapph excitation laser (M2 SolsTiS) over the inhomogeneous distribution in
frequency steps much smaller than the emitter lifetime, using the setup
described in the Supplementary Information. For Sample B, weak 515 nm Cobolt
laser was applied continuously to repump the emitters. We tuned the resonator
internal to the resonant laser in voltage steps that corresponded to 10 MHz
steps in frequency, and locked the laser to a HighFinesse WS7 Wavemeter (60
MHz absolute accuracy, 2 MHz resolution) at each step. Once tuning was
complete, the EMCCD was exposed for 0.5 s for Sample A and for 1 s for Sample
B.

Here, we present an example of the image processing performed to extract
widefield PLE data from the raw widefield images collected. At each frequency
step, the raw image was first cropped to remove area outside the QR region, as
shown in Fig. S2a. Then, we filtered the image with a 2D Gaussian filter. We
generated a 2D Gaussian kernel $f_{g}(x,y)$ with standard deviation $\sigma=2$
pixels selected to approximately match the diffraction limited spot size:

$f_{g}(x,y)=e^{-\frac{(x^{2}+y^{2})}{2\sigma^{2}}}$ (7)

At each frequency step $\nu=\omega/2\pi$, we discretized and convolved the
kernel with the image $M_{\nu}(x,y)$ via discrete 2-dimensional convolution to
yield a filtered image $C_{\nu}(x,y)$:

$C_{\nu}(x,y)=\sum_{i}\sum_{j}M_{\nu}(i,j)f_{g}(x-i+1,y-j+1)$ (8)

Here, the range of $i$ and $j$ in the sum spans the dimension of the image and
the kernel.

After filtering each image, we sectioned the data into frequency bands to
facilitate image processing. At each frequency band spanning approximately 10
GHz, we generated an aggregate image $A(x,y)$ summarizing the fluorescence
over the full band by taking the maximum value of each pixel over the images
taken at all frequency steps. An example of an aggregate image generated for
images taken while scanning the resonant laser from 405.8816-404.9005 THz is
shown in Fig. S2b. We then used this aggregate image to identify candidate
emitter sites for each frequency section, using the bandpass filtering and 2D
Gaussian fitting process described previously in Methods Section 2, Eqs. 3-6.
An example candidate site is circled in red in Fig. S2a-b.

At each candidate emitter site, we determined the fluorescence intensity as a
function of excitation frequency by binning pixels around the spatial center
of the 2D Gaussian fit. An example site is shown in Fig. S2c, with the group
of binned pixels shown in a red box. Then, this group of pixels was summed at
each frequency step to find the fluorescence intensity as a function of
excitation frequency, $I_{p,q}(\nu)$ for an emitter located at location $x=p$,
$y=q$ in the convolved image $C_{\nu}(x,y)$:

$I_{p,q}(\nu)=\sum_{i=p-3}^{p+3}\sum_{j=q-3}^{q+3}C_{\nu}(i,j)$ (9)

We chose the number of pixels to include in the binned region to maximize the
signal-to-noise ratio. Although we used the bandpass-filtered image $F(x,y)$
to generate the candidate sites, we generated the PLE intensity function
$I_{p,q}(\nu)$ using the convolved images at each frequency step,
$C_{\nu}(x,y)$. An example intensity function $I_{p,q}(\nu)$ for the candidate
SiV site is shown in Fig. S2d. In principle, both the emitter fluorescence
signal $S_{p,q}$ at a site and background fluorescence from the sample $B$
both depend on the intensity of the excitation laser. A simple model is
considered to account for fluctuating laser intensity $L(\nu)$, where $\nu$ is
the frequency bin:

$I_{p,q}(\nu)=S_{p,q}(\nu)L(\nu)+BL(\nu)$ (10)

We model this as a linear process since the emitters are driven below
saturation. We determined the intensity function $L(\nu)$ by calculating the
average value of all pixels in the convolved image $C_{\nu}(x,y)$ at each
frequency:

$L(\nu)=\frac{1}{xy}\sum_{x}\sum_{y}C_{\nu}(x,y)$ (11)

While $L(\nu)$ accounts for global fluctuations of intensity, it does not
account for regional fluctuations, including the point spread function of the
widefield microscope. Finally, we determined the frequency-dependent SiV
fluorescence signal at a given site $S_{p,q}(\nu)$ by dividing the measured
intensity by the noise function:

$S_{p,q}(\nu)+B=\frac{I_{p,q}(\nu)}{L(\nu)}$ (12)

An example of the frequency-dependent intensity function $L(\nu)$ at one site
is shown Fig. S2e, and the final corrected signal to be fit is shown in Fig.
S2f. This model assumes that there are many color centers such that the
emission frequencies of the population of color centers are uncorrelated, and
that the dominant intensity fluctuation of the entire image is correlated with
the excitation frequency.

This assumption is valid for the case of Sample B, which has a broad
inhomogeneous distribution of emitters even at individual sites. However, this
assumption breaks down for Sample A, since the inhomogeneous distribution is
narrow. Instead, for Sample A, we use a liquid-crystal noise-eater to
stabilize the laser power, and fit the raw PLE data as given by Eq. 9.

Figure S2: Analysis sequence to extract photoluminescence excitation (PLE)
spectra from widefield fluorescence imaging. a, Widefield image at a single
frequency, 406.070480(2) THz, exposed for 1 s. A handful of SiVs are observed
as diffraction-limited bright spots. b, Reconstructed image of all sites with
widefield PLE peaks between 406.062985(2) and 406.070993(2) THz. For each
spatial pixel, the value shown here represents the maximum pixel brightness
for that pixel over all frequencies in the frequency interval A 2D Gaussian
smoothing function was then applied to the resulting image. c, Zoomed-in view
of the reconstructed site highlighted in b. All of the pixels that fall within
the bounds of the red box are summed at each frequency slice and used to
represent the widefield PLE intensity at that frequency. d, Raw widefield PLE
data as a function of frequency for the site highlighted in a-c. e, Background
spectrum constructed by averaging the pixel values of the entire widefield
image at each frequency. f, Processed widefield PLE spectrum determined by
dividing the raw spectrum by the background. The frequency at which the image
shown in a was excited is indicated with a red line.

###  4 QR encoding and convolutional QR detection

Custom-designed binary codes etched into the diamond surface serve as our QR-
style codes. These markers consist of a 2-dimensional array of bits, with 16
bits to encode the location, 4 bits to encode a version, 1 bit as a constant
pad, and 3 bits as an error-detecting checksum.

Figure S3: QR code design and image processing. a, QR-style code design. i,
Vertical and horizontal arrays of dots serve as alignment markers. ii, Row and
column information is written for human-readability. iii, QR data: bits 2-5
encode the QR version, bits 7-14 encode the row, bits 15-22 encode the column,
and bits 23-25 encode a checksum. b, SEM micrograph of a QR-style code
fabricated in diamond. c, Widefield optical image showing the area bounded by
four QR-style codes. d, Horizontal convolution to detect the horizontal QR
arms. e, Vertical convolution to detect the vertical QR arms. f, Summing the
cubes of the horizontal and vertical detections. The bright points that remain
show the right angle between the QR alignment axes.

Fig. S3a-c show an example of the layout and design of these markers, a SEM
micrograph after the QR codes are patterned via lithography and etching, and a
typical optical image under our microscopes.

We make use of a convolutional approach to quickly detect and decode the
position of QR markers in an image. Given precharacterized sample rotation and
scale, a kernel is generated, corresponding to the two large dots and three
small dots of a single arm of the QR code bounding box (Fig. S3a). Convolving
a flattened version of this image with this kernel and its 90∘ rotation yields
two images with bright peaks corresponding to candidate positions for
horizontal and vertical arms (Fig. S3d,e). The cubed sum of these two images
leaves bright peaks at positions where horizontal and vertical arms are both
detected, i.e. good candidates for full QR codes (Fig. S3f). At each candidate
site, the $5\times 5$ grid which stores the coded data is binarized and
decoded, with errors detected by checksum failure. Altogether, this process is
efficient at extracting QR candidates and data from images ($<100$ ms typical
processing time), to the point that real-time video data is easily processed
and displayed with detected QRs.

As an additional failsafe, we update a belief model for all QR candidates with
positive checksum within a field of view via majority vote, to deduce the true
location. This avoids situations where false-positive checksums yield failure.
Importantly, this detection procedure is also robust when other features (e.g.
fabricated structures) are present within the field of view. Altogether, this
robust process for real-time QR detection enables rapid feedback to the user,
along with automated traversal across a sample and reliable localization of
fluorescent data with the global sample coordinate system.

###  5 Advantage of widefield microscopy

Here, we present relevant considerations when choosing between confocal and
widefield microscopy, and define the regimes in which our widefield approach
results in a speed-up. The time to complete a photoluminescence excitation
(PLE) experiment can vary widely depending on the specific approach: number of
frequencies sampled, number of averages at each frequency point, whether a
repump laser is used, microscope collection efficiency, and sensor efficiency
all play a role. We therefore define a general scheme to determine whether a
parallelized widefield approach will provide a time benefit. The time to
collect a confocal PLE scan at $m$ sites in a field of view, in $n$ frequency
bins, is given by:

$\begin{split}t_{\text{confocal}}=m\big{(}t_{\text{move}}+t_{\text{tune laser,
coarse}}+t_{\text{repump}}\\\ +n(t_{\text{tune laser,
fine}}+t_{\text{collect,c}})\big{)}\end{split}$ (13)

Similarly, the time to collect a PLE scan in widefield for $m$ sites in a
field of view is given by:

$\begin{split}t_{\text{widefield}}=t_{\text{tune laser,
coarse}}+t_{\text{repump}}+\\\ n(t_{\text{tune laser,
fine}}+t_{\text{collect,w}})\end{split}$ (14)

These equations hold in the case of a narrow inhomogeneous distribution: if
all emitters are close in frequency, and $t_{\text{move}}$ is negligible, the
time to collect data for $m$ emitters in a field of view in $n$ frequency bins
scales simply as

$\frac{t_{\text{confocal}}}{t_{\text{widefield}}}=m\frac{t_{\text{collect,
c}}}{t_{\text{collect, w}}}$ (15)

As long as the integration time to collect the widefield data at each point is
less than $m$ times the confocal case, our widefield approach is faster.

However, this approximation breaks down for the case of a large inhomogeneous
distribution. Consider the far limiting case, in which there are $m$ emitters
in the field of view that are all detuned in frequency such that they do not
spectrally overlap. In this case, the time to collect data for $m$ emitters in
a field of view in $n$ frequency bins is given by the ratio of collection
times alone:

$\frac{t_{\text{confocal}}}{t_{\text{widefield}}}=\frac{t_{\text{collect,
c}}}{t_{\text{collect,w}}}$ (16)

We therefore define an equation to determine the approximate speed-up factor
(SF) of widefield over confocal PLE as a function of the number of color
centers, $N$, the lifetime-limited linewidth $\gamma$, and the inhomogeneous
distribution $\Gamma$:

$\text{SF}=N\cdot\frac{\gamma}{\Gamma}\cdot\frac{t_{\text{collect,
c}}}{t_{\text{collect, w}}}$ (17)

A SF $>1$ represents a speed-up for widefield over confocal microscopy.

We now calculate the value of the SF for the two samples presented in the main
text, Sample A and Sample B. Sample A represents the case of a very small
inhomogeneous distribution. Four widefield scans were taken in the same field
of view, covering the optical excitation frequencies around the A, B, C, and D
transitions of the SiV in the absence of significant strain. All four
transitions were found at 784 diffraction-limited widefield sites,
representing 3,936 PLE peaks. We note that 200 of these diffraction-limited
widefield sites contained eight peaks corresponding to two groups of SiV
transition frequencies, but we count only unique spatial sites in our
analysis, as the transition frequencies of the two SiV groups are so close in
frequency. With $t_{\text{collect, c}}\approx t_{\text{collect, w}}$, and
considering all emitters to lie in the same frequency bin, it would have taken
$\text{SF}=784$ times longer to measure the same strain distribution with our
confocal microscope. For Sample B, with 40,186 peaks measured over 1.12 THz,
we achieved a speed-up of $\text{SF}=4$.

###  6 Diamond fabrication

The fabrication procedure of patterning QR codes is the same as the one for
fabricating nanopillar arrays. Each diamond sample was first deposited with
silicon nitride (hard mask) via chemical vapor deposition. QR code and
nanopillar array patterns were transferred into the nitride hard mask through
electron beam lithography and CF4 reactive-ion etching (RIE). Inductively-
coupled plasma RIE with oxygen plasma subsequently transferred the mask
patterns into bulk diamond. Finally, the samples were submerged in
hydrofluoric acid to remove the nitride layer.

###  7 Focused ion beam implantation

We used a focused ion beam (FIB) Schröder  _et al._ (2017) tool at the Ion
Beam Laboratory (Sandia National Laboratories) to implant 29Si ions (spot size
of about 50 nm $\times$ 45 nm) at an effective areal dose of $1\times
10^{0}-1\times 10^{6}$ ions/cm2. The 29Si ion energy was 180 keV. After
implantation, we annealed the sample at 1200∘C in an ultrahigh vacuum furnace.
Finally, we tri-acid cleaned the sample in a 1:1:1 mixture of nitric,
perchloric, and sulfuric acids by boiling for 1 hour.

## Declarations

### Funding

M.S. and E.B. acknowledge support from the NASA Space Technology Graduate
Research Fellowship Program. I.C. acknowledges support from the National
Defense Science and Engineering Graduate Fellowship Program, the National
Science Foundation (NSF) EFRI ACQUIRE program EFMA-1641064, and NSF award
DMR-1747426. M.S. and M.P.W. acknowledge partial support from the NSF Center
for Integrated Quantum Materials (CIQM), DMR-1231319. K.C.C. acknowledges
support from the NSF RAISE-TAQS CHE-1839155 and the MITRE Corporation Moonshot
program. D.R.E. acknowledges partial support from the NSF Center for Quantum
Networks (CQN), EEC-1941583.

Distribution Statement A. Approved for public release. Distribution is
unlimited. Diamond growth is based upon work supported by the National
Reconnaissance Office (NRO) under Air Force Contract No. FA8702-15-D-0001. Any
opinions, findings, conclusions or recommendations expressed in this material
are those of the author(s) and do not necessarily reflect the views of the
National Reconnaissance Office.

The focused ion beam implantation work was performed at the Center for
Integrated Nanotechnologies, an Office of Science User Facility operated for
the US Department of Energy (DOE) Office of Science. Sandia National
Laboratories is a multimission laboratory managed and operated by National
Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary
of Honeywell International, Inc., for the US 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 US DOE or the United
States Government. This work made use of the Shared Experimental Facilities
supported in part by the MRSEC Program of the NSF under award number
DMR-1419807.

### Competing Interests

The authors declare no competing interests.

### Availability of data and materials

Available on request to M.S.

### Authors’ contributions

M.S., I.C., E.B., and M.P.W. conceived and performed experiments, developed
software, and built optical setups. I.C. developed software and optical setups
for widefield data collection and chip-scale sample screening. M.S. analyzed
the data and wrote the manuscript with assistance from I.C., E.B., M.P.W., and
K.C.C. K.C.C. fabricated QR codes designed by M.P.W. SiV Sample A was produced
by J.M., A.M., S.H., D.B., and P.B.D. SiV Sample B was focused ion beam
implanted by M.T. and E.S.B. D.R.E. supervised the project. All authors
discussed the results and contributed to the manuscript.

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## Extended data

This work investigates approaches for large-scale data acquisition applied to
fluorescent emitters. We attach five Extended Data Videos which illustrate the
scope of this work. These videos, also hosted on figshare at
https://figshare.com/s/185ccecd555aa21b5a50, are condensed or cropped versions
of larger scans to reduce file size to 80 MB.

The full uncropped videos (with file size 940 MB) are hosted separately on
figshare at https://figshare.com/s/81a38527722002e996f6. In the case of chip-
scale scans, these show all of the fields of view investigated in each dataset
to reduce selection bias.

Extended Data Video 1: Widefield photoluminescence excitation (PLE) of
silicon-vacancy centers in chemical-vapor deposition diamond. a, b, c, d,
Scanning over the A, B, C, and D optical transitions of the silicon-vacancy
center in diamond, in a field of view. As expected, the C transition is the
brightest of the four Müller  _et al._ (2014). The frequency of the resonant
laser for a given frame is noted in the lower left of the panel. The scale bar
represents 10 $\upmu$m. Every frame represents approximately half a second of
measurement (video displayed at 10$\times$ speed). All panels are linearly
scaled to the same fixed color limit.

Extended Data Video 2: Chip-scale measurement of a sample with nano-fabricated
pillars. a, Bright-field images of each field of view, with boxes marking
features which are detected as checksum-satisfying QR codes. Green boxes
satisfy majority vote conditions for the field of view, and are considered
correct. Yellow boxes usually result from noise which happens to satisfy the
checksum, or from a bit error event which fails in majority vote condition. b,
Fluorescence measurements with a 737 nm bandpass filter targeting SiV color
centers. c, Fluorescence measurements with a 640 nm long-pass filter, with
lower signal-to-noise ratio. This is likely due to fluorescence from NV
centers or other emitters in the sample, especially in the bulk. Scale bars
represent 10 $\upmu$m. Every frame represents approximately 40 seconds of
alignment and 20 seconds of measurement (video displayed at 600$\times$
speed). Each panel is linearly scaled to the maximum and minimum of each
frame, except for b, which is scaled to a fixed color limit.

Extended Data Video 3: Chip-scale measurement of a sample with deleterious
noise. a, Bright-field images with the same box color coding as Extended Data
Video 2. This video demonstrates the robustness of our convolutional QR
detection algorithm: we are able to detect QRs even through regions coated
with stochastic particulates which pose a challenge for non-convolutional
approaches. Every frame represents approximately 20 seconds of alignment and
20 seconds of measurement (video displayed at 400$\times$ speed). This panel
is linearly scaled to the maximum and minimum of each frame.

Extended Data Video 4: Chip-scale measurement of a sample with complex
fabricated structures. a, Bright-field images with the same box color coding
as Extended Data Video 2. Despite the bright and varying nature of these
fabricated structures, we are still able to conduct full-chip measurements. b,
Fluorescence measurements at each field of view. Bright spots on the
waveguides are attributed to either color centers, largely tin-vacancy in this
case, or points where waveguide-coupled fluorescence is scattered upward.
Scale bars represent 10 $\upmu$m. Every frame represents approximately 20
seconds of alignment and 10 seconds of measurement (video displayed at
300$\times$ speed). a is linearly scaled to the maximum and minimum of each
frame. b is scaled to a fixed color limit.

Extended Data Video 5: Chip-scale measurement of sample B, a sample
coimplanted with silicon, germanium, and tin. a, Bright-field images with the
same box color coding as Extended Data Video 2. b, Fluorescence images with a
640 nm long-pass filter. c, False-color images composited from three
fluorescent measurements using 737 nm, 620 nm, and 600 nm bandpass filters
with $\approx$10 nm bandwidth on the red, green, and blue color channels.
These filters target the zero-phonon lines of silicon-, tin-, and germanium-
vacancy color centers, respectively, though germanium appears as cyan due to
its phonon sideband overlapping with the filter targeting the zero phonon line
of tin. Scale bars represent 10 $\upmu$m. Every frame represents approximately
30 seconds of alignment and 25 seconds of measurement (video displayed at
550$\times$ speed). a and b are linearly scaled to the maximum and minimum of
each frame. c is shown with a fixed color range in log scale, to increase
visibility of regions implanted with low dose.

## Supplementary information

### S1. Cryogenic microscope

Figure S4: Cryogenic confocal microscope. Details are provided in text.

We employ a homebuilt cryogenic confocal microscope as shown in Fig. S4.
Samples are cooled to $<4$ K in a Montana Instruments Cryostation equipped
with three-axis piezoelectric stages (Attocube ANP101 Nanopositioners) to
coarsely position the sample. Off-resonant excitation is provided by a 515 nm
Hubner Cobolt laser. A Newport Velocity modulated by a free-space G&H 3080
acousto-optic modulator is used to resonantly excite NVs, while an M2 SolsTiS
Ti:sapphire is used to resonantly excite SiVs. An incoherent white light
source is also available for imaging. The excitation and collection paths are
combined on a 90:10 beamsplitter, and scanning galvanometers enable beam
steering over the field of view. Image planes and Fourier planes are indicated
by white dots.

Sample fluorescence is collected through the 90% port in the beamsplitter, and
the position of automated flip mirrors determine whether the fluorescence is
collected on a camera (Photometrics Cascade 1K EMCCD), spectrometer (Princeton
Instruments Isoplane), or avalanche photodiode (APD, Excelitas SPCM-AQRH-14).
For resonant excitation, the excitation laser frequency is blocked with an
optical filter (longpass with 650 nm cutoff for NV experiments, 775/46 nm
bandpass for SiV experiments) such that only the phonon side-band reaches the
APD. The full experimental sequence is controlled via a computer with
homebuilt software.

Figure S5: Cryogenic widefield microscope. Details are provided in text.

Our confocal microscope is rapidly converted to a widefield microscope by
adding a telescope – consisting of a Galilean beam expander and a long focal-
length lens – the focus of which is mapped through the 4f to the back aperture
of the objective, as shown in Fig. S5. The telescope is placed using a
magnetic mount. The galvanometers are fixed in place for widefield
measurements, and the fluorescence image is collected onto the EMCCD camera.

### S2. Room temperature microscope

Our room temperature widefield microscope is shown in Fig. S6. Off-resonant
excitation is provided by a 532 nm Verdi laser. An incoherent white light
source is also available for imaging. The excitation and collection paths are
combined on a dichroic mirror, and fluorescence is collected on a Princeton
Instruments ProEM EMCCD camera. An automated filter wheel enables selection of
the fluorescence bandwidth to collect. A computer is used to feed back on
Thorlabs 3-axis NanoMax linear translation stages to position the sample in X
and Y, and to focus in Z, using custom image processing software and the
fabricated QR codes. Examples are provided as Extended Data Videos.

Figure S6: Room temperature widefield microscope. Details are provided in
text.

### S3. Nitrogen-vacancy centers in diamond

The energy structure of a negatively charged nitrogen-vacancy center in
diamond yields two optical transitions between the excited state and ground
state manifolds that correspond to $m_{s}=0$ transitions, labeled $E_{x}$ and
$E_{y}$. A schematic of a single nitrogen-vacancy center in diamond as well as
an energy level structure showing the relevant optical transitions absent a
magnetic field are shown in Fig. S7. Strain breaks the degeneracy of $m_{s}=0$
optical transition, yielding two optical transitions distinct in frequency,
$E_{x}$ and $E_{y}$.

Figure S7: Nitrogen-vacancy center in diamond. a, Ball and stick diagram
showing one possible orientation of a nitrogen-vacancy center in diamond. Blue
atoms represent carbon; the red atom is a substitutional nitrogen and the
white V represents a carbon vacancy. There are four energetically equivalent
NV orientations along each of the $\langle 111\rangle$ family of
crystallographic directions. b, Energy level diagram of a single negatively
charged nitrogen-vacancy center in diamond under zero magnetic field. There
are two relevant optical transitions between the excited state and ground
state manifolds corresponding to $m_{s}=0$ transitions, labeled $E_{x}$ and
$E_{y}$. The optically-active singlet pathway is labeled to the side.

The response of NV centers to electric fields and strain can be equivalently
described in the orbital basis $\\{\ket{E_{x}},\ket{E_{y}}\\}$ by the DC Stark
perturbation Bassett  _et al._ (2011). The energy eigenvalues under the Stark
effect are of the form

$E_{\pm}=\hbar\bar{\omega}\pm h\frac{\delta}{2}$ (18)

for mean transition frequency $\bar{\omega}/2\pi$ and splitting $\delta$.
Because $\bar{\omega}/2\pi$ scales with the longitudinal component and
$\delta$ with the transverse component of the perturbing electric field, these
eigenvalues enable observation of the local strain environment around a given
NV center.

In Fig. 2c of the main text, we observe that the change in mean frequency
$\delta\bar{\omega}/2\pi$ splits into two groups following tri-acid cleaning.
The dipole orientation of the NV is constrained to 8 possible configurations
given by the $\langle 111\rangle$ family of crystallographic directions and
the dipole orientation of the nitrogen atom and the vacancy center.

### S4. Silicon-vacancy centers in diamond

The energy structure of a negatively charged silicon-vacancy center in diamond
yields four optical transitions labeled A, B, C, and D, where A is the highest
energy transition between the upper excited state and the lower ground state,
and D is the lowest energy transition between the lower excited state and
upper ground state. A schematic of a single silicon-vacancy center in diamond
as well as an energy level structure showing the optical transitions under
zero magnetic field are shown in Fig. S8.

Figure S8: Silicon-vacancy center in diamond. a, Ball and stick diagram
showing one possible orientation of a silicon-vacancy center in diamond. Blue
atoms represent carbon; the red atom is a substitutional silicon surrounded by
a single split carbon vacancy. There are four energetically equivalent SiV
orientations along each of the $\langle 111\rangle$ family of crystallographic
directions. b, Energy level diagram of a single negatively charged silicon-
vacancy center in diamond under zero magnetic field. There are four relevant
optical transitions between the excited state and ground state manifolds,
labeled A, B, C, and D. Spin orbit coupling and strain split the ground state
manifold by $\Delta_{GS}$ and the excited state manifold by $\Delta_{ES}$.

We label the SiV transitions by mean frequency $\bar{\omega}$, ground state
splitting $\Delta_{\text{GS}}$, and excited state splitting
$\Delta_{\text{ES}}$, which are calculated from experimentally-measured
spectra:

$2\pi\bar{\omega}=\frac{1}{4}\left(\omega_{A}+\omega_{B}+\omega_{C}+\omega_{D}\right)$
(19) $2\pi\Delta_{\text{GS}}=\omega_{C}-\omega_{D}$ (20)
$2\pi\Delta_{\text{ES}}=\omega_{B}-\omega_{D}$ (21)

The strain environment around the SiVs found in Sample A can be determined
directly from the measured optical transitions by using the eigenvalues of the
diagonalized strain Hamiltonian for the $D_{3d}$-symmetric SiV Meesala  _et
al._ (2018). The strain dependence of the mean zero-phonon line (ZPL) emission
$\Delta_{ZPL}$ and using the strain susceptibility in the ground and excited
state manifolds described in Meesala  _et al._ (2018), the ground state
splitting $\Delta_{GS}$, and the excited state splitting $\Delta_{ES}$ are:

$\begin{split}\bar{\omega}=\Delta_{ZPL,0}+\left(t_{\|,e}-t_{\|,g}\right)\epsilon_{zz}+\left(t_{\perp,e}-t_{\perp,g}\right)\left(\epsilon_{xx}+\epsilon_{yy}\right)\end{split}$
(22)
$\begin{split}\Delta_{GS}=\big{(}\lambda_{SO,g}^{2}+4\left(d_{g}\left(\epsilon_{xx}-\epsilon_{yy}\right)+f_{g}\epsilon_{yz}^{2}\right)^{2}+4\left(-2d_{g}\epsilon_{xy}+f_{g}\epsilon_{zx}\right)^{2}\big{)}^{1/2}\end{split}$
(23)
$\begin{split}\Delta_{ES}=\big{(}\lambda_{SO,e}^{2}+4\left(d_{e}\left(\epsilon_{xx}-\epsilon_{yy}\right)+f_{e}\epsilon_{yz}^{2}\right)^{2}+4\left(-2d_{e}\epsilon_{xy}+f_{e}\epsilon_{zx}\right)^{2}\big{)}^{1/2}\end{split}$
(24)

for strain susceptibilities $t_{\|,g(e)}$, $t_{\perp,g(e)}$, $d_{g(e)}$,
$f_{g(e)}$ in the ground (excited) state manifold. Axial strain
$\epsilon_{zz}$ primarily yields a shift in the mean ZPL frequency
$\bar{\omega}$, while transverse strain primarily yields increased splitting
$\Delta_{GS}$ and $\Delta_{ES}$. The two classes of mean ZPL frequency
$\bar{\omega}/2\pi$ observed in our experiment are indicative of two classes
of axial strain $\epsilon_{zz}$ in Sample A, as shown in Fig. 3b-d of the main
text. Similarly, the single population of $\Delta_{GS}$ and $\Delta_{ES}$
shown in Fig. 3e-f of the main text indicate a uniform transverse strain
environment in Sample A.