# Near perfect two-photon interference out a down-converter on a silicon
photonic chip

Romain Dalidet1 $\dagger$ Florent Mazeas2 $\dagger$ Edgars Nitiss2  Ozan
Yakar2  Anton Stroganov3  Sébastien Tanzilli1  Laurent Labonté1  and Camille-
Sophie Brès2  1Université Côte d’Azur, CNRS, Institut de Physique de Nice,
06108 Nice Cedex 2, France
2Ecole Polytechnique Fédérale de Lausanne, Photonic Systems Laboratory
(PHOSL), CH-1015, Switzerland
3Ligentec SA, Lausanne Switzerland †The two authors contribute equally to this
work<EMAIL_ADDRESS>
††journal: osajournal††articletype: Research Article

Integrated entangled photon-pair sources are key elements for enabling large-
scale quantum photonic solutions, and addresses the challenges of both
scaling-up and stability. Here we report the first demonstration of an energy-
time entangled photon-pair source based on spontaneous parametric down-
conversion in silicon-based platform through an optically induced second-order
($\chi^{(2)}$) nonlinearity, ensuring type-0 quasi-phase-matching of
fundamental harmonic and its second-harmonic inside the waveguide. The
developed source shows a coincidence-to-accidental ratio of 1635 at 8 of
$\mu$W pump power. Remarkably, we report two-photon interference with near-
perfect visibility of 99.36$\pm 1.94\%$, showing high-quality photonic
entanglement without excess background noise. This opens a new horizon for
quantum technologies requiring the integration of a large variety of building
functionalities on single chips.

Quantum science benefits from a worldwide research effort for developing
disruptive technique finding repercussion in communication and processing of
information. The realization of flexible, scalable and operational devices in
quantum technologies and systems requires new approaches for hardware
components. Integrated quantum photonics addresses the challenges of both
scaling-up and stability, enabling the realization of key physical resources,
such as on-chip photon pair generators, filters, modulators and detectors, and
especially their interconnects, leading the quest for advanced large-scale
monolithic devices [1, 2]. The range of desired building functions, each
performing a special task, has motivated the emergence of hybrid platforms
combining the best of different photonic technologies, including $\chi^{(2)}$
and $\chi^{(3)}$ nonlinearities based platforms [3, 4] in single functional
chips [5, 6, 7, 8]. The price to pay lies in the complex hybrid integration of
each elementary building blocks revealing new technological issues, such as
excessive optical losses due to transitions [9]. An elegant solution, still
keeping additional benefits of merging $\chi^{(2)}$\- and
$\chi^{(3)}$-nonlinearities based platforms, without compromising the overall
functionality of the single device, lies in inducing an effective $\chi^{(2)}$
nonlinearity in a silicon (Si)-based chip.

Among multiple physical approaches, the Si-based technology remains an
outstanding option due to ubiquitous capabilities developed by the
microelectronics industry. While the linear circuitry in Si photonics is well
established, achieving flexible, efficient and integrated quantum sources that
would allow entangled photon-pair generation has remained challenging[10, 8].
The latter is essential for further advances of photonic quantum devices and
applications [11]. The creation of entangled photons in Si-based devices is
naturally obtained through spontaneous four-wave mixing (SFWM), which
generates photonic noise, degrading the overall system’s performance. Recent
publications show that the ability to detect photon correlations
(entanglement) is limited by spurious effects such as two-photon and free-
carrier absorption (TPA and FCA) [12]. Furthermore, restrictive phase-matching
conditions limit the spectral coverage since the entangled photon pairs are
created only over a few tens of nanometers apart from the pump wavelength. In
contrast, $\chi^{(2)}$ materials represent a viable alternative by leveraging
spontaneous parametric down-conversion (SPDC) and thus relaxing the stringent
condition for on-chip filtering as the generated photon pairs are spectrally
far separated from the pump. Previous works have already shown the possibility
of enabling an efficient $\chi^{(2)}$ response in a $\chi^{(3)}$ Si substrate
providing new grounds for exploiting SPDC on this platform [13, 14, 15, 16,
17]. All these works have reported only either technological or non-linear
characterizations. Also, temporal correlation measurements for revealing the
degree of indistinguishability between the paired photons have been performed
on aluminium nitride [18]. In addition to demonstrating SPDC, qualifying
quantum correlations in a rigorous way, i.e., by means of a Bell-type
entanglement witness, is mandatory for a large variety of quantum applications
such as secret key distribution[19], superdense coding[20], teleportation
[21], sensing[22], and computing[23]. Such an entanglement characterization
still remains unrealized for photon pairs generated via SPDC on a Si-based
platform.

In this work, we demonstrate and qualify a photon-pair source obtained via
SPDC process on an Si-based platform. The source relies on an effective
$\chi^{2}$ induced by all-optical poling in a stoichiometric silicon nitride
(Si3N4) waveguide [24], resulting in the inscription of a self-organized
grating enabling quasi-phase-matching (QPM) of $1560~{}{\rm nm}$ and
$780~{}{\rm nm}$ light in a second-harmonic (SH) generation process. The
spectrum out of the chip is fully telecom compliant, and spreads over the C-
and L-bands. Low noise performance is demonstrated by measuring high
coincidence-to-accidental ratios (up to 1500). We proceed to the qualification
of energy-time entanglement carried by the photon pairs using a standard
Franson-type interferometer. Remarkably, we show two-photon interference
fringes with a near perfect raw visibility exceeding 99.36$\pm 1.94\%$. To our
knowledge, this work stands as the first demonstration of entangled photons
out of an Si-based platform through SPDC, and opens new horizon for these
platforms in the framework of quantum technologies.

We obtain the generation of entangled photons at $1560~{}{\rm nm}$ from a pump
at $780~{}{\rm nm}$ in a $81~{}{\rm mm}$ long Si3N4 waveguide with a cross-
section of $0.57\times 0.81~{}{\rm\mu m^{2}}$ folded in meanders on a chip
(Fig. 1a). The coupling of light to and off the chip is implemented by inverse
tapers. We measure coupling losses for $1560~{}{\rm nm}$ and $780~{}{\rm nm}$
light to be $2.7~{}{\rm dB}$ and $4.6~{}{\rm dB}$ per facet, while the
propagation loss is $0.33~{}{\rm dB/cm}$ and $0.73~{}{\rm dB/cm}$,
respectively. The fundamental TE00 modes for $1560~{}{\rm nm}$ and $780~{}{\rm
nm}$ light are shown in Fig. 1b and c, respectively. The $\chi^{(2)}$ in the
waveguide is achieved using an all-optical poling technique as described in
ref [25]. All-optical poling relies on high peak power ns pulses coupled to
the waveguide which, in the presence of weak SH, enables the spontaneous
build-up of a charge-separated $\chi^{(2)}$ grating due to photogalvanic
effect[26, 27]. The latter ensures automatic type-0 QPM of the fundamental
harmonic (FH) $1560~{}{\rm nm}$ and SH $780~{}{\rm nm}$ waves during the
grating writing process, and high versatility such that the process can occur
for a wide range of poling periods and waveguides indifferent of dimensions
[28]. For this study we all-optically poled the waveguide at $1561~{}{\rm nm}$
for operation in TE mode. Based on the simulated effective refractive indices,
the criterion for type-0 QPM between the TE00 modes at both the fundamental
and SH waves requires a grating with small period $\Lambda=3.14~{}{\rm\mu m}$,
owing to the large wavevectors mismatch. All-optical poling automatically
results in the inscription of such grating as confirmed by two-photon
microscope (TPM) image shown in Fig. 1e. The shape of self-organized
$\chi^{(2)}$ grating is directly linked to the mixing of the FH and SH modes
along the waveguide. The latter results in an optimal overlap integral of the
profiles of optical modes and the nonlinearity throughout the waveguide length
[28].

Once the grating is inscribed, it is characterized by measuring the SH
generation spectrum. The obtained on-chip conversion efficiency (CE) for an SH
generation process as a function of the wavelength is shown in Fig. 1f. Here
CE is defined as $CE=P_{SH}/P^{2}_{P}$ where $P_{SH}$ and $P_{P}$ are the on-
chip SH and pump powers, respectively. The CE spectra is fitted using the
standard QPM function[29, 30]:

${\rm CE}=\frac{(\omega L_{\rm g}\chi^{(2)}_{\rm
eff})^{2}}{2\epsilon_{0}c^{3}n^{2}_{\rm P}n_{\rm SH}}\frac{S_{\rm
SH}}{S^{2}_{\rm P}}\left(\frac{{\rm sin}\left(\frac{\Delta kL_{\rm
g}}{2}\right)}{\left(\frac{\Delta kL_{\rm g}}{2}\right)}\right)^{2},$ (1)

where $\omega$ is the FH optical frequency, $L_{\rm g}$ the grating length,
$c$ the speed of light in vacuum, $\epsilon_{0}$ the vacuum permittivity, and
$\Delta k$ the net wavevector mismatch after QPM compensation, i.e. ${\Delta
k(\omega)}={k_{\rm SH}}-{2k_{\rm P}}-2{\pi}/{\Lambda}$. $k_{\rm P(SH)}$,
$n_{\rm P(SH)}$, and $S_{\rm P(SH)}$ are the propagation constants, effective
refractive indices, and the effective mode areas at FH and SH wavelength,
respectively. Here $S_{\rm P}=0.74~{}{\rm\mu m^{2}}$ and $S_{\rm
SH}=0.32~{}{\rm\mu m^{2}}$. By fitting the CE spectrum we extract the grating
length, grating period and effective second-order nonlinearity to be $L_{\rm
g}=69~{}{\rm mm}$, $\Lambda=3.14~{}{\rm\mu m}$ and $\chi^{(2)}_{\rm
eff}=0.05~{}{\rm pm/V}$, respectively. The value of the grating period
extracted from TPM image is $\Lambda_{\rm TPM}=3.24\pm 0.31~{}{\rm\mu m}$
which is in excellent agreement with the one obtained from fitting of the CE
data and with the theoretically expected value, confirming the fundamental
mode interaction between the FH and the generated SH.

Figure 1: a Cross-section of the Si3N4 waveguide (see also a top-view in Fig.
2(a). b Simulated TE00 mode at the FH near 1550 nm. c Simulated TE00 mode at
SH near 775 nm. d Effective refractive indices. e TPM image of the waveguide
after all optical poling at 1561 nm showing the inscribed grating. f SH
generation CE spectrum as a function of FH wavelength. Dots are data points
and line is a fit according to Eq. (1).

The waveguide with the inscribed grating is then used for SPDC and
characterization in the quantum regime, as shown in the experimental setup of
Fig. 2a. A $780~{}{\rm nm}$ continuous-wave pump laser is coupled to the all-
optically poled Si3N4 waveguide. The polarisation of the pump laser is
adjusted using a polarisation controller and aligned with the TE mode of the
waveguide. At the output, the pump laser is rejected using a spectral filter.
The produced twin photons are then sent to either a 50/50 fiber coupler,
followed by two superconducting nanowire single-photon detectors (SNSPDs)
(part A), or to a folded Franson consisting of a single unbalanced Michelson
fiber interferometer (part B) in order to experimentally acquire two-photon
interference fringes.

Figure 2: a Experimental setup. The output of the optically poled Si3N4
waveguide is connected to either (A) a coincidence measurement setup or (B) to
the entanglement qualification setup in a folded-Franson configuration. The
interferometer is an unbalanced Michelson made of long and short arms. PC:
polarization controller; F: filter and isolators; 50/50: fiber coupler; $\tau$
time delay; D: superconducting nanowire single-photon detector; $\&$:
coincidence counting electronics; FM: fiber Faraday mirror; C: circulator. b
Coincidence count histogram in case pump power is 36 $\rm\mu W$. c Measured
PCR produced by SPDC as a function of the coupled pump power. d Measured CAR
as a function of PCR. Dots are data points, red lines are fits. The inset
shows the count histogram at pump power of 36$\rm\mu W$. The coincidence
counts $C_{C}$ are collected within a 80 ps time window e Normalized SPDC
coincidence spectrum of the all-optically poled Si3N4 waveguide under test.
Dashed line is a guide for the eye.

We exploit energy-time entangled photons as information carriers due to their
inherent invulnerability against polarization mode dispersion and drifts [31],
making this approach more robust for long distance distribution [32]. A
signature of energy-time entangled photon pairs is obtained by acquiring a
coincidence histogram between the single-photon detectors (D1 and D2) as shown
in Fig. 2b. To characterize the correlated photon pairs, we measure the
coincidence counts ($C_{C}$) and accidental-coincidence counts ($A_{C}$) as a
function of the pump power. The $C_{C}$ is collected within a 50 ps time
window covering the peak of the count histogram. The $A_{C}$ is estimated by
collecting the total number of coincidence counts outside the central peak
over a time window of 240 ps, much greater than the one of the central peak,
before normalisation. The external pair coincidence rate (PCR) is calculated
for several values of the coupled pump power and the results are shown in Fig.
2c together with a fitted line whose slope is 0.58 kHz/mW. We now consider the
internal brightness of SPDC-based sources, which is generally described by the
slope efficiency given as the photon-pair flux per unit spectral width and per
unit power, taking into account the overall losses of the setup. The overall
coincidence spectrum, as will be detailed below, spreads over a spectral
bandwidth of 30 nm, and shows an average of 400 coincidences per second with
14 dB of losses. We thus estimate an internal brightness of $\sim 5\cdot
10^{-3}$ pairs/s/mW/MHz.

The measured coincidence-to-accidental ratio (CAR = $C_{C}/A_{C}$) with
respect to PCR is shown in Fig. 2d. For low pump powers ($<$1$\mu$W), we could
not register accidental coincidences outside the coincidence peak within the
measurement time of around 30 s. For a coupled pump power of 8 $\mu$W, we
measure a CAR equal to 1635, which is a clear signature of correlated events
without the presence of extra photonic noise. At low pump powers, the CAR is
mainly limited by the detector’s dark counts. Then, the CAR decreases with the
pump power, following the trend CAR $\propto$ PCR-1 as shown in Fig. 2d. The
CAR drops because the pair rate increases quadratically with the pump power,
yielding an increased probability of detecting multiple pairs within a given
time window. To our knowledge, CAR obtained at low pump powers is the best
value reported to date in the literature for entangled photon pairs emitted
from Si-based platforms[33, 34, 35, 36, 37, 38, 39, 40]. This confirms our
strategy of considering SPDC process in CMOS photonics platform.

Fig. 2e shows the spectrum of the biphoton state out of the Si3N4 waveguide
measured via non-local filtering by placing a variable filter in one arm of
the setup, exploiting energy correlation of the photon pairs. The spectrum
centered at 1560 nm spreads over part of both the C- and L-bands, thus
covering 25 telecom channels. This flexibility, combined with the potential to
center the spectrum at will as leveraged by all-optical poling, is
particularly appealing for exploiting higher dimensions available in a large
multiplexed telecom-channel spectrum [41].

Figure 3: a Coincidence histogram for the constructive interference setting at
a pump offset of 7.35 pm (point A) from initial wavelength of 779.75 nm. b
Coincidence histogram for the destructive interference setting at a pump
offset of 10.65 pm (point B). Red-color dashed rectangle: analyzers time
window. c Normalized interference fringes of energy-time entangled photons as
a function of the pump offset. Error bars correspond to the Poissonian
distribution inherent to the pump laser. From fit the obtained visibility is
99.36$\pm$1.94 %.

The photon pairs are genuinely energy-time entangled as they are produced by
SPDC [32]. To measure the quality of the produced entanglement, we use a setup
as shown in Fig. 2a part B. The photons pairs are directly sent to the folded-
Franson interferometer and a typical three-peak coincidence histogram is
recorded (Fig 3 a and b). The contribution to these peaks depends on the path
taken by the two photons. If the twin photons travel both via different arm,
the time delays being $\tau_{short-long}$ ($|SL\rangle$) and $\tau_{long-
short}$ ($|LS\rangle$) give rise to the two side peaks, arriving earlier and
later, respectively. However, if the twin photons take both the same optical
path, then, whether it is the long arm or the short arm, the time delays
$\tau_{short-short}$ and $\tau_{long-long}$ ($|SS\rangle$ and $|LL\rangle$)
will contribute to the central peak in an indistinguishable way. The inability
to distinguish the "which-path information" for these coincidences, is at the
origin of the two-photon interference. In order to achieve high visibility
two-photon interference fringes, our analysis system fulfils two requirements.
First, the difference of time travel between the two arms is greater than the
coherence time of the single photons to avoid single-photon interference
$\tau_{sp}\approx 270fs<\tau\approx 30ps)$. Then, this time travel difference
is shorter than the coherence time of the CW pump laser $(\tau_{pump}>10\mu
s)$ to guarantee a coherent superposition between the indistinguishable states
recorded in the central peak.

We quantify the amount of entanglement by varying the pump wavelength offset
and measuring the interferogram. As expected, the height of the side peaks
remains the same during the scan, as they correspond to distinguishable events
(see Fig. 3a and b). The height of the central peak contains two
(indistinguishable) contributions ($|SS\rangle$) and ($|LL\rangle$), instead
of the side peak which gathers only one (distinguishable) contribution
($|SL\rangle$) or ($|LS\rangle$), leading a double amplitude, in average, for
the central peak with respect to the side ones. Due to constructive
interference (Fig. 3a), the central peak amplitude increases by a factor 4
with respect to the side peak, whereas, destructive interference (Fig. 3b)
cancels any coincidence counts within the time analyzer window (Fig. 3b). The
normalized height of the central peak as a function of pump offset is plotted
in Fig. 3c. As expected, the trend is well fitted by a sinusoidal, revealing a
near-ideal visibility of 99.36$\pm$1.94 % without background subtraction, thus
demonstrating the high quality of both the entanglement generator and
associated measurement setup. Note that all results are well above the
threshold of $71\%$ required to violate adapted Bell-Clauser-Horne-Shimony-
Holt inequalities. This result stands as the first demonstration of correlated
photon pairs through SPDC in CMOS compliant photonics platform, but also among
the highest raw quantum interference visibility for time-energy entangled
photons from a nanoscale integrated circuit.

In conclusion, here we demonstrate, for the first time to our knowledge, the
realization of an entangled photons-pair source on Si-photonics platform based
on SPDC, standing among the lowest-noise photon pair generators on a
nanophotonic chip. The device relies on an effective $\chi^{(2)}$ induced by
all-optical poling in a Si3N4 waveguide that enables near-perfect visibility
entangled photon generation. Our device, whose fabrication process fulfils the
requirements in terms of flexibility, compactness and scalability, could open
a new horizon in the ongoing quest of monolithic photonic platforms compliant
with the stringent demands of most quantum applications.

Funding This work was supported in part by ERC grant PISSARRO (ERC-2017-CoG
771647). Disclosures The authors declare no conflicts of interest.

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