Near-infrared Hong-Ou-Mandel interference on a
silicon quantum photonic circuit
Xinan Xu1, Zhenda Xie1, Jiangjun Zheng1, Junlin Liang1, Tian Zhong2, Mingbin Yu3, Serdar
Kocaman1 , Guo-Qiang Lo3, Dim-Lee Kwong3, Dirk R. Englund4, Franco N. C. Wong2, and Chee Wei
1 Optical Nanostructures Laboratory, Center for Integrated Science and Engineering,
Solid-State Science and Engineering, and Mechanical Engineering, Columbia University, New York, NY 10027
2 Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts
3The Institute of Microelectronics, 11 Science Park Road, Singapore, Singapore 117685
4 Quantum Photonics Laboratory, Columbia University, New York, NY 10027
Author e-mail address: email@example.com, firstname.lastname@example.org
Abstract: Near-infrared Hong-Ou-Mandel quantum interference is observed in silicon
nanophotonic directional couplers with raw visibilities on-chip at 90.5%.
Spectrally-bright 1557-nm two-photon states are generated in a periodically-poled
KTiOPO4 waveguide chip, serving as the entangled photon source and pumped with a
self-injection locked laser, for the photon statistical measurements. Efficient four-port
coupling in the communications C-band and in the high-index-contrast silicon photonics
platform is demonstrated, with matching theoretical predictions of the quantum
interference visibility. Constituents for the residual quantum visibility imperfection are
examined, supported with theoretical analysis of the sequentially-triggered multipair
biphoton contribution and techniques for visibility compensation, towards scalable
high-bitrate quantum information processing and communications.
OCIS codes: (190.4410) Nonlinear Optics, parametric processes; (270.5585) Quantum information
and processing; (270.5290) Photon Statistics; (230.7370) Waveguides.
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In recent years, quantum information has been popular for its robust applications on cryptography [1–
5], computation [6–8] and communication [9,10], and chip-scale cavity quantum electrodynamics 
involving single photons and single excitons [12–17]. Working with biphoton or multiphoton states and
atom-photon interactions, entanglement in various degrees of freedom [17–20], such as time-energy [21,22],
spatial-momentum, and polarization  has been utilized to harness the efficiency and complexity of
quantum information processing. In parallel, quantum secure communications with various protocols [1–
3,5,10,24–27], has been proposed to enhance the security of channels and networks. Recent breakthrough
experiments are typically achieved in free-space , while recent theoretical in-roads on photon transport
on-chip [17,29–33] have led in studies on quantum information processing and communication. Emerging
measurements of entangled photons on-chip [34–39] have benefited from the arrayed scalability in the
nanophotonics platform and potentially robust phase-sensitivity of chip-scale samples albeit with the
challenges of device nanofabrication, design, and low-fluence single photon level measurements against
chip-scale Rayleigh-scattering photon and coupling losses. In the silica system with remarkable phase
control, visibilities up to 98.2% were observed ; in the compact silicon system, raw visibilities up to 80%
were observed . Most chip-scale measurements have been performed at the visible wavelengths and
with bulk nonlinear crystal sources, although there are some recent instances at near-infrared and
telecommunications wavelengths [40–42].
Here we report observations of near-infrared Hong-Ou-Mandel (HOM) quantum interference in
chip-scale silicon nanophotonics circuits, introducing the biphoton experiments to the integrated optics
regime. Employing spectrally-bright type-II periodically-poled KTiOPO4 waveguides (PPKTP) as the
entangled photon source, we demonstrate raw quantum visibilities up to 90.5% on-chip – one of the highest
visibilities observed in the silicon CMOS-compatible platform. Furthermore, we evaluate the various
sources of residual distinguishability including multiphoton pairs, chip-scale excess loss and non-ideal
splitting ratios, and polarization effects. The observed interference visibility matches our theoretical
predictions, for the different symmetric and asymmetric integrated directional couplers examined.
2. Near-infrared Hong-Ou-Mandel experimental setup
Figure 1 illustrates the experimental setup. A 1-cm periodically-poled KTiOPO4 waveguide  from
AdvR serves as the source for indistinguishable photons ; in this case, the waveguide is poled and
designed for quasi-phase-matching and high-fluence spontaneous parametric downconversion (SPDC) at
approximately 1556-nm to 1558-nm wavelengths. We use a relatively high power (100-mW; QPhotonics
QLD-780-80S) semiconductor laser diode as the pump for sufficiently high biphoton rates at approximately
107 per second, to compensate for losses in the fiber and free-space chip coupling setup. The laser is
thermally-tuned and stabilized by self-injection locking to 778.9-nm, which is exactly half of the center
working wavelength of the PPKTP waveguide. The temperature of the PPKTP waveguide is typically
controlled to ~ 25C for optimal phase matching. A long-pass-filter with cutoff at 1064-nm (Semrock
BLP01-1064R-25) blocks pump photons after the SPDC process, and a band-pass filter with 3-nm
(Semrock NIR01-1570/3-25) passes the non-degenerate biphoton states. The polarization controller right
before the fiber-based PBS is used to tune the polarization so that the fiber-based polarization beamsplitter
(PBS) spatially separates the correlated photons. In one branch, a tunable delay is realized by a
retroreflector (Thorlabs PS971-C) and a picomotor stage with loss less than 1-dB. In both branches,
polarization controllers are introduced to respectively change the polarization of each channel to match the
transverse magnetic (TM) mode for coupling into the chip waveguides (Figure 1b).
The chip coupling setup is built with six aspheric lenses, each mounted on individual three-axis
precision stages. The two input and output beams are separated by a D-shaped mirror after 60 cm
divergence to avoid crosstalk. Single and coincidence measurements are performed by two InGaAs single
photon Geiger-mode avalanches detectors D1 and D2 from Princeton Lightwave, with ~ 300 ps gate widths
and ~ 20% detection efficiencies. The clock of D1 is set to 15 MHz, and its output signal triggers D2. This
allows the coincidence rate to be read directly from the D2 counting rate, with the optical delay calibrated to
compensate the electronic delay.
Fig. 1. (a) Experiment setup for near-infrared Hong-Ou-Mandel interference in silicon quantum
photonic chip. The pump laser source is realized by an injection-locked semiconductor laser. Fiber
polarization controllers are used to ensure biphoton splitting via fiber polarization beam splitter,
and to equalize the TM polarization coupling onto the silicon chip. The photon statistics are
collected with one single photon detector triggering the other to diminish the dark counts and
accidentals. QWP: quarter-wave plate; HWP: half-wave plate; PPKTP: periodically-poled
KTiOPO4 waveguide; LPF: low-pass filter; BPF: band-pass filter; PBS: polarization beam splitter;
BS: beam splitter. (b) Optical micrograph of nanofabricated directional coupler in
silicon-on-insulator. The side trenches (in white) are intended to mark and locate the device. Inset:
zoom-in optical micrograph of the waveguide directional. Both scale bars: 1-um. (c) SEM of
silicon inverse taper couplers with top oxide cladding waveguides. Scale bar: 20-um. Inset:
end-view of protruded silicon waveguide. Scale bar: 200-nm.
3. Design and fabrication of silicon chip-scale two-photon interference directional coupler
To ensure good quantum interference on-chip, we examined the design space of the directional
couplers, in both transverse electric (TE) and TM polarization states as shown in Figure 2. Differential gap
widths (g), cross-over coupling lengths (lc) and waveguide widths (w) are illustrated for the optimal
coupling length and splitting ratios. The silicon waveguides are designed with a 250-nm thickness and for
operation at 1550-nm wavelengths.
To calculate the phase velocity of different polarization and symmetry, we use the frequency-domain
Maxwell equation fully-vectorial eigenfrequency solver (MPB), which computes by preconditioned
conjugate-gradient minimization of the block Rayleigh quotient in a planewave basis . The cross-over
coupling length lc of the two waveguides is then represented as
c p sym p anti ym
, in which the
phase change of π between the symmetric mode and anti-symmetric mode  allows for complete
crossover from one waveguide to another  in an ideal scenario. For a perfect 50-50 splitting ratio, the
desired length for the coupler should be
p symp anti sym
in which leff is the effective coupler length for the incoming and outgoing bend regions, which can be
estimated by an integral of coupling length as a function of gap size along the bending region and
computed to be 3-um in our designs (Figure 1b). In addition to the MPB and integral computations, the
designs were examined with both rigorous finite-difference time-domain computations and semi-vectorial
BeamPROP method from RSoft. With the birefringent character of the directional coupler, we work with
the TM mode rather than the TE mode due to its shorter coupling length and greater length control
sensitivity. Furthermore, our simulation models and experimental measurements confirm lower loss in the
TM mode for straight waveguide as well as the directional coupler regime due to lower electromagnetic
field amplitude at the sidewalls (typically rougher than the top and bottom surfaces) [48–51]. The lower
loss helps to increase the coincidences count rates and reduce the internal phase shift fluctuations of
directional coupler. A quantitative calculation suggests the loss of TE mode is 7.4 times higher than TM
mode for a consistent sidewall roughness. In one optimized instance, the waveguide width and coupler
length for TM symmetric splitting is chosen to be 400-nm and 15-um, respectively, as illustrated in Figure
2 (Design 1). In this design, the corresponding TE-polarization splitting ratio imbalance was numerically
computed to be 9-dB. The excess loss at the optimized directional coupler of Design 1 is estimated to be
0.1-dB by finite-difference time-domain computations.
Further increasing the coupler length will change the splitting ratio imbalance (SR), which could be
For a general comparison, we illustrate and select two other directional couplers with 28-um and 30-um
coupling lengths for experimental comparison (Figure 2, Designs 2 and 3). These designs have splitting
ratio imbalances corresponding to 2.3-dB and 7.7-dB respectively. Such a large splitting ratio imbalance
will remove the indistinguishability and enable the path information, potentially modifying the
Hong-Ou-Mandel dip visibility, given by
beamsplitter but is estimated to reduce to 97%, 80% and 47% for splitting ratio imbalances of 1-dB (1.27×),
3-dB (2×), and 6-dB (4×) respectively. For balanced chip-scale splitting, we note that multi-mode
interference  and Y-splitters are also good elements for physical realization. Directional couplers on the
other hand provides differential and accurate thermal tuning on the SR, enabling controlled asymmetries
such as for various C-NOT gate , quantum cloning [54,55], and Fock state filtration [56,57]
[34,52]. The visibility is 100% for a perfect
Fig. 2. Design map of silicon photonic directional coupler for two-photon interaction, in both
transverse electric (TE; left panels) and transverse magnetic (TM; right panels) polarizations.
Panel (a): cross-over coupling length (lc) versus directional coupler gap widths (g) and waveguide
width (w). Panel (b): splitting ratio versus designed cross-over coupling length lc and g. The
device thickness is fixed at 250-nm on a thick (typically 3-um) silicon oxide, and the biphoton
state input center wavelength is in the 1550-nm telecommunications band. The discretization in
each of the panels is from finite numerical simulations. The white circle points denote the
designed and fabricated device choices.
Supported by these designs, the devices were next fabricated at the Institute of Microelectronics.
Silicon-on-insulator wafers were used, with 248-nm deep-ultraviolet lithography for resist patterning.
Sidewall roughness was minimized by optimized lithography, resist development and etching. The
measured linear scattering loss of 3-dB/cm in the channel waveguides is determined by folded-back
(paperclip) waveguide structures. The inverse couplers are implemented with a tapered silicon
nanotaper  and top oxide cladding as shown in Figure 1c. The samples are diced and prepared for
measurement. The typical total lens-chip-lens coupling loss is approximately 11-dB, or a -14-dB
transmission including the -3-dB on-chip splitting. With a measured waveguide propagation loss of
3-dB/cm, the estimated facet coupling loss is 4-dB/facet. Taking into account the waveguide-to-fiber
coupling, transmission efficiencies of optical components, and detector efficiencies, the overall single
photon detection efficiency is estimated near 1%.
4. 1557.8-nm Hong-Ou-Mandel visibilities on-chip
For a pump power of 2.5-mW, the single photon rates coupled in the four-port chip are determined to
be about 1000 per second, with dark count rates around 200 per second. The coincidence rate is about 1
pair per second through the silicon photonic chip, with about 1/600 accidental photon pairs per second.
With our sequential triggering approach (detector D2 triggered by D1), instead of time-tagging, the
coincident dark counts are negligible. An example coincidence versus the relative optical delay is
illustrated in Figure 3a, with the observed near-infrared Hong-Ou-Mandel quantum interference on-chip.
Fig. 3. (a) Coincidences measured on the optimal directional coupler chosen experimentally with
a splitting ratio (SR) less than 1-dB. A triangle fit is used for visibility estimation. A raw
visibility of 90.5% is observed without accidental subtraction, and 90.8% with accidentals
subtraction. (b) Visibility measured with different pump powers for both chip and fiber beam
splitter implementations, for comparison. The visibility is approximately linearly related to the
pump power as more probability of multiple biphoton pairs generated in one gate window. The
first order theory is plotted as dashed line. The On-chip visibility is slightly lower than off-chip
one by about 3%, which could be considered to be induced by the chip.
These measurements are performed on a device carefully selected from an array of devices,
particularly one with splitting ratio imbalance of less than 1-dB. The sweep resolution and integral time
near the dip are set at 50-um and 1200-seconds respectively, which are twice higher resolution and integral
time compared to that away from the zero-delay point. The resulting long 21-hour measurement results in
small coupling drifts with slightly lower coincidence rate on the negative relative delays. The optimized
lowest coincidence is 25 per 600 seconds with a swing coincidence (away from the zero-delay point) of 499
per 600 seconds, giving a raw quantum visibility of 90.5%. The visibility is 90.8% after background
accidentals subtraction. An inverse triangle fit is used to estimate the shape of the dip. The measured
base-to-base width of Hong-Ou-Mandel dip is 1.36 mm ± 0.07 mm, corresponding to two-photon
coherence time of 4.53 ps, or an obtained SPDC bandwidth of 1.79 nm.
5. Sources of chip-scale interaction distinguishability
To further uncover the sources of distinguishability, we compare the on-chip Hong-Ou-Mandel
visibility with that of a fiber beam splitter (without chip) as illustrated Figure 3b. We plot the visibility
against different pump powers or the mean photon pair number to estimate the effects of the chip on the
visibility. Since a higher pump power with more biphoton pairs will cause a higher probability of multiple
biphoton pairs in one detector gate window, the visibility is inversely proportional to the pump power .
Triangle Dip Fit
0.00 0.020.04 0.06
Mean pair number
First order theory
Here we note that the effect of multipair biphoton generation in our sequential triggering approach is
different from the time-tagging approach. For a baseline model, we assume that the two detectors have
uniform detection efficiencies, gate widths and response times, with an infinitesimal timing jitter compared
to the gate width. Then the probability of ? photon pairs generated in the gate time obeys Poisson
( , )|) / !/ !(
p t nen a en
, where ? is mean pair number within the gate . To
maximize the coincidences, the photon transmitted to the triggered detector is delayed by half of the gate
time (/2) to guarantee it will always appear within the gate whenever the other photon arrives first (Figure
4a). To calculate the swing coincidences, or the probability of the coincidence event when two photons are
relatively delayed and totally distinguishable, we consider only one photon pair per gate to neglect higher
order terms (Figure 4a):
where the one half denotes the 50% probability that the biphotons will separate to two gates, and ?
denotes the overall detection efficiency, including all losses and intrinsic detector efficiency. To calculate
the probability of coincidence when two photons are indistinguishable, we consider only one and two
photon pairs within the gate. Here we notice that even when there is only one photon pair within the
detection gate of triggering detector D1, there are still some coincidences contributions (Figure 4b):
[1 (1(,1)(,1) (1)
Cp dtpt dt
where the photon pair is considered uniformly distributed within the gate window, and the possible photon
pair within the leak window due to gate time mismatch is considered (Figure 4b). If there are two photon
pairs within the gate window of D1, there are four possible situations: (a) the first photon pair is in the path
to D1, and second photon pair is in the path to D2 (Figure 4c); (b) the first photon pair is to D2, and the
second photon pair is to D1; (c) both photon pairs are to D2; (d) both photon pairs are to D1. Thus we have:
(2 )( ,2) ) ]( )[1 (1
aptptC dt p
] [1 (1
,1) ( )
p dt p
Taking the first order approximation, we have that:
(2)(2 )(2 )
(2 )(2 )
,which denotes the probability distribution of the first arriving photon pair. We
notice here the difference between the sequential triggering approach versus the time-tagging approach is
that there is a situation that the second photon pair will be located within the gate window of one detector,
but is cut off by the gate window of the other detector (Figure 4c). This portion equals to
2 ( ,2) 1/4 [1 (1
( ) (1/2
, which is exactly the same as the contribution of
coincidence conditioning only one photon pair per gate (Equation 4) even when disregarding the detection
efficiency distribution within the gate and timing jitter. As these two terms compensates each other, we
conclude that, to first order, the visibility for the sequential triggering scenario is as same as time-tagging
Fig. 4. Scenario of the timeline for the photon pairs. (a) The delay of two photon pairs is set to
/2 to maximize the coincidences. (b) When there is only one photon pair in the gate window of
D1, there is still possibility that D2 will record a photon event due to gate window time
mismatch. (c) When there are two photon pairs within the gate window and separated to two
detectors, there is possibility that the latter photon pair will be cut off due to the gate window
From fitting the chip result with the same slope as suggested by the above theory, we conclude that 6%
of the imperfect visibility is therefore likely to be from the multiphoton pairs. The residual 3% is likely to
be induced by processes on-chip. To further understand the chip mechanisms for visibility reduction, we
next compared the visibility for different splitting ratios. We selected two devices with coupler lengths of
28-and 30-um, which has the TM mode splitting ratio imbalance of about 3-dB and 6-dB as measured. The
comparison of the coincidence measurements between the three silicon chip devices is shown in Figure 5a
(before normalization, with lower integral time of 120 seconds compared to Figure 3a). The inverse
triangular fit is utilized to estimate the visibility and corresponding deviations. For the 28-um directional
coupler, the visibility is measured to be 74 ± 8%, close to the theoretical estimate of 80%. For 30-um
directional coupler, the visibility after fitting is 31 ± 11%, compared to the theoretical estimate of 47%, in
similar ballpark. The deviations here from theory are due to on-chip directional coupler internal loss and
high pump power. For our optimal 15-um directional coupler, the less than 1-dB splitting ratio imbalance
(limited by precision of lens-chip coupling loss variations) with its 97% theoretical visibility can therefore
account of a sizable portion of the residual 3% decrease in visibility.
Moreover, to understand the quantum interference effect with variation of polarization, we rotate the
polarization for one branch of the input path before the chip using a half waveplate. The resulting visibility
versus the linear polarization angle is depicted in Figure 5b. The result shows cosinusoidal behavior that
reaches maximum visibility with no polarization rotation, and diminished visibility with orthogonal
polarization. The maximum visibility in this set of measurements is 83% due to higher pump power of
5-mW. Here we note that the different splitting ratio of TE mode does not affect the visibility, since the
probability amplitude of both reflected photons
on the biphoton states basis
, and both transmitted photons
1/ 2cos ,0,
. The visibility
cos x, which does not require
the splitting ratio of TE mode as long as TM mode has balanced splitting. In our measurements, the input
polarizations are optimized and hence unlikely to be cause of the residual 3% decrease in visibility.
Fig. 5. (a) Coincidences measured on three different directional couplers measured with different
splitting ratio imbalances: 6-dB, 3-dB, and less than 1-dB. (b) Visibility versus polarization
detuned at one of the input paths.
Another major possible contribution to the chip-induced visibility reduction can be from excess loss
of the directional coupler. An ideal free space beamsplitter gives a 180˚ phase shift for one path of
reflection and 0˚ for the other path, while fiber-based beamsplitter or directional coupler should give both
90˚ phase shifts for reflected light compared to transmitted light to satisfy the energy conservation. The
sum of those phase shifts, or the inherent phase shift, accounts for the 180˚ phase difference between the
probability amplitude of the ??? and ???, causing the Hong-Ou-Mandel dip. When the on-chip directional
coupler has excess loss Lexcess, however, the inherent phase shift will not be 180˚ anymore. Performing a
matrix optics calculation, we have the inherent phase shift as
for a symmetric (SR = 0-dB) directional coupler. The visibility reduction caused by the excess
loss of the directional coupler can therefore be expressed as
Here we estimate that the 0.1-dB excess loss via vertical scattering from the chip even with ideal sidewalls,
or 170˚ internal phase shift, computed by FDTD method as noted in the earlier design section, in the
balanced directional coupler will reduce the visibility by 1.5%. This excess loss will be larger when
including fabrication disorder-induced losses. For unbalanced directional coupler, the internal phase shift
will be further away from 180˚ with corresponding reductions in the visibility. Formally, the output
annihilation and creation operators of a lossy directional coupler have to include Langevin noise operators
to maintain the commutation relation, while at the same time inducing additional phase shifts .
6. Compensation method for chip-scale two-photon interference
Fig. 6. (a) Compensation scenario for splitting ratio imbalanced directional coupler. The input
sides are kept TE in this case. A half waveplate is inserted into the lower branch before the chip,
rotating the linear polarization at θ1. One of the polarizer inserted after chip at the upper branch
is rotated to TE polarization, and another at the lower branch is rotated at θ2 referencing the TE
polarization. The second waveplate is inserted in one output branch in order to compensate the
birefringence. (b) Nomenclature of the reflectivity and transmission for TE and TM polarization
of the directional coupler. α denotes the birefringence at the directional coupler, β denotes half
the internal phase shift for the TE polarization, and γ denotes half the internal phase shift for the
TM polarization. In the waveguide region, the differential birefringence has a ϕ phase shift in the
TM mode relative to the TE mode, and the differential loss from TM to TE is denoted as ld. The
waveplate delays the TM mode with an additional ψ phase.
imperfections or slight residual design), one of the co-authors has proposed an approach to compensate the
imbalance and regain the indistinguishability , albeit for lossless and non-birefringent fiber
beamsplitters. For the scalable chip implementation, a simple but lossy approach (shown in Figure 6a)
would be to place half waveplates in one path before the chip and two polarizers after the chip,
post-selecting the photons and removing the polarization information. When the splitting ratios are different
for TE and TM modes, there exists a continuum of solutions for the angles of the polarizers to achieve the
probability amplitude of
With the splitting ratio imbalance and excess loss of the directional coupler (due to fabrication
tt A with the same amplitude and inverse phase. Here the
distinguishability is removed as long as the following condition is met:
tantan 1 2
te te tm
However, the birefringence of the directional coupler as well as the silicon waveguides brings additional
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polarization information projection to the polarizer. In more complete scenarios where loss and
loss-induced internal phase shifts are considered for TE and TM modes, this distinguishability could still be
compensated in our approach since only two adjustable elements, for example the angles of the polarizer
and of the waveplate, are needed to recover the two probability amplitudes inverse in phase and equal in
amplitude. We define the directional coupler birefringence, internal phase shifts, waveplate phase, and
waveguide differential birefringence and loss in Figure 6. In this complete case, we have
tete d tm
l r eA r r
A t e
, where the visibility could be
We have observed 1550-nm Hong-Ou-Mandel interference in silicon quantum photonic circuits, with
raw quantum visibility up to 90.5% in near-symmetric directional couplers. With thermally-stabilized
spectrally-bright PPKTP chip-scale waveguides as the entangled biphoton source, we examined the
constituents of residual distinguishability through numerically-designed directional couplers, multiphoton
pairs, polarization effects, excess loss, and imperfect phase shifts. With our sequential triggering approach
for negligible coincidental dark counts, we present the theoretical analysis for multipair biphoton
contribution to Hong-Ou-Mandel visibility reduction. Techniques for visibility compensation in chip-scale
birefringent directional couplers in the presence of loss are described. The results presented here support
the scalable realization of two-photon interaction elements on-chip, for quantum information processing
The authors acknowledge discussions with Fangwen Sun, Philip Battle, Tony Roberts, Xingsheng
Luan, Andrzej Veitia, and Felice Gesuele. We acknowledge the scanning electron micrograph images of
Figure 1 from James F. McMillan. This work is supported by the DARPA InPho program under contract