# Expanding the Quantum Photonic Toolbox in AlGaAsOI

J. E. Castro  Electrical and Computer Engineering Department, University of
California, Santa Barbara, CA 93106  T. J. Steiner  Materials Department,
University of California, Santa Barbara, CA 93106  L. Thiel  Electrical and
Computer Engineering Department, University of California, Santa Barbara, CA
93106  A. Dinkelacker  Electrical and Computer Engineering Department,
University of California, Santa Barbara, CA 93106  C. McDonald  Electrical and
Computer Engineering Department, University of California, Santa Barbara, CA
93106  P. Pintus  Electrical and Computer Engineering Department, University
of California, Santa Barbara, CA 93106  L. Chang  Electrical and Computer
Engineering Department, University of California, Santa Barbara, CA 93106  J.
E. Bowers  Electrical and Computer Engineering Department, University of
California, Santa Barbara, CA 93106  Materials Department, University of
California, Santa Barbara, CA 93106  G. Moody  Electrical and Computer
Engineering Department, University of California, Santa Barbara, CA 93106
<EMAIL_ADDRESS>
###### Abstract

Aluminum gallium arsenide-on-insulator (AlGaAsOI) exhibits large
$\chi^{\left(2\right)}$ and $\chi^{\left(3\right)}$ optical nonlinearities, a
wide tunable bandgap, low waveguide propagation loss, and a large thermo-optic
coefficient, making it an exciting platform for integrated quantum photonics.
With ultrabright sources of quantum light established in AlGaAsOI, the next
step is to develop the critical building blocks for chip-scale quantum
photonic circuits. Here we expand the quantum photonic toolbox for AlGaAsOI by
demonstrating edge couplers, 3-dB splitters, tunable interferometers, and
waveguide crossings with performance comparable to or exceeding silicon and
silicon-nitride quantum photonic platforms. As a demonstration, we demultiplex
photonic qubits through an unbalanced interferometer, paving the route toward
ultra-efficient and high-rate chip-scale demonstrations of photonic quantum
computation and information applications.

††preprint: AIP/123-QED

##  I Introduction

Photonic integrated circuits (PICs) have already shown promise as platforms
for quantum informationMoody  _et al._ (2020); Vigliar  _et al._ (2021);
Llewellyn  _et al._ (2019); Arrazola  _et al._ (2021); Zhao  _et al._ (2020a);
Wang  _et al._ (2018). However, development of PICs for problems of interest
in fields such as communication, computing, sensing, and metrology will
require circuits with both scale and functional complexity well beyond even
the most mature of quantum PICs (QPICs). QPIC functionality of any complexity
relies on a small set of components for on-chip manipulation of quantum states
of light, including active modulators and switches as well as passive routing
components, beamsplitters, and on/off chip couplers Moody  _et al._ (2022).
The largest demonstrations to date using these components and on-chip photon
sources have been realized on siliconVigliar  _et al._ (2021); Ma  _et al._
(2017), whose swift progress as a quantum photonic platform has benefited from
its prominence in classical photonics and the complementary metal oxide
semiconductor (CMOS) industry. Other demonstrations include material platforms
such as silicon nitrideZhao  _et al._ (2020a); Jaramillo-Villegas  _et al._
(2017), aluminum nitrideGuo  _et al._ (2016), lithium niobateZhao  _et al._
(2020b); Boes  _et al._ (2018), and indium phosphideKumar  _et al._ (2019);
however, no single platform clearly wins out on performance across all
metrics, including material absorption, waveguide propagation loss,
$\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities, and thermo-optic coefficients
for tuning and modulation. Recent improvements in fabrication have opened the
possibility of alternative materials with better suitability towards specific
functionalities than silicon, such as the aluminum gallium arsenide-on-
insulator (AlGaAsOI) platformXie  _et al._ (2020).

As a QPIC platform, AlGaAsOI is attractive for its large $\chi^{(2)}$ and
$\chi^{(3)}$ nonlinear coefficients, which enable more efficient spontaneous
parametric down conversion (SPDC) and spontaneous four wave mixing (SFWM) than
silicon, strong modal confinement due to its large refractive indexOttaviano
_et al._ (2016), a thermo-optic coefficient comparable to silicon for
efficient tuningKomma  _et al._ (2012); Cocorullo, Corte, and Rendina (1999);
Corte  _et al._ (2000), and electro-opticWalker  _et al._ (2019) and piezo-
opticForsch  _et al._ (2020) effects for cryogenic tuning. Additionally,
varying the aluminum content of AlGaAs enables bandgap engineering such that
two-photon absorption, a major challenge in silicon QPICs, is minimal at
telecommunication wavelengthsAdachi (1994). Until quite recently, the utility
of the AlGaAsOI platform has been restricted by high waveguide propagation
lossMariani  _et al._ (2014). Improvements in the fabrication process Xie  _et
al._ (2020) have reduced propagation losses to less than 0.2 dB/cm, enabling
demonstrations of microring resonators with quality factors above 3 $\times
10^{6}$. In combination with low material absorption and a large $\chi^{(3)}$
nonlinear coefficient, this has led to record-low Kerr comb generation
threshold powers and entangled photon pair sources 1000 times brighter than
state-of-the-art in siliconChang  _et al._ (2020); Steiner  _et al._ (2021).

Figure 1:  Illustrative example of a programmable QPIC for on-chip optical
computing and communications, shown here as a generic m-mode unitary operator
for Boson sampling. A general platform comprises: (i) tunable microring
resonators or waveguides for quantum light generation; (ii) tunable unbalanced
Mach-Zehnder interferometers for filters and qubit demultiplexers; (iii)
waveguide crossings for connecting non-nearest neighboring qubits; and (iv)
tunable balanced Mach-Zehnder interferometers for linear optical programming.

Because of its novelty, the AlGaAs platform has lacked the same level of
individual circuit component development as more established platforms
including silicon and silicon nitride. Here, we report on high-performance
AlGaAsOI components including edge couplers, waveguide crossings, and tunable
interferometers that, along with previously demonstrated ring resonator
sources, form the foundation of a functional on-chip platform with potential
not only in QPICs but classical PICs as well, including applications in
optical communications and spectroscopyGaeta, Lipson, and Kippenberg (2019);
Kippenberg  _et al._ (2018); Spencer  _et al._ (2018). Interferometers serve
many purposes for on-chip optical quantum computing schemes including pump
filtering, demultiplexing distinct frequency modes, acting as beamsplitters,
and serving as linear optical quantum gates. Following the protocol proposed
by Knill, Laflamme, and Milburn Knill, Laflamme, and Milburn (2001), scalable
linear optical computing can be realized using only linear optical
interferometers (reported here), single photon sources (shown in our previous
manuscript Steiner  _et al._ (2021)), and single-photon detectors (available
commercially and also on-chipMcDonald  _et al._ (2019)). Thus, with the design
of high quality interferometers and low-loss chip-to-fiber couplers, the
necessary components for many linear optical quantum computing protocols have
been established. The other component discussed here–waveguide
crossings–enables more complex circuit design where interactions between non-
next nearest-neighbor qubits is necessary. Since the circuit elements are all
fabricated using the same photonic layer, the routing requires waveguide
crossings with minimal loss and crosstalk to adjacent channels. The
development of these components opens the door for demonstrations of chip-
scale QPICs using the AlGaAsOI platform, leveraging the benefits that AlGaAs
offers over silicon and other nonlinear optical platformsChang  _et al._
(2022). The components described below are designed assuming eventual full
integration with AlGaAsOI ring resonator entangled-photon pair sources
optimized for $\chi^{(3)}$ spontaneous four-wave mixing like that detailed in
Ref. [(24)]. As an example, Fig. 1 shows a quantum photonic circuit for chip-
scale Boson sampling to illustrate the opportunities that the development of
interferometers and waveguide crossings can enable. The individual components
are highlighted where they may reside in complex quantum photonic circuitry.
In the remainder of this manuscript, we describe the design, simulation, and
experimental results of many of the fundamental components to develop a
quantum photonic platform.

##  II Quantum Photonic Toolbox

All of the components were fabricated using an AlGaAs photonic layer grown via
molecular-beam epitaxy (MBE). The full fabrication procedure has been detailed
previouslySteiner  _et al._ (2021); Chang  _et al._ (2020). Briefly, a GaAs
chip with a 400-nm-thick AlGaAs photonic layer is bonded onto a 3-$\mu$m-thick
thermal SiO2 buffer layer on a Si substrate. After removing the substrate
through selective wet etching, the AlGaAs surface is passivated using an 8-nm
film of Al2O3 grown via atomic layer deposition (ALD). Deep ultraviolet
photolithography is used to pattern photoresist, which is used to etch an SiO2
hardmask and then the AlGaAs photonic layer to define the components. Another
ALD deposition of Al2O3 passivates the surface before a 1.0-$\mu$m thick SiO2
cladding layer is deposited. Finally, 10 nm of titanium and 100 nm of platinum
are deposited as resistive heaters for thermo-optic tuning.

###  II.1 Edge Couplers

Before a fully integrated QPIC is fabricated, it is necessary to utilize
either fiber-based or free-space optical testing instruments. Thus, one of the
first components to design is an efficient structure to couple light into and
out of the photonic chip. Various strategies have been explored for efficient
coupling Marchetti  _et al._ (2019), but many of the methods that achieve
ultra-high efficiency require additional fabrication steps, electron-beam
lithography, anti-reflection coatings, or a full redesign of the input/output
facet structure. For high throughput testing of individual components, much
simpler structures can be used; as long as the fiber-to-chip coupling
efficiency can be adequately characterized, any undesirable effects due to the
input/output coupling can be isolated from the component performance.

There are two main categories of fiber-to-chip couplers: vertical couplers and
edge couplers (also called "in-plane" or "butt" couplers, respectively). As
the name suggests, vertical couplers accept incoming light from the top of the
chip (out of plane) while edge couplers couple light impinging from one of the
facets of the photonic chip (in plane). Depending on the desired application
or testing design, there may be a benefit for utilizing either type of
coupler. Vertical couplers are useful for more compact designs as they do not
require waveguides to be routed completely to the edge of the photonic
chipCheng  _et al._ (2020). Generally, vertical couplers utilize periodic
gratings that satisfy the Bragg condition in the waveguide to couple light
into an optical fiber oriented almost perpendicularly to the surface Cheng
_et al._ (2020); Taillaert  _et al._ (2006). Edge couplers, on the other hand,
can be much simpler to design and less sensitive to fabrication variation.
Instead of relying on grating-based structures, edge couplers manipulate the
waveguide dimensions to expand the waveguide mode to be closer matched with
the mode in the fiberMu  _et al._ (2020). The easiest way to achieve this
conversion is to taper the waveguide to a narrow tip (called an "inverse
taper") where the mode becomes weakly confined and expands closer to the mode
size of the fiber. A standard taper, where the waveguide width is expanded at
the facets, can also serve as an edge coupler. However, in high-index contrast
platforms the design typically has lower efficiencies since the strongly
confined mode will remain smaller than the fiber mode. The waveguide becomes
capable of supporting multiple modes, and the high-index contrast produces
large back reflectionsMu  _et al._ (2020). Other edge coupling strategies
include utilizing multiple inverse tapers in a trident or dual-tip design Liu
and Yu (2007), polymer-based spot size converters Roelkens  _et al._ (2005),
or multi-layer spot size converters Fang  _et al._ (2010). Due to the much
simpler design, here we report only on inverse taper AlGaAsOI edge couplers. A
scanning electron microscope image of several inverse tapers is shown in Fig.
2a). The facet is on the right side of the image, and the waveguides taper
from 600 nm width (on the left) down to 200 nm at the facet. For a more in-
depth study of the various types of coupling strategies, readers are referred
to Ref. [(31)], which highlights various vertical and edge coupling strategies
on the silicon-on-insulator (SOI) platform.

The inverse taper design reduces the confinement of the waveguide mode,
increasing its effective modal area and decreasing its effective index of
refraction. This allows for moderately high simulated coupling efficiencies
(losses $<3$ dB) to a (typically) lensed fiber aligned with the waveguide
facet. The overall coupling loss is determined by effects such as reflection
at the chip facet (due to refractive index mismatch), fiber-to-waveguide mode
mismatch, and mode-conversion within the waveguide taper.

Figure 2: a) Scanning electron microscope (SEM) image of an array of inverse
taper edge couplers. b) Simulated mode overlap between a 2.5 $\mu$m Gaussian
beam and an AlGaAsOI waveguide for various widths of the input taper and a
fixed height of 400 nm. The star indicates an experimental measurement of the
coupling loss through a straight waveguide device with 200 nm input/output
couplers.

To determine the optimal design for an inverse taper edge coupler, the
dimensions of the waveguide taper were varied and simulated using Lumerical
Mode software. Here we only show the results for inverse tapers designed for
the fundamental transverse electric (TE) mode because the components shown in
the rest of this article are designed to operate with TE polarized light.
Similar calculations can be made for the transverse magnetic (TM) mode. For a
given Gaussian beam and waveguide geometry, the power overlap between the
waveguide mode and fiber mode is calculated to estimate an upper bound on
coupling efficiency and determine the optimum waveguide dimensions. This
calculation does not include loss due to mode conversion or reflection at the
interface. Figure 2b) illustrates the simulated mode overlap between a
Gaussian beam with a mode field diameter of 2.5 $\mu m$ (which matches the
mode field diameter of commercially available lensed fibers) and a 400-nm
thick AlGaAsOI waveguide with various taper widths. Narrow taper widths
enlarge the waveguide mode to be nearly mode-matched with the incoming fiber
mode, but the weak confinement of these narrow waveguides typically comes with
additional loss as the light propagates through the narrow taper back to a
waveguide width of $\geq$400 nm for the components. The fabrication of
sub-200-nm features is challenging using the standard photolithography
process, so we limit our taper designs to 200 nm or larger. Along with the
simulated data, Fig. 2b) also shows a measured value for the coupling loss for
a 200 nm edge coupler at a wavelength of 1550 nm. The measured value was
collected by sending 10 dBm (10 mW) of light into a straight waveguide with
200 nm inverse tapers on the input and output facet. The collected power
through the waveguide was 2.2 dBm, indicating an approximate loss of 3.9
dB/facet (the waveguide propagation loss is $<1$ dB/cm and the waveguide is
less than 2 mm, so the contributions of propagation loss are ignored in this
measurement). The measured loss is larger than the simulated mode overlap,
which is expected because the measurements also include reflections and mode
conversion loss in the taper. The simulated mode overlap acts as an upper
bound for the efficiency of the inverse taper. The 3.9 dB/facet of coupling
loss in the AlGaAsOI platform is slightly larger than the sub-3 dB coupling
loss expected from standard SOI inverse taper edge coupler designs Mu  _et
al._ (2020). The use of narrower taper widths (as shown in Fig. 2b)) or an
anti-reflection coating will improve the coupling efficiency further, but ease
of fabrication and reliability are prioritized, so for our initial devices,
200 nm inverse tapers are utilized.

###  II.2 Waveguide Crossings

Several methods have been explored for creating low-loss waveguide crossings
including vertical coupling into polymer strip waveguides Tsarev (2011),
multi-planar crossingsChiles  _et al._ (2017), multimode interference-based
crossingsChang and Zhang (2020); Bogaerts  _et al._ (2007); Wu  _et al._
(2020), and subwavelength gratingsBock  _et al._ (2010). Many of these methods
involve additional fabrication steps that can introduce excess loss and system
design and fabrication challenges. A basic approach for a waveguide crossing
relies on tapering an input single-mode waveguide section into a larger
waveguide cross section that can support higher-order modes and relies on the
beating between the fundamental mode and the higher-order mode to create an
electric field maxima that is centered in the waveguide at the crossing
location. By focusing the mode into the center of the wide waveguide,
evanescent coupling to the perpendicular waveguide is minimized. This design
can be completed with a basic linear taper (which will be referred to as a
"simple crossing"), or a more complex structure. Here, we consider simulations
of both simple and inverse-design crossings and report results from an inverse
design approach (which will be referred to as a "13-width crossing") that
utilizes 13 different widths in a parabolic taper that requires no additional
fabrication steps and maintains low-loss and high-isolation transmission. This
second design utilizes a swarm optimization protocol such that the optical
mode is transmitted with minimal coupling to the crossed waveguide.

Figure 3: a) Schematic image of the simple waveguide crossing design. The
relevant design variables are indicated on the image. b) Simulated mode
profile for the optimized simple crossing design. The beating between the
higher order modes and the fundamental mode results in a maximum electric
field intensity in the center of the waveguide at the crossing, which
minimizes the coupling to the vertical waveguide. c) Simulated transmission
through the simple waveguide crossing as a function of the wavelength. d)
Schematic image of the 13-width crossing design where a swarm optimization
varies the width of the parabolic taper at 13 locations and minimizes the
transmission loss. e) Simulated mode profile of the optimized 13-width
crossing. f) Simulated transmission through the 13-width crossing design as a
function of wavelength.

The simple crossing design is illustrated in Fig. 3a) and uses the beating
between the fundamental and higher-order mode to create a confined optical
mode centered at the location of the crossing. The beat length, $L_{\pi}$, is
defined as $L_{\pi}=\pi/(\beta_{0}-\beta_{1})$ where $\beta_{(0,1)}$ are the
propagation constants of the fundamental and first-order waveguide modes,
respectively. For a 1.5 $\mu$m multimode waveguide width ($w_{m}$), the
fundamental and first-order TE modes have effective indices of approximately
3.00 and 2.87, respectively, at a wavelength of 1550 nm. Using these effective
indices, the beat length is calculated as 5.95 $\mu$m. Finite difference time
domain (FDTD) simulations were utilized to account for the transition region
between the single-mode waveguide and the wider, multimode waveguide as well
as allow for a larger bandwidth crossing to be designed where the average loss
across a 100 nm bandwidth is utilized instead of maximizing at a single
wavelength. The simulated mode profile for the simple crossing design and the
simulated transmission through the device is shown in Fig. 3b,c),
respectively. From the mode profile simulation, it is clear that the beating
between the fundamental and higher order mode create a local maxima at the
location of the crossing that minimizes the optical mode scattered into the
perpendicularly oriented waveguide. The simulated loss through this structure
is 0.15 dB at a wavelength of 1550 nm.

Figure 3d) shows the 13-width waveguide crossing with critical dimensions
depicted. This design utilizes a swarm optimization protocol in an FDTD solver
to optimize the transmission through the crossing by allowing the width to
vary at 13 equally spaced sections along the taper. A parabolic interpolation
between the 13 widths ensures a smooth transition between the various widths.
The 13-width crossing design was also optimized for a bandwidth of 100 nm to
maintain low-loss performance of the crossing across a broad bandwidth, which
will be compatible with broadband entangled photon pair generation in quantum
photonic circuits. Lower loss structures can be made when optimizing for a
smaller bandwidth. Starting with an input waveguide width of 400 nm and total
crossing length (L) of 9 $\mu$m, the optimizer was allowed to vary the widths
w2-w13 between 200 nm and 2000 nm. Figure 3e) shows the electric field profile
for the optimal crossing design at a wavelength of 1550 nm, and Fig. 3f) plots
the simulated transmission through the waveguide crossing as a function of the
input wavelength. This crossing design has a simulated loss of approximately
0.1 dB at a wavelength of 1550 nm. Since the loss of the 13-width crossing
design is smaller than the simple crossing design, the 13-width crossing was
fabricated and tested initially.

Figure 4:  a) Optical image of cascaded waveguide crossings for loss
characterization. b) Normalized waveguide crossing transmission loss at a
wavelength of 1550 nm using the cutback method. The orange trend line
indicates an insertion loss of $0.23$ dB/crossing.

With the simulated waveguide crossing loss on the order of 0.1 dB, the cutback
methodBogaerts  _et al._ (2007) is used to measure the loss per crossing to
remove coupling-dependent loss and reduce detector sensitivity limitations.
For the 13-width crossing, waveguides with between 10 and 50 crossings were
fabricated, and the loss through each line of crossings was measured across
eight trials with complete re-alignment of the input and output fibers for
each trial to remove any systematic variations due to coupling loss. Figure
4a) shows a microscope image of a few of the waveguide crossings in one of the
lines. The vertical waveguide channels are terminated with tapered waveguides
in a spiral geometry to prevent back-reflections into the crossing. The
horizontal spacing of the crossings is varied randomly between 25 $\mu$m and
35 $\mu$m to avoid photonic cavity effects. Using the cutback method, the
transmission through the crossings was measured at a wavelength of 1550 nm,
and the results are shown in Fig. 4b). The dashed line indicates a linear fit
of the loss as a function of the number of crossings, providing an estimated
loss of $0.23$ dB/crossing. The error bars on the data points indicate the
standard deviation of the eight independent measurement trials.

These results for the 13-width waveguide crossing (Fig. 3b) indicate that the
fabricated crossings have slightly higher loss than the simulated loss at a
wavelength of 1550 nm. This additional loss is likely due to fabrication
variations in the widths along the device; the inverse design is more
sensitive to fabrication variation than the use of a simple waveguide
crossing. The measured $0.23$ dB of loss for the AlGaAsOI 13-width crossing is
comparable to the $0.2$ dB of insertion loss reported from a genetic
algorithm-designed SOI waveguide crossing Sanchis  _et al._ (2009) and less
than the loss of $0.3$ dB from silicon nitride waveguide crossings Yang  _et
al._ (2019). Other manuscripts report $\leq 0.1$ dB of insertion loss for
elliptical tapers Fukazawa  _et al._ (2004) and even on the order of $0.02$ dB
for sub-wavelength grating-based structuresZhang  _et al._ (2013). Ref. [(42)]
compares various results of waveguide crossing on the SOI platform.

###  II.3 3 dB Couplers
Multimode Interferometers and Directional Couplers

A standard building block in both classical and quantum PICs is a 3-dB
coupler. In QPICs, 3-dB couplers are utilized as their classical counterparts
to distribute light evenly between two waveguides, to interfere single
photons, and to serve as a component for tunable Mach-Zehnder Interferometers
(MZIs) for programmable PICs. This places strict requirements on the devices,
such as low loss for potential scalability, a large bandwidth to support
broadband quantum light generation, and precise splitting ratios to maximize
the extinction ratio and minimize cross-talk in MZIs. We explore two designs
for creating on-chip 3-dB couplers: multimode interferometers (MMIs) and
directional couplers (DCs). MMIs are based on the self-imaging principle,
similar to the aforementioned simple waveguide crossings; however, unlike in
the waveguide crossing design, the beat length between the two modes,
$L_{\pi}$, is used to calculate the core length necessary to achieve a
splitting ratio as close to 3-dB as possible. The second coupler design based
on DCs uses the overlap of evanescent modes between two neighboring
waveguides, allowing the mode to fully couple into the adjacent waveguide. The
full crossover length relies on the difference in refractive index between the
even and odd supermodes created when two waveguides are in close proximity.
DCs are straightforward couplers to design and are capable of any splitting
ratio by adjusting the coupling length, but they are also more susceptible to
fabrication imprecision and errors compared to MMIs.

Figure 5:  a) Schematic illustration of a directional coupler with the
relevant design parameters. b) Simulated transmission of various directional
coupling lengths to determine the appropriate coupling length for a 3-dB
directional coupler. c) Schematic illustration of a multimode interferometer
with the relevant design parameters. d) Simulated mode profile of an MMI
depicting 3-dB coupling behavior with a length near 16.0 $\mu$m.

Figure 5 depicts two MMI and DC designs and results from FDTD simulations. For
the MMIs, a core width of 2.1 $\mu$m was selected. Because the self-imaging
length scales with the MMI core width, a narrow width was chosen to reduce the
component footprint. Symmetric input and output tapers expand the mode from a
waveguide width of 0.4 $\mu$m to 0.9 $\mu$m nearest to the core. A 0.3 $\mu$m
separation leaves no excess core width beyond the dimensions of the tapers in
an effort to reduce Fabry-Perot effects due to reflections. The core length
design began by first calculating the beat length and multiplying it by a
factor of 1.5, resulting in $L_{\pi}=18.75$ $\mu$m. The full device was then
simulated using FDTD, and the electric field profile is shown in Fig.5b). With
a combination of the calculated beat length and FDTD simulations, a core
length of 17.2 $\mu$m was chosen. The 1.55 $\mu$m difference between both
methods is due to the input taper expanding the mode prior to reaching the MMI
core not being considered during the beat-length calculation.

Unlike the MMIs, the DC design utilizes the same waveguide width, 0.4 $\mu$m,
across the entire device. Symmetric sine bend waveguides on the input and
outputs with transverse displacements of 1.0 $\mu$m and 8.0 $\mu$m enable
light to propagate near the coupling region. The minimum radius of these sine
bends is kept to 20 $\mu$m to reduce bending loss. The separation between the
waveguides in the coupling region where the evanescent modal overlap occurs is
0.3 $\mu$m. The coupling length for the full transfer of light from one
waveguide to the other was first calculated with
$L=\frac{\lambda}{2(n_{0}-n_{1})}$ to give an estimate of the full crossover
length of the mode, where $n_{(0,1)}$ is the effective indices of the even and
odd supermodes that exist when the two waveguides are brought in close
proximity. The finite difference eigenmode (FDE) results for the full
crossover length is 48.47 $\mu$m. Thus for a 3-dB coupler, $L=24.23$ $\mu$m. A
sweep of the coupling region using FDTD simulations of the full DC structure
is depicted in Fig. 5d). The results of this simulation suggest an optimal
3-dB coupling length of 17.0 $\mu$m. The difference between the two values is
due to extra coupling effects in the sine bends. From the MZI measurements
discussed in the next section, we can extract the performance of the couplers.

###  II.4 Mach-Zehnder Interferometers (MMI and DC)

Figure 6:  a) Optical image of an MZI (DC) with a 30 $\mu$m path imbalance. b)
Extinction ratios of the different input and output combinations in a 10.23 nm
FSR MZI (DC). c) Transmission spectra of the bottom input, bottom output and
bottom input, top output port combinations of an MZI (DC). d) Extracted
coupling values of each directional coupler in the MZI (DC).

Tunable MZIs are a key component in QPICs by playing an important role for
numerous functions, including as reconfigurable postselected entangling gates
(R-PEGs)Adcock  _et al._ (2018), demultiplexersHorst  _et al._ (2013),
variable beamsplittersWilkes  _et al._ (2016), filtersPiekarek  _et al._
(2016), and single photon quantum logic gatesAdcock  _et al._ (2019). In an
MZI, a 3-dB coupler splits light evenly into two different paths that may be
equal (balanced MZI) or unequal (unbalanced MZI) in length, which then
recombine with another coupler. Here, we focus on two variations of thermo-
optically tunable unbalanced MZIs employing both DCs and MMIs. These devices
were designed using the transfer matrix methodTran  _et al._ (2016), where
each component of the MZI can be represented by a matrix, two equivalent
matrices for the 3-dB couplers, and a standalone matrix representing the path
imbalance. Since many MZIs are required for a complete QPIC, the loss across
each device must be minimized. Each coupler also should exhibit as close to a
3-dB splitting ratio as possible to achieve a maximum extinction ratio (ER),
defined here as the power ratio of neighboring MZI fringes in the transmission
spectrum.

Figure 6a) shows an optical image of an MZI utilizing DCs as couplers with a
30 $\mu$m path imbalance on the top arm with the metal thermal tuner above the
1 $\mu$m thick cladding to sweep and control the MZI phase. One advantage of
thermo-optic tuning with AlGaAs is its inherent large thermo-optic
coefficient, which, for an MZI with a 60 um path imbalance and a 10.28 nm free
spectral range (FSR), allows for a full 2$\pi$ phase sweep with 20 mW/$\pi$
efficiency, which is 10 (0.6) times more efficient than silicon nitrideLee
_et al._ (2022) (siliconLee  _et al._ (2017)). The transmission spectrum of a
60 $\mu$m path imbalance MZI with DC couplers is shown in Fig. 6b) for two
different input/output configurations. The legend indicates which port light
was coupled into and collected from, respectively, where T represents top and
B represents bottom. The ER of all four ports are graphed in Fig. 6c). We
typically observe an ER above 10 dB across $\geq 100$ nm bandwidth for through
ports and $\geq 200$ nm for cross ports, comparable to silicon MZIsLee  _et
al._ (2019); Piekarek  _et al._ (2016). With these ER measurements versus
wavelength, the true coupling coefficient $\kappa$ of each DC can be
extractedTran  _et al._ (2016), as shown in Fig. 6d). The DC couplers exhibit
an average coupling coefficient of 0.504$\pm$0.034 across a 100 nm bandwidth
centered at 1570 nm.

##  III Qubit Demultiplexing

To benchmark our platform, we use a tunable MZI chip to demultiplex signal and
idler photons generated from SFWM in a separate AlGaAsOI microring resonator
chip previously reportedSteiner  _et al._ (2021). The experimental setup
schematic is shown in Figure 7a). The microring resonator temperature is
stabilized with a thermo-electric cooler and control electronics. A tunable,
narrow-linewidth continuous wave (cw) laser is tuned into resonance with a
microresonator mode near 1557 nm. Tunable etalon-based bandpass filters are
tuned to the pump wavelength and placed immediately after the laser to
suppress amplified spontaneous emission at the wavelengths of the signal and
idler modes, which helps improve the coincidence-to-accidental ratio in our
experiments. The laser is polarized along the TE mode of the microresonator
chip, and light is coupled onto the chip with high-numerical aperture lensed
fiber. Pump light is coupled into the microring resonator using a critically
coupled pulley coupler, where time-energy entangled signal and idler photon
pairs are generated. The signal, idler, and pump photons are collected with a
lensed fiber and then routed with polarization maintaining fiber to the MZI
chip. When the phase of the MZI is properly tuned, it demultiplexes the signal
and idler photons into separate waveguides. Light from one output port is
coupled off chip using a lensed polarization-maintaining single-mode fiber.
The output is then coupled to a 3-dB fiber beamsplitter, the output of which
is demultiplexed with low-loss narrow-band filters and sent to superconducting
nanowire single-photon detectors (SNSPDs) for coincidence detection.

Figure 7:  a) Experimental schematic of qubit demultiplexing utilizing a
AlGaAs ring resonator source and a 10.23 nm FSR MZI (MMI). b) Transmission
spectra of MZI tuned to relative zero and $\pi$ along with the pump, signal,
and idler wavelengths. c) Normalized counts on the SNSPDs after
demultiplexing.

We chose to use an MMI-based MZI with a 60 $\mu$m path imbalance for these
experiments, despite the fact that its maximum ER is shifted away from 1550 nm
due to the MMI design, because the FSR of this design most closely matches
that of our microring resonator entangled-photon pair source. While the ER of
this MZI is lower than that measured for the DC-based MZI, we show below that
the performance of our demultiplexing experiment is at the maximum capability
of our MZI based on its ER, demonstrating the promise of this platform for
future all-on-chip demultiplexing. Figure 7b) shows the transmission spectrum
of the MZI chip when coupling into and out of the top ports for two different
thermo-optic heater voltages of 1 V and 1.8 V, which correspond to MZI phase 0
and $\pi$ radians, respectively, with an extinction ratio of 15 dB near the
signal and idler wavelengths. As the phase is swept from 0 to $\pi$, the
transmission at a single wavelength sweeps from maximum to minimum. Vertical
lines in the plot depict the wavelengths of the pump (1557.4 nm), signal (1565
nm), and idler (1550 nm) photons from our microring resonator. We next couple
the entangled-photon pairs into the MZI for demultiplexing. Normalized counts
from the two SNSPDs are shown in Fig. 7c) as a function of applied MZI
voltage. We measure an extinction ratio of $\sim$14 dB near 1.65 V, which is
comparable to the measured MZI extinction ratio shown in Fig. 7b). While these
results are encouraging, we expect further improvements demultiplexing by
improving the MMI splitting ratios to increase the demultiplexing ER and by
designing an MZI with twice the FSR of the source.

##  IV Conclusion

Here we demonstrate many of the fundamental components necessary to develop
fully integrated quantum photonic circuits on AlGaAsOI. With high-quality
entangled photon pair sourcesSteiner  _et al._ (2021) and the efficient edge
couplers, 3 dB splitters, waveguide crossings, and MZIs demonstrated in this
manuscript, a plethora of application-oriented integrated quantum circuits
become available. Demonstrations of chip-to-chip quantum
teleportationLlewellyn  _et al._ (2019), multi-photon quantum information
processing Adcock  _et al._ (2019), and other large-scale quantum photonic
circuits have already been realized on the SOI platformMoody  _et al._ (2020);
Lu  _et al._ (2021). The benefits of the AlGaAsOI platform should enable more
efficient demonstrations of these circuits at significantly lower optical pump
power, reducing the required time to collect useful data and allowing for
larger-scale circuits to be created. A summary of a few of the components
discussed in this report is shown in Table 1 along with the performances of
comparable components made on the SOI and Si3N4 platforms, which are also
commonly used for quantum photonic circuits. It is important to note that the
selected device performances were for Si and Si3N4 components that follow
similar designs to the AlGaAsOI components that are relevant and routinely
used for QPICs. For example, sub-edge couplers with 0.35 dB of loss have been
fabricated using silicon with silicon nitride, but these were achieved with
multiple layersWang  _et al._ (2019). Here we compare similar component
designs across the three platforms–using only a single photonic layer and
standard photolithography to fabricate the devices. Overall, the AlGaAsOI
components have similar or better performance to their SOI and Si3N4
counterparts, indicating that the transition to fully AlGaAsOI-based photonic
circuits will have little to no degradation in performance compared to the
current state-of-the-art platforms. Although the components detailed in this
work were fabricated using a 22 mm by 24 mm bonded AlGaAs chip, wafer-scale
bonding with compound-semiconductor-on-insulator is possibleStanton  _et al._
(2020); Chang  _et al._ (2022), enabling larger circuits to be created in the
near future.

Table 1: Table comparing the AlGaAsOI platform with SOI and Si3N4 designed for integrated quantum photonics. | AlGaAsOI | SOI | Si3N4
---|---|---|---
| (this work) |  |
Inverse Taper |  $3.9$ dB |  $<3$ dBMu  _et al._ (2020) |  $2-3$ dBRamelow  _et al._ (2015)
Coupling Loss |  |  |
Waveguide Crossing |  $0.23$ dB |  $0.2$ dBSanchis  _et al._ (2009) |  $0.3$ dBYang  _et al._ (2019)
Loss |  |  |
MZI Extinction |  $>30$ dB |  $>30$ dBWang  _et al._ (2016) |  $>40$ dBRao  _et al._ (2021)
Ratio |  |  |
MZI Bandwidth |  $200$ nm Cross |  $>40$ nmLee  _et al._ (2019) |  $180$ nmRao  _et al._ (2021)
($>10$ dB ER) |  $90$ nm Through |  |
MZI Heater | 20 mW/$\pi$ |  $12$ mW/$\pi$Lee  _et al._ (2017) |  $200$ mW/$\pi$Lee  _et al._ (2022)
Efficiency | (10.2 nm FSR) | (5.8 nm FSR) | (NA)

###### Acknowledgements.

This work was supported by the NSF Quantum Foundry through Q-AMASE-i program
Award No. DMR-1906325, AFOSR YIP Award No. FA9550-20-1-0150, and NSF Award
CAREER-2045246. We also gratefully acknowledge support from the Cisco Research
University Gift Program. T.J.S. and J.E.C. contributed equally to this work.

## Data Availability Statement

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

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