# An integrated photonic engine for programmable atomic control

Ian Christen1,∗, Madison Sutula1, Thomas Propson1, Hamed Sattari2, Gregory
Choong2, Christopher Panuski1, Alexander Melville3, Justin Mallek3, Scott
Hamilton3, P. Benjamin Dixon3, Adrian J. Menssen1, Danielle Braje3, Amir H.
Ghadimi2,∗, and Dirk Englund1<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>1Research Laboratory of Electronics, Massachusetts Institute
of Technology, Cambridge, MA 02139, USA
2Centre Suisse d’Electronique et de Microtechnique (CSEM), 2000 Neuchâtel,
Switzerland
3Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA
02421, USA

###### Abstract

Solutions for scalable, high-performance optical control are important for the
development of scaled atom-based quantum technologies. Modulation of many
individual optical beams is central to the application of arbitrary gate and
control sequences on arrays of atoms or atom-like systems. At telecom
wavelengths, miniaturization of optical components via photonic integration
has pushed the scale and performance of classical and quantum optics far
beyond the limitations of bulk devices Sun  _et al._ (2013); Poulton  _et al._
(2020); Harris  _et al._ (2017). However, these material platforms for high-
speed telecom integrated photonics Rahim  _et al._ (2018); Kish  _et al._
(2018) are not transparent at the short wavelengths required by leading atomic
systems Wan  _et al._ (2020); Benhelm  _et al._ (2008); Ebadi  _et al._
(2021). Here, we propose and implement a scalable and reconfigurable photonic
architecture for multi-channel quantum control using integrated, visible-light
modulators based on thin-film lithium niobate Desiatov  _et al._ (2019); Celik
_et al._ (2022). Our approach combines techniques in free-space optics,
holography, and control theory together with a sixteen-channel integrated
photonic device to stabilize temporal and cross-channel power deviations and
enable precise and uniform control. Applying this device to a homogeneous
constellation of silicon-vacancy artificial atoms in diamond, we present
techniques to spatially and spectrally address a dynamically-selectable set of
these stochastically-positioned point emitters. We anticipate that this
scalable and reconfigurable optical architecture will lead to systems that
could enable parallel individual programmability of large many-body atomic
systems, which is a critical step towards universal quantum computation on
such hardware.

photonic integrated circuits, lithium niobate on insulator, thin-film lithium
niobate, large-scale, multi-channel, visible modulator, silicon-vacancy,
quantum control

##  I Introduction

Figure 1:  Multi-channel optical addressing of atomic systems. Individually-
controlled optical beams are incident upon single or grouped atomic systems,
providing programmable control. a, An example spectrogram of a waveform
$\Omega_{1}$ consisting of a chirped pulse followed by a fast pulse incident
on the channel labeled “1”. Large switching bandwidth $\Delta\omega$ and,
correspondingly, small switching time $\Delta t$ are desired for flexible
spectro-temporal control. b, Numerous atomic systems—from solid state
memories, to ions, to neutral atoms—have visible wavelength transitions near
780 nm, a regime inaccessible by active photonics developed in silicon or
indium phosphide for telecommunications. We note a canonical example for each
category, including especially the negatively-charged silicon-vacancy center
in diamond which we use in Sec. V to demonstrate the capabilities of our
device.

Controlling coherent light is essential to the use and understanding of atomic
systems Wineland  _et al._ (1978); A. Ashkin and J. M. Dziedzic and J. E.
Bjorkholm and Steven Chu (1986); M. H. Anderson and J. R. Ensher and M. R.
Matthews and C. E. Wieman and E. A. Cornell (1995); Monroe  _et al._ (1995). A
number of features are desired in optical control: the application of
frequency shifting Ebadi  _et al._ (2021) or frequency-domain shaping Debroux
_et al._ (2021); Levine  _et al._ (2022); the execution of fast operations,
for instance to compensate for finite atom lifetime Bernien  _et al._ (2017);
and the precise delivery of these optical phase and amplitude profiles.
Together, these features comprise the ideal of spectro-temporal control over
an optical mode, where light is manipulated across frequency and time with
precision. The switching bandwidth of an optical modulator defines the extent
and speed at which a spectro-temporal waveform can be realized.

Large-scale programmable quantum information processing on atomic systems
requires the implementation of spectro-temporal control on individual
spatially-distributed optical modes corresponding to atomic sites Cong  _et
al._ (2022) (Fig. 1). Previous work demonstrating multi-channel atomic
addressing has largely involved extending bulk acousto-optic (AO)
technologies—limited to $\mathcal{O}(\text{GHz})$ switching bandwidth—to
multiple spatial channels, whether by mapping frequency domain signals to
spatial sites via AO deflectors Lee  _et al._ (2016); Omran  _et al._ (2019);
Kranzl  _et al._ (2022); Graham  _et al._ (2022) or by arraying many AO
modulators Debnath  _et al._ (2016); Wright  _et al._ (2019). Site count and
modulation speed for AO deflectors is currently limited by acoustic velocity
and bandwidth, especially when used in a rasterized mode, and the frequency
gradient present in AO-deflected patterns is problematic for frequency-
sensitive protocols without additional complexity Graham  _et al._ (2022).
Arrayed bulk modulators face the problem of scaling beyond the tens of
channels demonstrated and towards the thousands or more necessary to realize
fault-tolerant quantum computation Fowler  _et al._ (2012). The complexity of
assembling such devices scales with channel count, making growth by these
orders of magnitude impractical. A similar challenge led to the development of
integrated classical computing technologies which transcended the limitations
of bulk electronics via miniaturization of components and parallelization of
fabrication Moore (1975).

Likewise, integrated photonics enables scales and capabilities surpassing bulk
optics Sun  _et al._ (2013); Poulton  _et al._ (2020); Harris  _et al._
(2017); Rahim  _et al._ (2018); Kish  _et al._ (2018); Rickman (2014).
However, photonic integration at visible wavelengths has largely been passive,
in part because silicon nitride (SiN), the prevailing material for visible
photonics, does not have a strong intrinsic electro-optic effect Blumenthal
(2020). While methods to add fast active modulation to SiN or similar passive
materials have been investigated, none combine large and broadband switching
bandwidth (DC to few GHz) with small switching voltages ($<$5 V) Phare  _et
al._ (2015); Yong  _et al._ (2022); Liang  _et al._ (2021); Dong  _et al._
(2022a, b); Tian  _et al._ (2020). Low switching voltages are important for
direct compatibility with scalable high-speed complementary metal-oxide
semiconductor (CMOS) electronics operating at $\mathcal{O}(1~{}\text{V})$
Johansson and Fritzin (2014).

Figure 2:  Architecture, optical fanout, and modulator performance. a, An
incident $s$-polarization hologram produced by a Fourier-domain SLM couples to
many transverse electric (TE) waveguide modes via grating couplers (i-iii; c).
Integrated MZIs impart programmed waveforms on each channel. Output grating
couplers direct light, now $p$-polarized, back to free-space towards the
target sites (iv). For better visibility, four channels—rather than the full
sixteen—are shown in this diagram. b, A top-down view of our setup illustrates
the lenses and objectives omitted from the simplified diagram in a. The half-
waveplate in front of the objective aligns the beamsplitter and grating
polarization axes. A double-4$f$ lens configuration, with one lens
participating in both 4$f$s, enables large fields of view. White dots
represent imaging or Fourier planes. c, The $1\times 16$ input and d, the
$4\times 4$ output grating coupler arrays on our device in white light (i) and
under coherent excitation (ii), showing the WGS-generated fanout hologram (c
ii) and the resulting uniform output beams (d ii). Scalebars represent 50
$\upmu$m. e, Several iterations of WGS yield peak-to-peak optical output power
errors $\sigma_{\text{pk-pk}}$ of approximately 1% and standard deviations
$\sigma_{\text{std}}$ of approximately 0.1%. f, Wirebonding to a PCB connects
each of our sixteen channels to external control electronics. The scalebar
represents 500 $\upmu$m. g, Switching bandwidth of a modulator channel. h, A
trace of device transmission versus voltage.

Thin-film lithium niobate (TFLN) has recently risen as an excellent platform
for integrated nonlinear optics Wang  _et al._ (2018); Zhang  _et al._ (2019);
Hu  _et al._ (2021). TFLN combines large switching bandwidth and small
switching voltage, with the state of the art pushing above 100 GHz Wang  _et
al._ (2018) and below one volt Ahmed  _et al._ (2020). Moreover, lithium
niobate possesses a wide bandgap with transparency down to 350 nm, allowing
the visible-wavelength operation Desiatov  _et al._ (2019); Celik  _et al._
(2022) which is critical for addressing many atomic systems. Significant work
over the past decade has made TFLN technologically ready to reliably fabricate
large-scale circuits at wafer scales Luke  _et al._ (2020); Zhang  _et al._
(2021), enabling us to focus on the system-level considerations which we
resolve in this work: cross-channel uniformity, precision stabilization, and
reconfigurable projective mapping between modulated channels and atomic
targets.

##  II Architecture

Our photonic engine for optical quantum control consists of sixteen TFLN Mach-
Zehnder interferometers (MZIs), routed to input ($1\times 16$) and output
($4\times 4$) grating banks at one side of the chip (Figs. 2c-d). Each grating
couples a waveguide mode at 780 nm into a free-space vertical Gaussian beam.
We measure channel insertion losses of approximately 20 dB at 780 nm, which we
attribute to be dominated by grating inefficiency. Each MZI amplitude
modulator consists of two directional couplers and 3-mm-long phase shifters in
push-pull ground-signal-ground configuration. The MZIs share grounds and are
wirebonded to a printed circuit board (PCB; Fig. 2f) for electrical control.
At 780 nm, we measure CMOS-compatible switching voltages of $V_{\pi}\sim 2.2$
V, extinction ratios exceeding 20 dB, and a PCB-limited 3 dB switching
bandwidth of 7 GHz (Fig. 2g-h).

Figure 3:  Stabilizing zero-point drift. a, A camera-based feedback algorithm
monitors and corrects the optoelectronic state of all channels by repeating
measurements at four voltages. b,c, On each channel, we balance the measured
modulator transmission $\eta$ of each voltage pair ($-,+$) and thus
continuously refine alignment with the points of lowest (LO) and highest (HI)
extinction. d, Upon a hardware trigger, we lift the lock and apply desired
waveforms to the modulators to control the target systems. After completion,
we reinstate the lock. e, Integrated pulse powers from a sequence of square
pulses on one channel; 1-$\sigma$ error derived from noise analysis is
plotted. f, A time trace of the first four microseconds of the same sequence.

We use a low-bandwidth commercial liquid crystal on silicon (LCoS) spatial
light modulator (SLM) to uniformly fanout optical power to our high-bandwidth
integrated photonic channels. This SLM produces a static hologram of beamspots
coupled to the input grating couplers through the reflection port of a
polarizing beamsplitter (Figs. 2a, 2c). The orthogonal rotation of the output
gratings relative to the input gratings (Fig. 2d) couples modulated light
through the other port of the beamsplitter and towards the target atomic
systems. We monitor the output power of each channel with a camera and apply
weighted Gerchberg–Saxton (WGS) feedback Leonardo  _et al._ (2007) on the
fanout hologram to refine cross-channel output uniformity, correcting for
hologram alignment errors and variations in channel insertion loss. A dozen
iterations of WGS feedback yields uniformities better than 1% (Figs. 2d ii,
2e). While power fanout to each modulator could be accomplished monolithically
with on-chip photonics or fiber-based splitters, the $\mathcal{O}(10^{6})$
stable degrees of freedom in commercial SLMs permit a greater level of fanout
precision and reliability.

Figure 4:  Beamsteering output optical channels to target topologies. a, A
microlens pattern $\phi(x,y)$ on a SLM which is defocused by $\Delta f_{i}$ is
used to refocus incident diverging light to an output imaging plane defocused
by $\Delta f_{o}$ (dashed lines). The small zeroth-order reflection is
defocused in this imaging plane, though this can be eliminated via Fourier
domain filtering. b, Adding a steering blaze to each microlens (ii) permits
reconfiguration of the pattern, in this example from a grid (i) to a triangle
(iii). c, Our beamsteering optics positioned between the modulators (from
left) and the target (to right). d,e,f, Experimental demonstration of
reconfiguration to example patterns: (d) square (no steering), (e) hexagonal,
and (f) triangular lattices. A microlens phasemask written on the SLM (i, top)
produces each imaging domain pattern (ii, bottom). A pickoff camera on the
output path is used to capture these images, which were measured with $\Delta
f_{o}\approx\Delta f_{i}$ at a wavelength of 737 nm. Scalebars represent 200
$\upmu$m at the SLM or camera (the camera has $\sim 3\times$ magnification
relative to the SLM). Scaling the output patterns to micron-scale pitches is
achievable with a shorter focal length imaging lens, as demonstrated in Fig.
5d.

##  III Stabilization

To stabilize the electrical degree of freedom of each optical channel, we
developed a method for closed-loop parallel feedback on the sixteen arbitrary
waveform generators controlling our channels. Lithium niobate is known to be
susceptible to zero-point drift, where the voltage corresponding to the point
of highest extinction varies over time, which is attributed to fluctuations in
charges trapped in the phase shifters Jiang  _et al._ (2017); Gozzard  _et
al._ (2020); Wang  _et al._ (2021). For bulk modulators, zero-point drift is
mitigated via photodiode feedback and analog stabilization circuitry in
commercial drivers. Rather than arraying sixteen such drivers, we developed a
CPU-based scheme that is scalable even beyond hundreds of channels. Monitoring
the optical channels with the same camera used for WGS optimization, we
measure the transmission of each channel at four voltages: two pairs, each
equally spaced around estimates for the modulator’s minimum (LO) or maximum
(HI) setpoint (Fig. 3a-b). Closed-loop locking our setpoints to voltages with
balanced pairwise transmission yields alignment with the locally-quadratic
points of minimum or maximum transmission (Fig. 3c), while avoiding the
challenge of directly measuring attenuated signals (i.e. LO) with short
integration times. We operate this locking loop at about 200 Hz, much faster
than the $\mathcal{O}(\text{s})$ timescale of drift.

Desired waveforms or pulse sequences for atomic control are applied after a
hardware trigger lifts the zero-point lock (Fig. 3d). To characterize the
performance of individual channels, we map output light to a fast photodiode
and capture time traces. Representative data from periodic square pulses is
shown in Fig. 3e-f, demonstrating integrated pulse power deviations below 1%.
For optical gates applied to quantum systems, this metric of integrated pulse
power indirectly maps to phase accumulated or population driven during a gate
pulse. Repeatably achieving this performance from run-to-run is enabled by the
quality of the closed-loop lock. We observe zero-point drift on the time scale
of several seconds when monitoring the drift of the modulators in a free-
running open-loop configuration. We find that this drift is negligible on the
$\mathcal{O}(\text{ms})$ timescale of pulsesequences relevant to atomic
experiments. However, each time the closed-loop lock is lifted, we find that
trajectory of zero-point drift is repeatable depending upon initial
conditions, especially the average applied voltage in preceding seconds.

##  IV Beamsteering

Next, we spatially reconfigure the output beam array of our device, which
generally does not directly map to atomic targets. In particular, the small
array fill factor—the ratio of spot diameter to spot pitch—is not matched to
densely packed atomic sites Graham  _et al._ (2022). Furthermore, topological
mismatch and beamline aberration limit the usefulness of directly projecting
our square array of beams onto patterns of atomic systems. For instance, ion
crystals have increasingly non-uniform pitches towards their ends Debnath  _et
al._ (2016); Wright  _et al._ (2019), and artificial atoms in solids are
generally randomly distributed Sukachev  _et al._ (2017); Bersin  _et al._
(2019). Moreover, novel qubit connectivities for neutral atoms make use of
free-form arrangements of optical traps Barredo  _et al._ (2018); Ebadi  _et
al._ (2021); Singh  _et al._ (2022). Our optical control hardware achieves a
level of reconfigurability that is able to address each of these cases, using
a second LCoS SLM positioned in a defocused imaging plane.

Microlenses written to this SLM refocus the beams to an output plane (Figs.
4a-c). Changing the defocusing distance $\Delta f_{o}$ of the output plane
controls lattice fill factor, to the point of unity fill factor when the beams
are each collimated by the microlenses ($\Delta f_{o}\rightarrow\infty$; see
Methods Sec. 10 and Fig. S6). Linear phase gradients, equivalent to blazed
gratings, added to each microlens steer the beams across the output plane,
thus enabling reconfiguration of spatial spotpatterns to match desired
topologies Ebadi  _et al._ (2021) (Figs. 4d-f). The patterns are refined
through WGS feedback on the input (fanout) SLM to recover uniformity lost to
differing microlens efficiencies and other beampath distortions. We emphasize
that each beamspot in each pattern is an individually-controllable optical
degree of freedom which can be modulated with the high speed and precision
demonstrated in sections II and III.

Such a beamsteering scheme amounts to the free-form spatial reconfiguration of
many fast temporal optical degrees of freedom, with applications from
optogenetics Moreaux  _et al._ (2020) to optical ranging Zhang  _et al._
(2022) to augmented reality Xiong  _et al._ (2021). In future upgrades, the
demonstrated steering and fill factor conversion can be extended toward
shaping unique holograms on each channel for enhanced beam uniformity or
multi-site targeting Ebadi  _et al._ (2021); Cong  _et al._ (2022), as well as
three-dimensional pattern generation Barredo  _et al._ (2018). The
reconfigurability of our architecture also permits pattern healing in the case
of non-unity modulator yield, where non-functional channels can be covered by
working channels to recover defect-free topologies, albeit with fewer total
channels.

##  V Application

Figure 5:  Silicon-vacancy characterization and individual addressing.
Population statistics for 953 emitters within our field of view: a, the
frequency ($f$) distribution of the emitters, revealing two sharp spectral
populations, and b, the measured spectral linewidth distribution. See extended
data video 1 for the full three-dimensional data ($xyf$) used to produce these
plots. c, Spatial ($xy$) image of emitters resonant with $f_{0}=406.70906$ THz
excitation. We select a subset of sixteen emitters (circled) which we d,
target with our modulator channels (labeled in hexadecimal; 0-F) using e, our
beamsteering scheme, through the microlens phasemask pictured. f, Spatial
image of emitters resonant with a second color $f_{1}=406.70750$ THz. Channel
2 also has spatial overlap with an emitter at this second spectral plane. g, A
PLE fluorescence scan acquired by shifting the frequency of channel 2, showing
peaks corresponding to the two targeted emitters. h, Sections of a pulse
sequence using our multi-channel device targeting different sets of emitters:
i, analog optical waveforms imparted upon the emitters yield j, globally-
collected fluorescence. Errorbars represent 1-$\sigma$. Scalebars for c, d, f,
and h represent 5 $\upmu$m. The scalebar for e represents 200 $\upmu$m.

With channel stability and reconfigurability established, we demonstrate the
capabilities of our photonic engine using a layer of silicon-vacancy (SiV)
color centers in mono-crystalline diamond cooled to 4 K Sukachev  _et al._
(2017). To characterize this distribution of artificial atoms in space ($x$,
$y$) and spectrum ($f$), we implement parallel-readout photoluminescence
excitation (PLE) spectroscopy. Exciting in widefield and collecting on a
camera with single-emitter-level sensitivity, we scan the frequency of an
incident laser and observe PLE signal on the frequency-detuned phonon sideband
(PSB) when individual emitters are resonantly excited. This process reveals an
exceptionally narrow SiV spectral distribution for a solid-state system, with
most emitters lying within two peaks which we attribute to orientation classes
of emitters under global strain (Fig. 5a) Sutula  _et al._ (2022). We
additionally measure most emitters to have linewidths close to the lifetime
limit (Fig. 5b). Setting the laser to the center of the denser distribution at
$f_{0}=406.70906$ THz (737.11772 nm), we couple power through our modulators
and steer the output beams to match the positions of sixteen isolated single
emitters selected from the field (see Methods and Figs. 5c-e).

One of these aligned beams, channel 2, has spatial overlap with a spectrally-
detuned second emitter at $f_{1}=f_{0}+520$ MHz (Fig. 5f). Using channel 2, we
demonstrate spectral addressability on two emitters by performing single
channel PLE, made possible by the GHz-level switching bandwidth of our
integrated modulators which exceeds the narrow spread of emitter frequencies
in our sample. We set the laser to $f_{0}-4.06$ GHz and frequency shift
channel 2 by scanning a tone from 2.5 GHz to 5 GHz, observing the expected
peaks at 3.54 and 4.06 GHz corresponding to the two emitters in channel 2 at
$f_{0}$ and $f_{1}$ (Fig. 5g). In this manner, a sample with wider or
otherwise engineered inhomogeneous spectral distribution could be used to
extend the number of emitters individually-addressable within a single field
of view by a factor corresponding to the number of resolvable spectral sites
Bersin  _et al._ (2019).

In addition to spectral addressing, we implement a 5 $\upmu$s-long pulse
sequence for site-wise spatial addressing. To measure these high speeds with
efficiencies inaccessible to our camera, we couple the output emission to a
free-space avalanche photodiode (APD), to map the sixteen emission spots to
the active area of this detector. The pulse sequence consists of three
sections, each with sixteen pulses on a 100 ns period, demonstrating important
concepts in multi-channel quantum optical control: (1) individual emitter
addressing, (2) simultaneous addressing of multiple emitters—for example,
towards pairwise entanglement generation—and (3) analog tuning of the state of
the modulators. Figs. 5h-j contains results from channels 0 through 2 and
pairs 0-1 through 2-3. More information is displayed in Methods.

##  VI Discussion

We have proposed and realized an architecture for scalable visible-wavelength
optical programming, capable of high-speed control of many optical modes, each
mode reconfigurable spatially and programmable across frequency and time.
Although this work has focused on the control of optical excitation, we
emphasize the importance of collection optics which could also benefit from
photonic integration. Collection and manipulation of single photons emitted
from atomic systems could facilitate on-demand entanglement generation between
targeted pairs of emitters or the construction of many-body nonclassical
photonic states. These collection schemes might take the form of spatial and
spectral modulation of light collected into integrated waveguides Wan  _et
al._ (2020) or free-space beamshaping, i.e. reciprocal to the integrated
modulation and free-form beamsteering demonstrated on excitation light in this
work.

Going forward, we see a number of paths to improve performance beyond these
first-iteration designs. For instance, grating efficiency will improve as
design and fabrication matures, as realized in wafer-scale silicon photonics
Vaerenbergh  _et al._ (2021). Device extinction ratio, important for high
fidelity quantum control, is likely limited by differences in splitting ratio
between the two directional couplers which make up each MZI. Avenues for
improving extinction include optimizing coupler parameters and topology for
increased tolerance to fabrication imperfections, or tuning couplers to
recover performance. At the cost of additional complexity, multiple MZIs could
be cascaded per channel to reach exponentially-higher levels of extinction.
The compactness of current uncladded devices is constrained by a single in-
plane layer of metal, which forces waveguides to be routed around large
wirebond pads. An additional out-of-plane layer of metal will allow us to
approach closer to the limit of TFLN MZI compactness and realize substantially
more channels. While the footprint of these millimeters-long MZIs is much
larger than that of resonant devices Liang  _et al._ (2021), channel count is
ultimately limited by the length of a chip’s perimeter in wirebonded control
architectures, as the number of bondable electrical pads scales with
perimeter.

Immediate scalability is an especially salient feature of these methods and
this platform, enabled by integrated fabrication and switching voltages which
can be directly synthesized by high-speed CMOS electronics. To this end, the
methods described in this work were investigated using dimensions compatible
with much larger channel counts. For instance, only a fraction of available
camera or beamsteering SLM area was used for the express purpose of field-
testing focal lengths, image sizes, and superpixel dimensions suitable for
operation with hundreds of channels. In this manner, we anticipate that these
advances in scalable optics will enable general quantum computation on the
hundreds of coherent memories demonstrated in arrays of atomic systems Wan
_et al._ (2020); Ebadi  _et al._ (2021).

Figure S1:  Setup diagram, summarizing components detailed in the main text
along with Methods sections 1 and 13.

## Methods

Figure S2:  Chip fabrication, following steps detailed in Methods Sec. 2.

###  1 Modulator Setup

Fig. S1 summarizes our optical setup. We collimate light from a polarization-
maintaining fiber (Thorlabs PM780-HP) to a free-space beam with cm-scale
diameter (Thorlabs ASL10142M-B; 79 mm asphere). White light (Thorlabs MWWHF2)
is flipped into the path for diagnostic images. The beam reflects off of the
fanout SLM (SLM1; Thorlabs Exulus-HD3). The plane of the SLM is scaled and
mapped to the back aperture of the main objective (Zeiss Plan-NeoFluar,
10$\times$, .3 NA) via a 4$f$ (250 mm and 100 mm achromats), passing through
the $s$ port of a polarizing beamsplitter (PBS; Thorlabs PBS252). The hologram
produced at the plane of the chip by SLM1 couples through each modulator
channel and out the $p$ port of the PBS. A second 4$f$ (100 mm achromats),
which shares a 100 mm lens with the first 4$f$, couples light to an
intermediate Fourier plane. From there, the light is partially reflected to a
first pickoff camera (CAM1; Thorlabs Quantalux; 75 mm imaging achromat) to
monitor the state of our channels. The remaining light propagates further to
the beamshaping setup. The beamshaping SLM (SLM2; Santec SLM-200-01-0002-02)
is positioned at a defocused imaging plane between two lenses (150 mm
achromat). A second pickoff camera (CAM2; Thorlabs Zelux; 50 mm imaging
achromat) monitors the state of beamshaping. From there, the light propagates
to the cryostat setup described in Methods Sec. 13.

This setup, including the modulators and beamshaping optics, are controlled by
a computer (PC1) with Python code. Experiments that do not include color
center addressing are controlled directly from this computer. 737 nm light is
sourced from a Ti:Saph laser (MSquared SolsTiS) stabilized with a wavemeter
(HighFinesse WS7; accuracy 60 GHz, precision 2 MHz). For data taken at 780 nm,
we use an external cavity diode laser (New Focus Velocity TLB-6712). Each
modulator is connected to an arbitrary waveform generator (AWG) channel
sourced from four 4-channel cards (4 $\times$ Spectrum Instruments
M2p.6566-x4, 16-bit, 125 Ms/s, 70 MHz). For frequency shifting experiments, a
faster AWG with only two channels (Tektronix AWG70002A, 25 Gs/s, 10 GHz) is
used with a broadband amplifier (Centellax OA4MVM) to produce chirped sweeps.
Fast visible-wavelength photodiodes are used for high-speed measurements: for
time traces (Melno Systems FPD510, 200 MHz) and bandwidth measurements
(Newport 818-BB-45AF, 10 GHz). An oscilloscope (Agilent Infiniium DSO81004A,
10 GHz, 40 Gs/s) and a microwave vector network analyzer (Keysight N5224A PNA,
10 MHz to 43.5 GHz) are used to record signal from these photodiodes.

###  2 Chip Fabrication

Our chip was fabricated using a pre-commercial multi-project wafer (MPW)
foundry service by CSEM. The fabrication process flow begins with thinning
down a $x$-cut lithium niobate on insulator (LNOI) thin film (NanoLN) from 600
nm thickness to 200 nm using blanket etching (Fig. S2a-b). The 200 nm
thickness is optimized for performance at wavelengths around 780 nm. The
resulting 200 nm LNOI thin-film is patterned using a HSQ mask via electron-
beam lithography and etched a further 100 nm to yield low-loss optical TFLN
waveguides with a sidewall slant approximately 30 degrees from normal (Fig.
S2c). For active electro-optic structures, 500 nm gold electrodes are
patterned via liftoff (Fig. S2d). We use 400 nm wide traces as standard single
mode routing waveguides. These are tapered out slightly to 500 nm inside the
phase shifters to reduce propagation loss. Phase shifters use a 3 $\upmu$m gap
between electrodes. Waveguides are tapered down to 200 nm in directional
couplers to increase the mode overlap between the two directional coupler
arms.

Figure S3:  Chip images. a, Our 5 mm $\times$ 5 mm chip imaged on top of a
dime for scale and b, under an optical microscope. c, Zoom upon the grating
coupling region.

###  3 Chip Layout

The photonic engine architecture described in the main text is fabricated on a
5 mm $\times$ 5 mm chip, consisting of a bank of sixteen MZIs with cross ports
routed to banks of input and output grating couplers (Fig. S3). The opposing
two cross ports of each $2\times 2$ MZI are routed to edge couplers via
waveguides threaded inbetween the grating waveguides. Our system could be
operated with these edge couplers instead of the grating couplers. In fact,
our packaging was designed with this feature in mind, where the design of the
chassis is compatible with a 90 degree rotation to expose the edge facet to
objective imaging (Fig. S4a-c). Edge-coupled operation is expected to perform
with efficiencies closer to 2 dB channel insertion loss, given compatible
optics and appropriate mode-matching. However, in this work, we chose to focus
on grating-coupled operation because of the greater generality of a two-
dimensional grating-based architecture, especially with respect to arbitrary
pattern generation and scalability. Nevertheless, quantum systems with 1D
topologies, such as linear ion crystals, are likely well suited to edge-
coupled operation.

Figure S4:  Chip packaging. a,b, The top and bottom of our chassis before chip
placement. The chip sits at the center of copper beam in a. c, A wirebonded
chip positioned in front of the objective. d, Zoom upon an array of wirebonds.

###  4 Chip Packaging

The chip is glued with thermal epoxy (Arctic Silver) to a custom copper mount.
The copper mount is secured to custom aluminum parts, insulated with a layer
of kapton tape and using teflon screws to enhance thermal isolation. The
copper mount is thermally stabilized with a thermoelectric cooler and
temperature controller (Arroyo 5300 series). The aluminum parts act as a
mounting plate and support structure for custom FR4 PCBs which interpose
sixteen SMA ports with the ground-signal-ground wirebond pads used to
interface with our chip. Together, these elements make up the chassis (Fig.
S4a-b). Chip and PCB pads are connected manually with a gold ball wirebonder
with unity yield (Fig. S4c) allowing operation of every modulator. Our
bandwidth is likely limited by the roughly 50 mm long traces on our lossy FR4
PCB, along with contributions from wirebond length and compactness.

Figure S5:  SLM amplitude distributions. The measured source amplitude
distributions on the fanout SLM a, for 780 nm and b, for 737 nm.

###  5 Fanout Wavefront Calibration

The generation of diffraction-limited holograms depends on accurate
characterization and compensation of beampath aberrations. We automatically
measure the source laser’s phase and amplitude distributions at the plane of
the SLM via imaging domain interference of light diffracted from SLM
superpixel clusters Čižmár  _et al._ (2010). Gerchberg–Saxton (GS) -type
algorithms use the amplitude distribution when numerically generating phase
profiles, enabling greater holographic accuracy. We find that the amplitude
distribution becomes significantly clipped as the reference position
approaches the edge of the field of view. To compensate for this, we
purposefully overclip the SLM with an iris such that the amplitude
distribution is equally clipped regardless of the reference position (clipping
oval from the iris is visible on the amplitude distribution pictured in Fig.
S5a). This allows us to generate more accurate holograms across the region
near the edge of the field of view where the input grating array is located.

###  6 Grating Design, Coupling, and Efficiency

The grating couplers are designed to couple light from a single mode waveguide
to a vertical Gaussian beam with .12 numerical aperture (NA) at 780 nm.
Vertical coupling is important to remain within the NA of the normally-
incident objective. In the longitudinal direction—in the direction of
propagation of the waveguide—we make use of gradient-based optimization Su
_et al._ (2018). In the transverse direction, we use analytic assumptions of
Gaussian phasefronts to shape the focus to that of the longitudinal direction.
We measure a slight ellipticity to the beam in waist and focus, corresponding
to mismatch between the transverse and longitudinal directions, though this is
compensated with the beamshaping microlenses. Metal guards (visible as U
shapes in Fig. 2di) are fabricated around the output gratings with the intent
of reducing crosstalk scatter to neighboring outputs.

We engineered degrees of freedom in our setup to account for deviations from
vertical grating coupling. The mirror on the excitation path immediately
before the polarizing beamsplitter is designed to be near an imaging plane
(see white dot), such that changing the angle of this mirror directly tunes
the angle of excitation at the sample’s imaging plane to optimally couple the
hologram into the gratings. At 780 nm, we find that the optimal angle of
excitation is close to normal and measure roughly 20 dB device insertion loss.
At 737 nm, we measure closer to 40 dB device insertion loss. We attribute this
additionally loss to a non-vertical grating coupling angle at this non-design
wavelength, finding evidence in the wavefront calibration for 737 nm, where
the angle producing optimal coupling also causes significant amplitude
distribution clipping (Fig. S5b). We interpret this as clipping on the edge of
the objective’s NA. More broadband gratings or gratings targeting 737 nm could
be fabricated to avoid loss at this wavelength.

Figure S6:  Microlens fill factor conversion. The influence of a variety of
$\Delta f_{o}$ upon the fill factor $\eta_{o}$ of the output beam: a, $\Delta
f_{o}=.5\Delta f_{i}$, b, $\Delta f_{o}=\Delta f_{i}$, c, $\Delta
f_{o}=1.5\Delta f_{i}$, and d, collimated output.  Figure S7:  Microlens
steering range. Lens efficiency $\eta$ versus normalized steering range $R$
for twelve channels with $\Delta f_{o}\approx\Delta f_{i}$. The $x$ and $y$
axes are normalized to the channel pitch $\Gamma$. Contours denote 80%
efficiency.

###  7 Imaging Domain Calibration

We locate the positions of input and output gratings in imaging domain
$x$-space manually using a reference image previously taken with white light.
The positions of the output gratings are used to center pixel integration
regions about each output spot, which we use to determine the output power of
each channel. We also calibrate the coordinate transform between SLM $k$-space
and the imaging domain of the chip. This amounts to generating a grid pattern
on the SLM and fitting the result to an affine transformation.

###  8 Fanout Hologram Generation

For this section, a sawtooth electrical signal with peak-to-peak amplitude of
$2V_{\pi}$ at a frequency of 100 cycles per camera frame is applied to every
modulator. This tone averages out fluctuations in device transmission due to
the electrical degree of freedom, and isolates the problem of optimizing
fanout coupling. The inverse of the calibration coordinate transformation and
$x$-space input grating positions found in Sec. 7 are used to target positions
in SLM $k$-space during GS fanout hologram optimization. This first guess
hologram is rarely perfectly aligned, which we attribute to chromatic
aberration between the white light image and the target wavelength along with
imperfections in our coordinate transform fitting. To correct for this
mismatch between guess and true $k$-vectors, we add a global steering blaze to
the SLM and scan the position of the hologram across the gratings, measuring
the coupling through the output gratings via camera readout. We iteratively
correct the $k$-vector guess for each channel by adding the blaze $k$-vector
that produced maximal coupling in the previous iteration. Four iterations
yield alignment below measurement noise.

With the $k$-space map corrected, we use WGS to compensate for remaining
pointing or device transmission errors. For the data presented in this work,
we optimize the uniformity of integrated spot power, though other figures of
merit such as spot amplitude uniformity are equally applicable for weighted
optimization. We believe that current uniformity is limited by small
mechanical vibrations between the objective and chip causing pointing errors
between the fanout hologram and input gratings. This effect can be mitigated
in future iterations by directly securing the objective to the chassis that
supports the chip, rather than separately securing them upon the same optical
breadboard. Without any optical feedback or temperature stabilization, our
system and holograms remain stable to within 10% of baseline coupling over the
course of 24 hours.

Figure S8:  Channel-emitter alignment. a, Composite blaze scans from each
microlens (colored by hue) are used to select an isolated emitter at a target
camera pixel for each channel (0-F). Scalebar represents 5 $\upmu$m. b, After
optimization in $x$, $y$, and focus, blaze scans collecting on the target
pixel show centered flourescence. The $x$ and $y$ axes use units of blaze
angle at the beamsteering SLM in milliradians.

###  9 Closed-Loop Zero-Point Stabilization

We preload the four-voltage locking sequence and desired pulse sequence to the
AWGs. The camera used to measure the state of each modulator at these voltages
is triggered via a digital AWG line to maintain synchronization. Updates to
setpoints are applied to the “amplitude” and “offset” voltage parameters of
the AWGs, which scale the unitless digital waveforms loaded to memory,
avoiding time-consuming waveform memory rewriting. We prioritize (via CPU-
based analysis) updating channels that have the largest absolute error between
the current setpoint and the measured target value, as updating these
parameters is still slow (to the point that we can only update two parameters
per camera frame). Hardware without such update latency limitations can be
used to eliminate this issue.

###  10 Microlens Fill Factor Conversion

We define the fill factors $\eta_{i}$ and $\eta_{o}$ of the input and output
beams as the ratios between the $1/e^{2}$ beamdiameters $2w_{i}$ and $2w_{o}$
and pitch $\Gamma$ of spots. For filled microlenses ($2w(z)=2w(\Delta
f)=\Gamma$) and an approximately diffraction-limited system, we estimate the
defocusing distances $\Delta f_{i|o}$ between the SLM and the input and output
planes to follow the relation:

$\displaystyle\Gamma=2w_{i|o}\sqrt{1+\left(\frac{\Delta f_{i|o}\lambda}{\pi
w_{i|o}^{2}}\right)^{2}},$ (1)

where $z_{R}^{i|o}=\pi w_{i|o}^{2}/\lambda$ is the Rayleigh range. While the
input defocusing distance $\Delta f_{i}$ is fixed by the choice of pitch
$\Gamma$ and the fill factor $\eta_{i}$ of our system, we can engineer $\Delta
f_{o}$ to target a desired $\eta_{o}$ (Fig. S6) according to:

$\displaystyle\Delta f_{o}(\eta_{o})$
$\displaystyle=\frac{\pi}{4}\frac{\Gamma^{2}\eta_{o}}{\lambda}\sqrt{1-\eta_{o}^{2}}.$
(2)

Unity fill factor can be achieved when the output beams are collimated (Fig.
S6d).

###  11 Microlens Steering Range

There are two main factors that limit steering range: (i) the SLM’s
diffraction efficiency versus steered angle, and (ii) the extent at which
steering can be realized through high magnification objectives.

For commercial LCoS SLMs, diffraction efficiency degrades as target blaze
gradients approach the point where they can no longer be resolved by finite
pixel size. The half-angular SLM steering bandwidth
$\theta_{\text{max}}^{\text{diff}}$ is usually on the order of two degrees
(the Bragg condition at 780 nm for a sawtooth blaze with a pitch of three 8
$\upmu$m pixels).

Steering angles in the domain of the SLM are mapped to angles at the domain of
the target, multiplied by a factor corresponding to the objective magnifcation
$M$. For the high ($M\sim 50\times$) objectives found in atomics experiments
and given an appropriate imaging lens, a steering angle of two degrees at the
SLM will not propagate through the objective as $M\times
2^{\circ}=100^{\circ}>90^{\circ}$ exceeds the NA of free-space. A shallower
angle may also clip upon the NA of the objective, bounded by
$\theta_{\text{max}}^{\text{obj}}=\theta_{\text{NA}}/M$. This limit could be
completely negated with a third SLM used to reorient the angle of the beams to
vertical incidence after they are spatially steered by the second SLM.

These bounds on steering angle pose a limit on $r$, the steering range, and
$R$, the steering range normalized to pitch $\Gamma$:

$\displaystyle R=\frac{r}{\Gamma}<\frac{\theta_{\text{max}}\Delta
f_{o}}{\Gamma}=\theta_{\text{max}}\frac{\pi}{4}\frac{\Gamma\eta_{0}}{\lambda}\sqrt{1-\eta_{0}^{2}}.$
(3)

In our system, with $\Gamma\sim.65$ mm and $\lambda\sim 780$ nm and using
$\theta_{\text{max}}=\theta_{\text{max}}^{\text{diff}}$, this evaluates to
roughly $R\sim 20\eta_{o}$. For small $\eta_{i|o}$, the phase gradient of the
parabolic focusing phase can also be large enough to locally exceed
$\theta_{\text{max}}^{\text{diff}}$ on the edges of the lens, limiting $R$
further. For the data presented in Fig. 4, we use $\eta_{o}\sim.05$. We
separately measure $R$ for this $\eta_{o}$, finding that steering within
$R\sim 1$ maintains efficiencies over 80%, in agreement with $R\sim
20\eta_{0}$ (Fig. S7).

Though we operate the beamshaping SLM at a roughly five degree reflection
angle, this does not mitigate performance. That is, focal detunings resulting
from this slant (e.g. at the edges of the microlens grid) do not exceed the
Rayleigh length of the beams, for the input and output parameters which we
consider. Aberrations from these small focal detunings are corrected on a
microlens-by-microlens basis via automated routines.

###  12 Microlens Pattern Generation

For the topologies displayed in Figure 4, we automatically steer beams to a
target pattern defined in the beamshaping camera’s (CAM2’s) basis. Channels
are matched to target points by framing the task as a linear sum assignment
problem. Using knowledge of the focal lengths and defocusing distances, we
analytically calculate and apply the blaze necessary to steer each channel to
the target position. Measuring the positional error between the steered
position and the target, we iteratively apply this process until the channels
are sufficiently aligned. Four iterations yield satisfactory alignment.

Figure S9:  Electrical breakdown damage. a, Overview and b, zoom upon
modulator charring and delamination which we attribute to an AWG over-voltage
state.  Figure S10:  Spatial Addressing Data. a, Target pulse sequence on
sixteen channels. Color represents channel amplitude for a given channel at a
given time. b, Pulse sequence with our truncated channel count. c, Expected
signal (red) as the sum of all globally-collected channels, compared with the
measured fluorescence (blue).

###  13 Cryostat Setup

Fig. S1 summarizes our optical setup. Modulated and beamshaped light passes
through a 4$f$ (300 mm achromats) from our modulator setup, passing through a
cleanup filter (ZPL BP; Semrock BrightLine 740/13). This merges with the
excitation path of our cryostat setup with a removable 50:50 pellicle
beamsplitter (Thorlabs BP145B2). Galvos normally used for scanning confocal
microscopy are used in this work for fine adjustments. These galvos are mapped
by a 4$f$ (200 mm achromats) to the back aperture of a cryo-optic objective
(Zeiss 100$\times$, .95 NA) inside a 4K cryostat (Montana Instruments
Cyrostation s50). Our diamond sample is positioned under the objective with
peizo slip stick stages (Attocube). Emission light is collected back through
the same path, to the other port of the pellicle. Excitation light is filtered
out, leaving the phonon sideband (PSB BP; Semrock Brightline 775/46). From
there, we collect on either a electron-multiplying charge-coupled-device
(EMCCD) camera (CAM3; Photometrics Cascade 1K; 100 mm imaging achromat) or to
an avalanche photodiode (APD; Excelitas Technologies SPCM-AQRH-14) with time-
tagged signal (Swabian Instruments Time Tagger 20). For widefield
characterization data collected with the camera, we remove the pellicle and
use a separate excitation port input on the 10 side of a 90:10 beamsplitter.
For this port, light is focused at the galvos (100 mm lens singlet), and
thus—via the 4$f$—focused at the back aperture of the objective. This focused
beam in the Fourier domain of the objective maps to a widefield beam in the
imaging domain. A beam expander (-35 mm singlet, 100 mm singlet) increases the
NA of the beam at the back aperture to fill the field of view in the imaging
domain. A compact noise eater (Thorlabs NEL03A) is used to stabilize power
fluctuations occurring during laser wavelength sweeping. Diamond experiments
are controlled from a computer (PC2) which interfaces with the modulator
computer (PC1) via an ethernet (TCP) link. A mixture of MATLAB and Python code
is used for these experiments.

###  14 Silicon-Vacancy Sample

Our diamond sample was produced by chemical vapor deposition (CVD) overgrowth
on a low-strain mono-crystalline substrate (New Diamond Technologies). Silicon
is incorporated during the CVD process, yielding SiV color centers in the
overgrown layer. CVD overgrowth has previously been shown to generate narrow
SiV inhomogeneous distributions similar to what we observe in this sample
Rogers  _et al._ (2014); Sipahigil  _et al._ (2014). Following overgrowth, the
sample was cleaned by boiling in a 1:1:1 mixture of nitric, sulfuric, and
perchloric acids for 1 hour Chu  _et al._ (2014), cleaned in a 3:1 sulfuric
acid:hydrogen peroxide piranha solution for 5 minutes, rinsed in a solvent
bath, and annealed at 1200∘C in ultra-high vacuum. To remove any graphite
formed during annealing, the sample was again cleaned in tri-acid and piranha
using the same processes.

###  15 Channel-Emitter Alignment

We adopt techniques from scanning microscopy, and use each microlens to scan
each channel over a region of diamond (Fig. S8a). For each channel, we select
a point in each scan corresponding to an isolated emitter. Then, we
iteratively optimize the blaze and focus of each microlens, maximizing camera
signal corresponding to the chosen isolated emitter (Fig. S8b).

###  16 Electrical Breakdown Damage

After aligning our modulator channels to a set of sixteen SiV emitters, we
proceeded to begin gathering final fluorescence data. Despite working
consistently for months beforehand, nine of our channels stopped coupling
light during this acquisition (channels 4 through B and channels E through F).
We attribute this channel loss event to an untimely Windows Update producing
an over-voltage state on the PCIe AWG cards which were active at the time,
thus exceeding the electrical breakdown field of the air gap between the
uncladded electrodes. Resulting sparking across the gap accounts for the
delaminated electrodes and charred waveguides which we observe on afflicted
channels (Fig. S9). As a result, the spatial addressing demonstration detailed
in Fig. 5 uses only the remaining modulator channels.

Breakdown can be nucleated by small sharp features which locally enhance
electric field Slade and Taylor (2002). The stochastic presence of such sharp
features on each channel is a potential cause of the partial, rather than
complete, destruction of our channels. Future work using a silicon dioxide
Austen and Whitehead (1940) cladding will eliminate this problem as lithium
niobate Luennemann  _et al._ (2003), a stronger dielectric than air by more
than an order of magnitude davies  _et al._ (1965), becomes the limiting
material for electrical breakdown. While this comparison is not strictly valid
over the relevant electrodes gap sizes—due to differing breakdown mechanisms
between solids and gasses along the with raised breakdown thresholds for small
gaps Slade and Taylor (2002)—the cited works illustrate the relative trends
for these materials. In cases where cladding is impractical, external
overvoltage protection or alternative electronics could be used to prevent
damage should a power outage or automated update occur.

###  17 Spectral and Spatial Addressing

The spectral plot Fig. 5g is acquired by chirping channel 2 at a frequency
$\delta f$ using our 25 Gs/s AWG and collecting signal on our EMCCD camera.
Error is estimated from Poisson statistics. Data is acquired with at 10 MHz
steps, then binned to 20 MHz steps for visibility. The choice of our sweep
from 2.5 to 5 GHz stays within the bandwidth of our AWG and amplifier while
avoiding spurious signal from higher order sidebands ($2\delta f$).

Our pulse sequence, as described in the main text, consists of a series of 80
ns pulses inside 100 ns bins. Fig. 5h illusrates the spatial state of our
modulators with camera images corresponding to a set of pulses, though these
images are integrated for 5 seconds, instead of the 80 ns in the pulse
sequence. Fig. 5j was collected via repeating our pulse sequence over 20
minutes of integration. Error is estimated from Poisson statistics. The
risetime slopes on Fig. 5i-j represent transitions from setpoint to setpoint
of our 125 MS/s AWGs (8 ns per setpoint). This risetime is nevertheless
competitive with commercial AOMs.

##  Acknowledgments

The authors thank Mikkel Heuck, Franco Wong, Artur Hermans, Alex Sludds,
Saumil Bandyopadhyay, Matthew Trusheim, Eric Bersin, Kevin Chen, Marco
Colangelo, Sara Mouradian, Xingyu Zhang, Nathan Gemelke, Noel Wan, Frédéric
Peyskens, Dongyuu Kim, Alex Lukin, Sepehr Ebadi, Dolev Bluvstein, David Lewis,
and Paul Gaudette for enlightening discussions.

## Declarations

### Funding

I.C. acknowledges support from the National Defense Science and Engineering
Graduate Fellowship Program and the National Science Foundation (NSF) award
DMR-1747426. M.S. acknowledges support from the NASA Space Technology Graduate
Research Fellowship Program and the NSF Center for Integrated Quantum
Materials. T.P. acknowledges support from the NSF Graduate Research Fellowship
Program and the MIT Jacobs Presidential Fellowship. C.P. acknowledges support
from the Hertz Foundation Elizabeth and Stephen Fantone Family Fellowship.
A.J.M. acknowledges support from the Feodor Lynen Research Fellowship, the
Humboldt Foundation, the MITRE Moonshot program, and the DARPA ONISQ program.
This material is based upon work supported by the Air Force Office of
Scientific Research under award number FA9550-20-1-0105, supervised by Dr.
Gernot Pomrenke. Lithium niobate fabrication at the CSEM was supported by the
European Union’s Horizon 2020 research and innovation programme under grant
agreement No. 101016138. Distribution Statement A. Approved for public
release. Distribution is unlimited. This material 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 authors and do not necessarily
reflect the views of the National Reconnaissance Office. ©2022 Massachusetts
Institute of Technology. Delivered to the U.S. Government with Unlimited
Rights, as defined in DFARS Part 252.227-7013 or 7014 (Feb 2014).
Notwithstanding any copyright notice, U.S. Government rights in this work are
defined by DFARS 252.227-7013 or DFARS 252.227-7014 as detailed above. Use of
this work other than as specifically authorized by the U.S. Government may
violate any copyrights that exist in this work.

### Competing Interests

D.E. is a scientific advisor to and holds shares in QuEra Computing. The CSEM
offers lithium-niobate-on-insulator-related design, fabrication, testing, and
integration services.

### Availability of data and materials

Available on request to I.C.

### Code availability

Available on request to I.C. SLM-related routines will be public on GitHub
under the `slmsuite` package.

### Authors’ contributions

I.C., A.J.M., and D.E. conceived the experiments. I.C. designed systems,
performed experiments, analyzed the data, and wrote the manuscript with
assistance from T.P. and C.P. (software) along with M.S. and A.J.M.
(experimental). H.S., G.C., and A.G. fabricated TFLN devices. M.S.
characterized the diamond sample produced by A.M., J.M., S.H., P.B.D., and
D.B. D.E. and A.G. supervised the project. All authors discussed the results
and contributed to the manuscript.

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