Spatially entangled photon pairs from lithium niobate nonlocal metasurfaces

Abstract

Metasurfaces consisting of nanoscale structures are underpinning new physical principles for the creation and shaping of quantum states of light. Multiphoton states that are entangled in spatial or angular domains are an essential resource for many quantum applications; however, their production traditionally relies on bulky nonlinear crystals. We predict and demonstrate experimentally the generation of spatially entangled photon pairs through spontaneous parametric down-conversion from a metasurface incorporating a nonlinear thin film of lithium niobate covered by a silica meta-grating. We measure the correlations of photon pairs and identify their spatial antibunching through violation of the classical Cauchy-Schwarz inequality, witnessing the presence of multimode entanglement. Simultaneously, the photon-pair rate is strongly enhanced by 450 times as compared to unpatterned films because of high-quality-factor resonances. These results pave the way to miniaturization of various quantum devices by incorporating ultrathin metasurfaces functioning as room temperature sources of quantum-entangled photons.

Full text

Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
1 of 8
OPTICS
Spatially entangled photon pairs from lithium niobate
nonlocal metasurfaces
Jihua Zhang1†, Jinyong Ma1†, Matthew Parry1, Marcus Cai1, Rocio Camacho-Morales1, Lei Xu2,
Dragomir N. Neshev1, Andrey A. Sukhorukov1*
Metasurfaces consisting of nanoscale structures are underpinning new physical principles for the creation and
shaping of quantum states of light. Multiphoton states that are entangled in spatial or angular domains are an
essential resource for many quantum applications; however, their production traditionally relies on bulky nonlinear
crystals. We predict and demonstrate experimentally the generation of spatially entangled photon pairs through
spontaneous parametric down-conversion from a metasurface incorporating a nonlinear thin film of lithium niobate
covered by a silica meta-grating. We measure the correlations of photon pairs and identify their spatial antibunching
through violation of the classical Cauchy-Schwarz inequality, witnessing the presence of multimode entanglement.
Simultaneously, the photon-pair rate is strongly enhanced by 450 times as compared to unpatterned films be-
cause of high-quality-factor resonances. These results pave the way to miniaturization of various quantum devices by
incorporating ultrathin metasurfaces functioning as room temperature sources of quantum-entangled photons.
INTRODUCTION
Quantum entanglement underpins a broad range of fundamental
physical effects (1) and serves as an essential resource in various
applications including quantum imaging (2), communications (3),
information processing, and computations (4). In optics, the most
common source of entangled photons is based on the spontaneous
parametric down-conversion (SPDC) process in quadratically non-
linear materials (5), which can operate at room temperature. The
generated photons can be entangled in transverse (6,7) and orbital
angular momenta (8), effectively accessing a large Hilbert space (9–11).
Strong transverse momentum entanglement was recently realized
with a micrometer-scale film of nonlinear material lithium niobate
(LiNbO3) (12), yet the compactness came at a cost of a strongly re-
duced generation rate. This leads to a fundamentally and practically
important research question on the potential for efficient genera-
tion of spatially entangled photons in ultrathin optical structures.
Over the past decade, marked enhancements of nonlinear
light-matter interactions were achieved in nanofabricated structures
with subwavelength thickness, known as metasurfaces (13,14), which
are also bringing advances to the field of quantum optics (15). An
enhancement of SPDC through localized Mie-type optical reso-
nances (16) in nanoantennas (17) and metasurfaces (18) was exper-
imentally demonstrated. Recent theoretical studies (19–21) suggested
that using metasurfaces with nonlocal lattice resonances (22,23) can
further boost the SPDC efficiency, yet the realization of this concept
remained outstanding.
In this work, we demonstrate experimentally, that strongly
enhanced generation of spatially entangled photon pairs can be
achieved from metasurfaces supporting nonlocal resonances at the
signal and idler in the telecommunication band around the 1570-nm
wavelength. The SPDC enhancement of ∼450 times compared with
unpatterned film and the coincidence-to-accidental ratio (CAR)
of ∼5000 are an order of magnitude higher than what has been
possible to date (18), benefiting from the nonlocal feature of the
resonances. This is the foundation for the preparation of strongly
entangled quantum states with a much higher spectral and spatial
brightness compared to localized resonances. Our experiments in-
dicate spatial entanglement of photon pairs by violating the classi-
cal Cauchy-Schwarz inequality (CSI), confirming the practical
path for the preparation of high-quality entanglement sources with
metasurfaces.
RESULTS
Concept and modeling
We develop a nonlocal metasurface based on the LiNbO3-on-insulator
platform, which was recently used for various applications includ-
ing electro-optic modulation (24,25) and classical optical frequency
conversion (26). The LiNbO3 material features large second-order
susceptibility, low fluorescence, and high optical transmission in a
broad wavelength range (27,28), which are essential for the quality
of generated photon pairs. We design a periodic SiO2 grating on top
of a lithium niobate film with subwavelength thickness (t ≃ 304 nm),
as schematically illustrated in Fig.1A.
We select the x cut of LiNbO3 and orient the grating along the
z axis of the film, such that the efficiency of SPDC is maximized when
the pump beam and emitted photons are linearly polarized along the
z axis, because of its highest nonlinear tensor coefficient 
zzz
(2) . Note
that this design does not require nanopatterning of the LiNbO3
film, in contrast to Mie-resonant metasurfaces (18), thereby avoid-
ing possible damage at the edges while preserving the total volume
of the nonlinear material.
The grating supports guided-mode resonances inside the LiNbO3
layer when the transverse wave number determined by the incident
wave and the grating matches the propagation wave number of the
slab modes (29–31). This physical mechanism underpins a strongly
nonlocal response since the resonant excitations can spread out in-
plane through the guided waves (32–34). Mathematically, the non-
locality in space is intrinsically linked to the presence of angular
1ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS),
Research School of Physics, The Australian National University, Canberra, ACT
2601, Australia. 2Advanced Optics and Photonics Laboratory, Department of
Engineering, School of Science and Technology, Nottingham Trent University,
Nottingham NG11 8NS, UK.
†Co-first authors with equal contribution.
*Corresponding author. Email: andrey.sukhorukov@anu.edu.au
Copyright © 2022
The Authors, some
rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. No claim to
original U.S. Government
Works. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).
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Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
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dispersion. We first discuss the key features by considering a case of
the incident plane wave wherein transverse wave number along the
grating is vanishing, i.e., kz = 0. In the weak-grating regime, which
does not exactly apply to metasurfaces yet captures the essential
physics, the first-order resonance happens when the following con-
dition is satisfied (35,36)
2
─
a ± sin  y
2
─
 = n eff
2
─
 (1)
where a is the period of the grating, y is the incident angle of the
input plane wave in the y-x plane,  is the wavelength in vacuum,
neff is the effective index of the waveguide mode in the LiNbO3 film,
and the sign ± corresponds to the two guided modes propagating in
opposite directions along the y axis. Equation 1 indicates the pres-
ence of two resonant wavelengths at  = a(neff ± sin y), which
depend on the incident angle and can be controlled by selecting the
period of the grating.
We determine an approximate grating period for the target
photon-pair wavelengths in the telecommunication band using
Eq. 1 and then fine-tune the structure parameters by performing
finite-element modeling of Maxwell’s equations to also facilitate
electromagnetic field localization inside the LiNbO3 layer. The op-
timized geometry is sketched in the inset of Fig.1A. We present the
characteristic transmission spectra in Fig.1B at normal and tilted
incidence as indicated by labels and show the dependencies of the
resonant eigenfrequencies () and bandwidths defined by the loss
coefficients (2) of the quasi-normal modes on the transverse wave
numbers along the y axis in Fig.1C. The corresponding quality fac-
tors of the resonances are Q = /(2).
Let us first analyze the mode features at the  point, i.e., ky = 0.
There is a small frequency splitting because of a second-order grating
scattering that is not captured by simplified Eq. 1. The lower-
frequency mode 1 has zero bandwidth and thus an infinite quality
factor. We check that this mode has an antisymmetric electric field
profile (see fig. S1), indicating its origin as a symmetry-protected
extended bound state in the continuum (BIC) (37). The single reso-
nant transmission dip at normal incidence (Fig.1B) corresponds to
an excitation of a bright mode 2, which has a quality factor of ≃500.
As shown in the inset, the mode has a symmetric standing-wave
intensity profile because of the interference of equally excited coun-
terpropagating guided modes.
For an incident angle of 1∘, with ky ≃ 0.07rad/m, two transmis-
sion dips appear at both sides of the resonance at ky = 0. The weakly
modulated intensity profiles shown in the insets of Fig.1B indicate
the dominance of one guided mode, in agreement with the general
properties of lattice resonances. For both modes 1 and 2, a strong
intensity enhancement of up to 600 times is observed inside the
LiNbO3 layer, which can accordingly increase the efficiency of the
nonlinear processes including second harmonic generation (SHG)
and SPDC as we demonstrate in the following.
The high Q-factors are retained for a broad range of incidence
angles, while the two resonance frequencies move further apart for
ky (rad/µm)
-
0.1
-
0.05 00.050.1
188
189
190
191
192
193
1594.6
1586.2
1577.9
1569.6
1561.4
1553.3
Wavelength (nm)
Frequency (THz)
Mode 2
Mode 1
Idler Signal
E
1560 1563 1566 1569 1572 1575
1560
1563
1566
1569
1572
1575
Signal wavelength (nm)
0
1
2
3
4
5
6
7
Pump wavelength 2 (nm)
×
-
0.2
-
0.100.1 0.2
-
0.2
-
0.1
0
0.1
0.2
0
200
400
600
800
t
h
a
Pump
Signal Idler
xz
y
SiO2
LiNbO3
A
D
d
Wavelength (nm)
Transmission
B
C
F
1545 1555 1565 1575 1585 1595
0
0.2
0.4
0.6
0.8
1
Incident
angle
°
°
Pump wavelength 2 (nm)
×
1560 15631566 15691572157
5
0
5
10
15
20
SPDC rate (Hz/mW)
Plane-wave
pump Gaussian
pump
k
y
(rad/µm)
kz (rad/µm)
Hz·µm2/mW
|Ez/E0|2
0
100
200
300
400
500
600
1/mW
Fig. 1. Nonlocal metasurfaces for efficient generation of spatially entangled photon pairs. (A) Sketch of spatially entangled signal and idler photon generation from
a LiNbO3 thin film covered by an SiO2 grating and pumped by a continuous laser. The optical axis of LiNbO3 and the grating are along the z direction. Inset shows the di-
mensions of the metasurface (not to scale), which we choose as a = 890 nm, d = 550 nm, h = 200 nm, and t = 304 nm. (B) Simulated transmission spectra of the metasurface
for z-polarized light, showing a single guided-mode resonance at normal incidence and two resonances with a nonzero incident angle. This angular dependent transmis-
sion features a nonlocal response. The insets are the field intensity at the resonances, showing strong field enhancement in the LiNbO3 layer. (C) Simulated eigenfrequen-
cies of resonances versus the transverse wave number ky at kz = 0. The shaded regions represent the bandwidth of the resonances. Signal and idler photons produced
symmetrically relative to the  point satisfy both the energy and transverse momentum conservation, when half the pump frequency p is within the resonance range.
The black dashed line marks p/2 = 191.19 THz, which is slightly blue-detuned from the normal incidence resonance of the bright mode 2. (D) Predicted photon emission
rate at the marked pump frequency as a function of transverse wave numbers. The black dashed line indicates the momentum matching conditions for the degenerate
SPDC. (E) Spectra of the signal photons for different pump frequencies. (F) The total emission rate after integrating over the signal spectrum for plane-wave and Gaussian
(100-m-diameter) pump beam. The vertical dashed lines in (E) and (F) relate to the pump frequency marked in (C).
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Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
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the larger values of ∣ky∣. This dispersion dependence defines the
group velocity of the quasi-guided modes in the lithium niobate lay-
er, g = ∂/∂ky. Noting that the characteristic mode lifetime where
the intensity decreases by a factor of 2 can be found as  ≃ ln(2)/
(2) = ln(2)Q/, we estimate the propagation distance in the y
direction of the quasi-guided mode 2 at ky ≃ 0.07rad/m as g ≃
71m. The latter value represents approximately 80 grating periods,
confirming a strongly nonlocal nature of the metasurface resonances.
In addition to the high-quality resonances, both the energy and
transverse momentum conservation conditions need to be satisfied
in the SPDC process of photon-pair generation. We designed the
meta-grating to satisfy an in-plane symmetry y → −y, such that the
resonances at ky and −ky appear at the same frequency. This proper-
ty allows the simultaneous fulfillment of phase and energy match-
ing of a spectral-degenerate SPDC process when the half-frequency
of a normally incident pump is in the guided mode resonance range.
For example, the black dashed line in Fig.1C corresponds to a
pump frequency p = 2 × 191.19 THz. Accordingly, the frequency
of the resonantly enhanced signal and idler photons and their emis-
sion angles can be controlled by tuning the pump frequency, which
allows one to tailor the spectrum and spatial entanglement of the
photon pairs.
The SPDC emission can occur over a range of transverse momenta
and photon frequencies, and accordingly, the associated quantum
biphoton states belong to a high-dimensional Hilbert space. Their
modeling requires fast and accurate simulation methods. For this
purpose, we adopt a coupled mode theory (CMT) (38,39) approach
to our metasurface design and verify that it precisely describes the
metasurface resonances, including all the angular and frequency
features (see section S1). We then use the CMT to efficiently simu-
late the sum frequency generation (SFG) process and calculate the
SPDC emission via quantum-classical correspondence (17,19).
Figure1D shows the predicted photon-pair rate integrated over their
frequency spectra versus the transverse momenta in the metasurface
plane, for a normally incident plane-wave pump with the frequency
p = 2 × 191.19 THz. The elongated emission pattern in the z direc-
tion reflects a weak quadratic dispersion dependence on kz (see fig.
S2). We mark with the black dashed line the transverse phase-matching
condition at the center of mode resonances, which aligns with the
emission peaks.
We present the dependence on the pump frequency of the photon
spectra integrated over all emission angles in Fig.1E and the total
emission rate in Fig.1F. Here, the frequency range corresponding
to the excitation of mode 2 is shown, while similar features are ob-
served for mode 1 away from the band edge, where tunable off-
normal photon emission can be achieved. The vertical dashed lines
correspond to the pump frequency p = 2 × 191.19 THz, at which
the highest total rate is predicted. The corresponding degenerate
photon frequencies are slightly blue-detuned from the bright mode
2 resonance at normal incidence, since in the latter case, the Q-factor
is lower and quadratic band-edge dispersion affects the phase matching.
We find that the SPDC rate can be enhanced by over two orders of
magnitude compared with an unpatterned LiNbO3 film of the same
thickness, with an even stronger increase in spectral brightness (see
fig. S4). The enhancement is preserved under the practical experi-
mental conditions of a Gaussian beam pump rather than an ideal-
ized plane wave, as shown in Fig.1F.
It is a remarkable feature that the enhanced photon rate stays
practically constant as the pump wavelength is decreased. The tuning
range of the signal and idler wavelengths, determined by twice the
pump wavelength, can be up to hundreds of nanometers without
temperature adjustment. These properties are facilitated by the
nonlocal metasurface resonances, in which dispersion also mediates
the tunability of the emission angles, offering great flexibility for
future applications.
Experimental characterization: Metasurface resonances
and enhanced SHG
We fabricate the metasurface by electron beam lithography and
etching processes as described in Materials and Methods. The scan-
ning electron microscopy (SEM) image of the meta-grating is shown
in Fig.2A, which confirms that the dimensions closely match the
optimal design geometry according to our theoretical analysis. The
experimental transmission measurements (Fig.2B and fig. S6) of
the metasurface identify a resonance at 1570.5nm with a bandwidth
of 3.5nm and a quality factor Q ∼ 455, for a normally incident light.
Note that another shallow dip at 1580nm corresponding to the
dark mode 1 resonance is also visible at normal incidence, because
the white light source has a finite angular range, and fabrication
imperfections break the symmetry and transform the mode into
a quasi-BIC one. Two resonances with a visible spectral splitting
manifest at a nonzero incidence angle. The observed angular disper-
sion confirms the nonlocal origin of resonances in agreement with
the theoretical modeling presented above.
The classical nonlinear effects, SHG and SFG, can be regarded as
the reverse processes of the SPDC (17,19). It was recently estab-
lished that SHG and SFG can occur in LiNbO3 thin films (40,41)
and can be enhanced in metasurfaces with Mie-type resonances
(42–45). Here, we test the nonlinearity enhancement by exploring
the SHG from the nonlocal metasurface, using the experimental
setup sketched in Fig.2C. The SHG is triggered with a femtosecond
laser whose central wavelength is tunable from 1540 to 1580nm. In
all SHG experiments, the laser is normally incident onto the sample
from the grating side.
We compare the efficiency of the SHG from the metasurface and
unpatterned film in Fig.2D and register up to 50 times the enhance-
ment. For both cases, the polarization of the incident laser is oriented
along the z axis of the nonlinear film to make use of the highest
nonlinear tensor coefficient 
zzz
(2) and maximize the SHG efficiency.
Note that the pulsed laser bandwidth is 23 nm, which is larger than
the linewidth of the metasurface resonances, significantly limiting
the measured enhancement. In addition, we characterize the SHG
enhancement by laser pulses with different central wavelengths (see
Fig.2E). The optimal enhancement is observed when the pulse cen-
tral wavelength sits within the bright-mode resonance of the meta-
surface. These results confirm the high quality of the fabricated
metasurfaces, which strongly boost nonlinear wave mixing in the
LiNbO3 layer because of nonlocal resonances according to our
theoretical concept.
Quantum measurements: Enhanced photon-pair generation
and spatial entanglement
We now proceed with the experimental investigations of the quan-
tum photon-pair generation. A setup sketch for characterizing
the SPDC is shown in Fig.3A. The metasurface is pumped with a
continuous-wave laser tunable around the 785-nm wavelength with a
beam diameter of ∼100 m. The correlations of photon pairs gen-
erated from the metasurface are analyzed with a Hanbury Brown–Twi ss
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Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
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setup, using a 50:50 multimode fiber beam splitter and two single-
photon detectors based on InGaAs/InP avalanche photodiodes (see
Materials and Methods).
The measured coincidences of photon pairs from the metasur-
face for different time delays between the detectors are displayed
in Fig.3B. We obtain a coincidence rate of 1.8Hz at a pump power
of 85 mW, corresponding to a photon generation efficiency of
21 mHz/mW. The efficiency of single-photon detectors calibrated
by the manufacturer is 25%, and the collection efficiency for each
photon is estimated as 25 to 30%, which results in an overall detec-
tion efficiency of 0.4 to 0.6% for the photon pairs. This suggests a
photon-pair emission rate of 2.3 to 3.5 Hz/mW from the metasur-
face over a collection angle range calibrated as ∼0. 7∘, which closely
agrees with the theoretical predictions (see fig. S3C).
For comparison, we also measure the photon-pair rate from an
unpatterned LiNbO3 film under the same experimental conditions,
which is found to be 0.047 mHz/mW at zero delay. On the basis
of the peak values of the histograms shown in Fig.3B, we identify a
rate enhancement of 450 times from the metasurface compared
to an unpatterned film, which agrees with the numerical modeling
(see fig. S4B). Our theory also predicts that the generated photon
pairs have a narrow bandwidth of ∼3 nm, and the spectral brightness
enhancement at the central wavelength is ∼1400 times (see fig. S4A).
We confirm that the measured coincidences can be attributed to
the generation of nonclassical photon pairs by analyzing the second-
order correlation function g(2)(0). For the resonantly enhanced emis-
sion from the metasurface, g(2)(0) reaches the value of ∼5000 (see
fig. S8A). The corresponding coincidence to accidental ratio (CAR =
g(2)(0) − 1) is ∼ 5000, which is over three orders of magnitude larger
than the classical bound of 2. Both the measured rate enhancement
and CAR in our metasurface, which are independent of the detector
and collection efficiencies, are an order of magnitude higher than
previously reported for photon-pair generation from nonlinear
metasurfaces with localized Mie resonances (18). These enhanced
rates are the foundation for the preparation of strongly entangled
quantum states with a much higher spectral and spatial brightness
(19,21) compared to localized resonances.
The SPDC efficiency is expected to nontrivially depend on the
pump wavelength, reflecting the pronounced dispersion of the non-
local metasurface resonances. We collect the real coincidence (total
peak coincidence with subtracted accidental coincidences) for dif-
ferent pump wavelengths, as shown in Fig.3C (red dots with error
bars), where the horizontal axis indicates the degenerate signal/idler
wavelength, i.e., two times of the pump wavelength. The data points
are taken with different wavelength steps determined by the tuning
characteristics of the pump laser (see section S2.3). The maximum
coincidence is found when the degenerate wavelength is slightly
blue-detuned from the bright-mode resonance at normal incidence
(gray curve), which is consistent with the theoretical predictions in
Fig.1F. We fit the experimental data to the formulated CMT with
two free parameters, the collection angle and overall detection effi-
ciency. The fitting results indicate a collection angle of 0.68∘ and a
total detection efficiency of 0.4%, which is a good match with the
experimental parameters presented above.
Experimental measurements confirm that the enhanced photon-
pair rate remains close to its maximum over a broad span of pump
wavelengths, when the spatial emission is within the range of collec-
tion angles. This efficient spectrum tunability of photon pairs is a
distinguishing feature of our metasurface with nonlocal resonances,
where the transverse phase matching is satisfied for a continuous set
z
x
y
Laser
HWP
Metasurface
Filter
Polarizer
Spectrometer
M
a
x
S
H
G
i
n
t
e
n
s
i
t
y
(a
.
u
.
)
Central wavelength (nm)
1550 1560 1570 1580
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
T
r
a
n
s
m
i
s
s
i
o
n
0 0.5 11.5 2 2.5 3
Incident angle (°)
1500
1520
1540
1560
1580
1600
1620
Wavelength (nm)
0.7
0.8
0.9
Wavelength (nm)
0
0.2
0.4
0.6
0.8
1.0
SHG spectrum (a.u.)
760770 780790 800810
A
x
z
y
B
C
DE
Metasurface
Unpatterned
film
Fig. 2. Classical experiment: Linear transmission and enhanced SHG of the nonlocal metasurface. (A) SEM image of the fabricated dielectric meta-grating on top of
an x-cut 304-nm-thick lithium niobate film. (B) Measured linear transmission as a function of incident angle and wavelength. The resonance is nearly degenerate at normal
incidence and shows a mode splitting at a larger angle. The transmission is measured with a tungsten-halogen broadband lamp. (C) Experimental setup for SHG. The
metasurface is pumped with femtosecond laser pulses from the grating side, with a tunable central wavelength and a bandwidth of 23 nm. The SHG signal is collected
with a spectrometer. (D) SHG spectra from metasurface (red curve) and unpatterned film (blue curve). The SHG intensity is normalized to its maximum from the metasur-
face. (E) Normalized peak SHG intensity versus the central wavelength of the input pulses. The shaded gray curve shows the Fano fitting of the metasurface transmission
measured with a tunable continuous-wave laser (1500 to 1575 nm) at normal incidence (see fig. S6). This measurement shows a narrower band but a higher resolution as
compared with the results obtained from the lamp. The red dots are maximum SHG intensity extracted from SHG spectra obtained at different pulsed laser central wave-
lengths, and the red line is the corresponding spline fitting. The optimal enhancement is found near the optical resonance. a.u., arbitrary units.
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Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
5 of 8
of pump wavelengths, while there are no limitations due to longitu-
dinal phase matching in contrast to bulk nonlinear crystals.
Next, we analyze the dependence of the SPDC on the pump po-
larization by rotating the half-wave plate (HWP) placed before the
metasurface and measuring the photon coincidences with a linear
polarizer placed after the metasurface oriented in the y or z direc-
tion. We show in Fig.3D that the real coincidence count is strongly
dependent on the pump polarization when the polarizer is parallel
to the z axis (LiNbO3 optical axis); meanwhile, almost no photons
are detected at any pump polarization angle when the polarizer is
rotated along the y axis. That is, the coincidence rate is maximized
when both the pump and emitted photon pairs are polarized along
the z axis of the film, when the nonlinear wave mixing is mediated
by the strongest quadratic susceptibility tensor component of LiNbO3.
The visibility of the polarization dependence is estimated to be above
99%, benefiting from the selective resonant enhancement of the
SPDC for the photon polarizations along the grating direction ac-
cording to our metasurface design.
Last, we experimentally confirm the spatial entanglement of the
photon pairs by selectively blocking photons with an aperture. Such
measurements allow us to reveal the presence of nonclassical cor-
relations between the photons at different spatial regions. We use
a square aperture placed after the photon emission (Fig.4A) and
translate it transversely in the y or z direction. The width of the ap-
erture is L = 4.5 mm, which is chosen to be larger than the aperture
of the collected photons (Fig.4B). The real two-photon coincidences
C(q) as a function of the aperture position q (q = y or q = z) are
presented in Fig.4 (C and D). Note that at q = 0, the center of the
aperture is aligned with the center of the beam. The diameters of the
collected beam dq (q = y, z), which are estimated by subtracting the
aperture width from the flat plateau region of the correlation curves
in Fig.4 (C and D), are dy = 0.55L and dz = 0.65L, respectively.
Let us consider a counterexample of classical light correlations,
which should satisfy the CSI that, for our setup, can be formulated
as (see section S3)
( q s ) ≡
(
√
_
C( q s − L / 2) +
√
_
C( q s + L / 2)
)
2 ≥ C(0) (2)
Here, C(qs − L/2) and C(qs + L/2) represent the two-photon co-
incidences within the two complementary emission regions A1 and
A2 separated at the position qs, as sketched in Fig.4B. The CSI can
be violated for quantum states, when (qs) < C(0), indicating non-
classical spatial correlations and multimode spatial entanglement (46).
The underlying physics can be interpreted as the spatial analog of
the photon antibunching effect (47). The quantities on the left-hand
side of Eq. 2 are proportional to the self-correlations within the re-
gions A1 or A2 and when their quadratic combination is below the
total correlations over the whole beam C(0), it means that the
cross-correlations between regions A1 and A2 are higher than what
is possible classically.
We identify the violation of CSI by applying Eq. 2 to the correlation
measurements from Fig.4 (C and D) and present the values of (qs) in
Fig.4 (E and F). For convenience, we normalize the data such that the plotted
value of C(0) is unity, which defines the classical bound. We see that (qs)
is significantly lower than the classical bound by over 3 standard deviations
(SDs) for a broad range of spatial region boundaries, −0.2 < qs/L < 0.2.
050100 150200 250 30
0350
Pump polarization (°)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Coincidence (Hz)
A
CD
Laser
HWP
Metasurface
Filters
Polarizer
SPAD
SPAD
Beam splitter
z
y
x
z axis
y axis
Photon polarization
1564 1566 1568 1570 1572 1574
50
100
150
200
Coincidence (5 min)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Transmission
Pump wavelength 2 (nm)
×
Experiment
Theory
Ex
p
erimen
t
Theor
y
−4 −3 −2 −1 01 23
4
Delay (ns)
0
50
100
150
200
Coincidence (2 min)
Metasurface
Unpatterned film
Sample
B
Fig. 3. Quantum experiment: Enhanced generation of photon pairs from the nonlocal metasurface. (A) Setup for SPDC. A laser beam with a wavelength at 785 nm
is focused on a metasurface fabricated on top of a lithium niobate film to produce photon pairs. The photon pairs pass through a 50:50 fiber beam splitter, and their
coincidence is then registered by two single-photon detectors. (B) Coincidence histograms of SPDC from metasurface (blue bar) and unpatterned film (gray bar). The gray
bar is obtained via the integration time of 2 hours, which is 60 times longer than the measurement of the blue bar. (C) Real coincidence as a function of the degenerate
signal/idler wavelength, which is two times the pump wavelength. The experiment (dots with error bars) shows a good agreement with the theoretical result (solid line).
Error bars indicate 2 SD (standard deviation). The transmission curve (gray) is the same as the one given in Fig. 2E. (D) Real coincidence as a function of pump polarization.
Points and lines are experimental results and theoretical fitting, respectively, for the photon-pair polarization along the z or y axis of the film as indicated in the inset.
Error bars indicate 1 SD. The pump powers used for (B) to (D) are 85, 35, and 75 mW, respectively.
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Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
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Let us estimate the degree of spatial antibunching for the case of
qs = 0, when half of the photons are blocked in either the horizontal
or vertical direction (at q = ± L/2 aperture positions). Then, for
the photon emission with the spatial reflection symmetry following
from the symmetric metasurface design, Eq. 2 simplifies to (0) =
4C( ± L/2) ≥ C(0). We see in Fig.4 (C and D) that the coincidence
rate drops by more than four times (within the area marked by
shading) at q = ± L/2, providing an additional visual confirmation
of CSI violation. Specifically, the rate reduces by a factor of ∼13 along
the y (∼6 along z) direction at q = L/2. The corresponding cross-
correlations between the half-beam regions, which we estimate
using eq. S23, are larger than the self-correlations by a factor of
5.5 for the y (∼2 for z) direction, confirming the pronounced spatial
antibunching.
These results demonstrate a noticeable difference between the
emission directions. Specifically, the correlation function (qs) values
at qs = 0 are 0.3C(0) and 0.5C(0) for the y and z directions, respec-
tively. The larger CSI violation for the y direction agrees with the
stronger antibunching estimated above. This suggests the presence
of stronger spatial entanglement along the y compared to the z
direction, which might be related to the off-normal emission of
photons in the y direction according to the theoretical predictions
shown in Fig.1D.
DISCUSSION
In summary, we have proposed and experimentally demonstrated
that enhanced generation of quantum photon-pair states can be fa-
cilitated through specially designed meta-gratings fabricated on top
of a lithium niobate film with a subwavelength thickness. The meta-
surface supports nonlocal resonances that allow transverse phase
matching of SPDC and the simultaneous control of the angular
emission pattern over a broad pump wavelength tuning range,
while the longitudinal matching requirements are removed because
of an ultrasmall thickness. These unique features strongly enhance
the photon-pair generation rate by over ∼450 times compared to
unpatterned structures, while the CAR reaches ∼5000, demonstrat-
ing the high quality of quantum states. Our metasurface platform
can lead to even higher photon rates and brightness by increasing
the quality factor of optical resonances through improvements in
the nanofabrication precision.
The generated photons can be strongly entangled in space while
being almost indistinguishable in other degrees of freedom. In par-
ticular, we detect a purely linear polarization state of the photons
with a high extinction ratio above 99%, which is achieved by design-
ing the grating to selectively enhance the electric field component
along the optical axis of the nonlinear film. On the other hand, the-
oretical modeling predicts a near-degenerate narrow emission spec-
trum of about ∼3nm. We experimentally characterized the spatial
correlations of photon pairs by partially blocking the emission with
an aperture and detected the violation of classical CSI, which serves
as a criterion of spatial antibunching and multimode entanglement.
We anticipate that future developments of this ultrathin platform,
including the incorporation of inhomogeneous and two-dimensional
meta-grating patterns, can allow even more flexibility in enhanc-
ing and shaping the photon emission and entanglement, paving the
way toward various applications such as quantum imaging.
MATERIALS AND METHODS
Numerical simulations
The simulations of transmission spectra and eigenfrequencies
are performed on the basis of the finite-element method by using
the Comsol Multiphysics software package. The fitting of the CMT
parameters and calculation of SPDC rate with CMT are done
in MATLAB.
Metasurface
Lens
Aperture
z
y
x
L = 4.5 mm
z
A
B
y
A1A2
0
Signal Idler
0
0.25
0.5
0.75
1
Real coincidence (a.u.)
−0.75 −0.5 −0.25 0 0.25 0.5 0.75
0
0.25
0.5
0.75
1
Real coincidence (a.u.)
0
0.2
0.4
0.6
0.8
1
−0.4−0.2 0 0.2
0.4
0
0.2
0.4
0.6
0.8
1
C
D
E
F
Classical bound
Classical bound
Fig. 4. Spatial entanglement of photon pairs. (A) Square aperture with a size of L × L (L = 4.5 mm) is introduced after the metasurface to characterize the spatial correla-
tions of photon pairs. (B) The aperture size is larger than the profile of the collected beam determined by the size of the fiber collection lens. The position where the
centers of the beam and the aperture are aligned is defined as zero. We characterize the correlations for the spatial regions A1 and A2 separated at the position qs. (C and
D) The real coincidence rate of collected photon pairs versus the aperture position along the y and z directions, normalized to the maximum value. The blue-shaded areas
indicate the violation of CSI at q = ± L/2. Error bars indicate 1 SD. (E and F) Violation of CSI for values below the classical bound. Error bars indicate 3 SD, corresponding to
>99.7% confidence interval.
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Zhang et al., Sci. Adv. 8, eabq4240 (2022) 29 July 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
7 of 8
Metasurface fabrication
The designed metasurface was fabricated in a cleanroom starting
from an LiNbO3 film on quartz substrate from NANOLN. After
ultrasonic cleaning, a thin layer of SiO2 with a thickness of 200nm
was deposited on the sample by plasma-enhanced chemical vapor
deposition. Then, polymethyl methacrylate (PMMA) was spin-coated
as the resist for the subsequent electron beam lithography. After
lithography, a thin layer of nickel with a thickness of 30nm was coated
by electron beam deposition followed by a lift-off process. The nickel
pattern was used as the mask for etching of the SiO2 layer by induc-
tively coupled plasma etching. With the chemical of CHF3 and pres-
sure of 0.1 Pa, the etching rate was calibrated to be ∼1.2 nm/s. Last,
the residual nickel mask was removed by chemical etching. The size
of the grating is 400mby400m.
Second harmonic characterization
The femtosecond laser (Chameleon Compact OPO, Coherent) used
to characterize the SHG from metasurface is set with the following
parameters: beam diameter of ∼100 m, power of 10 mW, pulse
width of 200 fs, linewidth of 23 nm, and repetition rate of 80MHz.
We use a lens with a focal length of 150mm to focus the laser and
an objective of 20× to collect the signal. The laser beam transmitting
through the metasurface is removed with a short-pass filter before
the signals are sent to the spectrometer.
SPDC experiments
The laser exciting the SPDC process is emitted from a Fabry-Perot
laser diode (FPL785P, Thorlabs). The laser wavelength can be tuned
from 780 to 790 nm, with a linewidth of ∼0.1nm. A short-pass filter
at 850nm before the metasurface and a long-pass filter at 1100nm
along with a band-pass filter at 1570nm (with a 50-nm full width at
half maximum) after metasurface suppress the fluorescence produced
by the metasurface and other optics. Two lenses with a focal length
of 100mm are used to focus the pump beam and collimate the pho-
tons emitted from the metasurface. The photon pairs are collected
with a multimode fiber and are probabilistically split into two opti-
cal paths with a 50:50 fiber beam splitter. The photons are registered
with two single-photon detectors based on Indium gallium arsenide/
Indium phosphide (InGaAs/InP) avalanche photodiodes (ID230,
IDQ). The detection events are characterized by a time-to-digital
converter (ID801, IDQ), whose coincidence window is set at 0.486 ns.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at https://science.org/doi/10.1126/
sciadv.abq4240
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Acknowledgments
Funding: We acknowledge the support by the Australian Research Council (DP190101559 and
CE200100010). Author contributions: A.A.S., L.X., and D.N.N. developed the theoretical
concept. J.Z. and M.P. performed the numerical modeling. J.Z. fabricated the sample and
performed the linear transmission measurement. J.M., M.C., and R.C.-M. developed the
experimental setup, performed the measurements, and processed the data. A.A.S. and D.N.N.
supervised the project. All authors analyzed the results and cowrote the paper. Competing
interests: The authors declare that they have no competing interests. Data and materials
availability: All data needed to evaluate the conclusions in the paper are present in the paper
and/or the Supplementary Materials.
Submitted 8 April 2022
Accepted 15 June 2022
Published 29 July 2022
10.1126/sciadv.abq4240
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Spatially entangled photon pairs from lithium niobate nonlocal metasurfaces
Jihua ZhangJinyong MaMatthew ParryMarcus CaiRocio Camacho-MoralesLei XuDragomir N. NeshevAndrey A.
Sukhorukov
Sci. Adv., 8 (30), eabq4240. • DOI: 10.1126/sciadv.abq4240
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