Assisted by the rapid development of photonic integrated circuits, scalable and versatile chip-based quantum light sources with nonlinear optics are increasingly tangible for real-world applications. In this review, we introduce the basic concepts behind parametric photon pair sources and discuss the current state-of-the-art photon pair generation in detail but also highlight future perspectives in hybrid integration, novel waveguide structures, and on-chip multiplexing. The advances in near-deterministic integrated photon pair sources are deemed to pave the way for the realization of large-scale quantum photonic integrated circuits for applications, including quantum telecommunication, quantum sensing, quantum metrology, and photonic quantum computing.

1.
J. L.
O'Brien
,
A.
Furusawa
, and
J.
Vučković
, “
Photonic quantum technologies
,”
Nat. Photonics
3
,
687
(
2009
).
2.
J.
Wang
,
F.
Sciarrino
,
A.
Laing
, and
M. G.
Thompson
, “
Integrated photonic quantum technologies
,”
Nat. Photonics
14
,
273
284
(
2020
).
3.
J. P.
Dowling
and
G. J.
Milburn
, “
Quantum technology: The second quantum revolution
,”
Philosoph. Trans. Roy. Soc. London. Ser. A: Math. Phys. Eng. Sci.
361
,
1655
1674
(
2003
).
4.
M. A.
Nielsen
and
I.
Chuang
, “
Quantum computation and quantum information
,” (
2000
).
5.
V.
Giovannetti
,
S.
Lloyd
, and
L.
Maccone
, “
Advances in quantum metrology
,”
Nat. Photonics
5
,
222
(
2011
).
6.
A.
Steane
, “
Quantum computing
,”
Rep. Prog. Phys.
61
,
117
(
1998
).
7.
J. L.
O'Brien
, “
Optical quantum computing
,”
Science
318
,
1567
1570
(
2007
).
8.
C. L.
Degen
,
F.
Reinhard
, and
P.
Cappellaro
, “
Quantum sensing
,”
Rev. Modern Phys.
89
,
035002
(
2017
).
9.
S.
Pirandola
,
B. R.
Bardhan
,
T.
Gehring
,
C.
Weedbrook
, and
S.
Lloyd
, “
Advances in photonic quantum sensing
,”
Nat. Photonics
12
,
724
733
(
2018
).
10.
N.
Gisin
and
R.
Thew
, “
Quantum communication
,”
Nat. Photonics
1
,
165
(
2007
).
11.
A. W.
Elshaari
,
W.
Pernice
,
K.
Srinivasan
,
O.
Benson
, and
V.
Zwiller
, “
Hybrid integrated quantum photonic circuits
,”
Nat. Photonics
14
,
336
(
2020
).
12.
J.-H.
Kim
,
S.
Aghaeimeibodi
,
J.
Carolan
,
D.
Englund
, and
E.
Waks
, “
Hybrid integration methods for on-chip quantum photonics
,”
Optica
7
,
291
308
(
2020
).
13.
S.
Tanzilli
,
A.
Martin
,
F.
Kaiser
,
M. P.
De Micheli
,
O.
Alibart
, and
D. B.
Ostrowsky
, “
On the genesis and evolution of integrated quantum optics
,”
Laser Photonics Rev.
6
,
115
143
(
2012
).
14.
B.
Jalali
and
S.
Fathpour
, “
Silicon Photonics
,”
J. Lightwave Technology
24
,
4600
(
2006
), available at https://ieeexplore.ieee.org/document/4063407.
15.
J.
Leuthold
,
C.
Koos
, and
W.
Freude
, “
Nonlinear silicon photonics
,”
Nat. Photonics
4
,
535
544
(
2010
).
16.
J. W.
Silverstone
,
D.
Bonneau
,
J. L.
O'Brien
, and
M. G.
Thompson
, “
Silicon quantum photonics
,”
IEEE J. Sel. Top. Quantum Electron.
22
,
390
402
(
2016
).
17.
S.
Bogdanov
,
M. Y.
Shalaginov
,
A.
Boltasseva
, and
V. M.
Shalaev
, “
Material platforms for integrated quantum photonics
,”
Opt. Mater. Express
7
,
111
132
(
2017
).
18.
M. D.
Eisaman
,
J.
Fan
,
A.
Migdall
, and
S. V.
Polyakov
, “
Invited review article: Single-photon sources and detectors
,”
Rev. Sci. Instr.
82
,
071101
(
2011
).
19.
L.
Caspani
,
C.
Xiong
,
B. J.
Eggleton
,
D.
Bajoni
,
M.
Liscidini
,
M.
Galli
,
R.
Morandotti
, and
D. J.
Moss
, “
Integrated sources of photon quantum states based on nonlinear optics
,”
Light: Sci. Appl.
6
,
e17100
e17100
(
2017
).
20.
A.
Orieux
,
M. A. M.
Versteegh
,
K. D.
Jöns
, and
S.
Ducci
, “
Semiconductor devices for entangled photon pair generation: A review
,”
Rep. Prog. Phys.
80
,
076001
(
2017
).
21.
R. W.
Boyd
,
Nonlinear Optics
(
Academic Press
,
2008
).
22.
Q.
Lin
,
O. J.
Painter
, and
G. P.
Agrawal
, “
Nonlinear optical phenomena in silicon waveguides: Modeling and applications
,”
Opt. Express
15
,
16604
16644
(
2007
).
23.
C.
Couteau
, “
Spontaneous parametric down-conversion
,”
Contemp. Phys.
59
,
291
304
(
2018
).
24.
X.
Cheng
,
M. C.
Sarihan
,
K.-C.
Chang
,
Y. S.
Lee
,
F.
Laudenbach
,
H.
Ye
,
Z.
Yu
, and
C. W.
Wong
, “
Design of spontaneous parametric down-conversion in integrated hybrid SixNy-PPLN waveguides
,”
Opt. Express
27
,
30773
30787
(
2019
).
25.
A.
Ling
,
A.
Lamas-Linares
, and
C.
Kurtsiefer
, “
Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes
,”
Phys. Rev. A
77
,
043834
(
2008
).
26.
Q.
Lin
,
F.
Yaman
, and
G. P.
Agrawal
, “
Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization
,”
Phys. Rev. A
75
,
023803
(
2007
).
27.
L. J.
Wang
,
C. K.
Hong
, and
S. R.
Friberg
, “
Generation of correlated photons via four-wave mixing in optical fibres
,”
J. Opt. B: Quantum Semiclassical Opt.
3
,
346
352
(
2001
).
28.
Q.
Lin
,
F.
Yaman
, and
G. P.
Agrawal
, “
Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization
,”
Phys. Rev. A
75
,
1
20
(
2007
).
29.
R. S.
Jacobsen
,
K. N.
Andersen
,
P. I.
Borel
,
J.
Fage-Pedersen
,
L. H.
Frandsen
,
O.
Hansen
,
M.
Kristensen
,
A. V.
Lavrinenko
,
G.
Moulin
,
H.
Ou
,
C.
Peucheret
,
B.
Zsigri
, and
A.
Bjarklev
, “
Strained silicon as a new electro-optic material
,”
Nature
441
,
199
202
(
2006
).
30.
X.
Lu
,
G.
Moille
,
A.
Rao
,
D.
Westly
, and
K.
Srinivasan
, “
Efficient photo-induced second harmonic generation in silicon photonics
,” arXiv:2003.12176 (
2020
).
31.
L.
Du
,
Y.
Dai
, and
Z.
Sun
, “
Twisting for tunable nonlinear optics
,”
Matter
3
,
987
988
(
2020
).
32.
S.
Tanzilli
,
H.
De Riedmatten
,
W.
Tittel
,
H.
Zbinden
,
P.
Baldi
,
M.
De Micheli
,
D. B.
Ostrowsky
, and
N.
Gisin
, “
Highly efficient photon-pair source using periodically poled lithium niobate waveguide
,”
Electron. Lett.
37
,
26
28
(
2001
).
33.
X.
Caillet
,
A.
Orieux
,
A.
Lemaître
,
P.
Filloux
,
I.
Favero
,
G.
Leo
, and
S.
Ducci
, “
Two-photon interference with a semiconductor integrated source at room temperature
,”
Opt. Express
18
,
9967
9975
(
2010
).
34.
J. W.
Silverstone
,
J.
Wang
,
D.
Bonneau
,
P.
Sibson
,
R.
Santagati
,
C.
Erven
,
J. L.
O'Brien
, and
M. G.
Thompson
, “
Silicon quantum photonics
,” in
Proceedings of the 2016 International Conference on Optical MEMS and Nanophotonics (OMN)
, Singapore (
IEEE
,
2016
) pp.
1
2
.
35.
H.
Takesue
,
Y.
Tokura
,
H.
Fukuda
,
T.
Tsuchizawa
,
T.
Watanabe
,
K.
Yamada
, and
S-i
Itabashi
, “
Entanglement generation using silicon wire waveguide
,”
Appl. Phys. Lett.
91
,
201108
(
2007
).
36.
C.
Xiong
,
X.
Zhang
,
A.
Mahendra
,
J.
He
,
D.-Y.
Choi
,
C. J.
Chae
,
D.
Marpaung
,
A.
Leinse
,
R. G.
Heideman
,
M.
Hoekman
,
C. G. H.
Roeloffzen
,
R. M.
Oldenbeuving
,
P. W. L.
van Dijk
,
C.
Taddei
,
P. H. W.
Leong
, and
B. J.
Eggleton
, “
Compact and reconfigurable silicon nitride time-bin entanglement circuit
,”
Optica
2
,
724
727
(
2015
).
37.
S.
Atzeni
,
A. S.
Rab
,
G.
Corrielli
,
E.
Polino
,
M.
Valeri
,
P.
Mataloni
,
N.
Spagnolo
,
A.
Crespi
,
F.
Sciarrino
, and
R.
Osellame
, “
Integrated sources of entangled photons at the telecom wavelength in femtosecond-laser-written circuits
,”
Optica
5
,
311
314
(
2018
).
38.
R. A.
Soref
and
J. P.
Lorenzo
, “
Single-crystal silicon: A new material for 1.3 and 1.6 μm integrated-optical components
,”
Electron. Lett.
21
,
953
954
(
1985
).
39.
R.
Soref
, “
The past, present, and future of silicon photonics
,”
IEEE J. Select. Topics Quantum Electron.
12
,
1678
1687
(
2006
).
40.
D.
Thomson
,
A.
Zilkie
,
J. E.
Bowers
,
T.
Komljenovic
,
G. T.
Reed
,
L.
Vivien
,
D.
Marris-Morini
,
E.
Cassan
,
L.
Virot
,
J.-M.
Fédéli
,
J.-M.
Hartmann
,
J. H.
Schmid
,
D.-X.
Xu
,
F.
Boeuf
,
P.
O'Brien
,
G. Z.
Mashanovich
, and
M.
Nedeljkovic
, “
Roadmap on silicon photonics
,”
J. Opt.
18
,
073003
(
2016
).
41.
M.
Cazzanelli
,
F.
Bianco
,
E.
Borga
,
G.
Pucker
,
M.
Ghulinyan
,
E.
Degoli
,
E.
Luppi
,
V.
Véniard
,
S.
Ossicini
,
D.
Modotto
,
S.
Wabnitz
,
R.
Pierobon
, and
L.
Pavesi
, “
Second-harmonic generation in silicon waveguides strained by silicon nitride
,”
Nat. Mater.
11
,
148
154
(
2012
).
42.
H. K.
Tsang
and
Y.
Liu
, “
Nonlinear optical properties of silicon waveguides
,”
Semicond. Sci. Technol.
23
,
064007
(
2008
).
43.
T.
Vallaitis
,
S.
Bogatscher
,
L.
Alloatti
,
P.
Dumon
,
R.
Baets
,
M. L.
Scimeca
,
I.
Biaggio
,
F.
Diederich
,
C.
Koos
,
W.
Freude
, and
J.
Leuthold
, “
Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries
,”
Opt. Express
17
,
17357
17368
(
2009
).
44.
A.
Rahim
,
E.
Ryckeboer
,
A. Z.
Subramanian
,
S.
Clemmen
,
B.
Kuyken
,
A.
Dhakal
,
A.
Raza
,
A.
Hermans
,
M.
Muneeb
,
S.
Dhoore
,
Y.
Li
,
U.
Dave
,
P.
Bienstman
,
N. L.
Thomas
,
G.
Roelkens
,
D. V.
Thourhout
,
P.
Helin
,
S.
Severi
,
X.
Rottenberg
, and
R.
Baets
, “
Expanding the silicon photonics portfolio with silicon nitride photonic integrated circuits
,”
J. Lightwave Technol.
35
,
639
649
(
2017
).
45.
M. H. P.
Pfeiffer
,
J.
Liu
,
A. S.
Raja
,
T.
Morais
,
B.
Ghadiani
, and
T. J.
Kippenberg
, “
Ultra-smooth silicon nitride waveguides based on the Damascene reflow process: Fabrication and loss origins
,”
Optica
5
,
884
892
(
2018
).
46.
K.
Luke
,
A.
Dutt
,
C. B.
Poitras
, and
M.
Lipson
, “
Overcoming Si3N4 film stress limitations for high quality factor ring resonators
,”
Opt. Express
21
,
22829
22833
(
2013
).
47.
K.
Alexander
,
J. P.
George
,
J.
Verbist
,
K.
Neyts
,
B.
Kuyken
,
D.
Van Thourhout
, and
J.
Beeckman
, “
Nanophotonic Pockels modulators on a silicon nitride platform
,”
Nat. Commun.
9
,
3444
(
2018
).
48.
G.-R.
Lin
,
S.-P.
Su
,
C.-L.
Wu
,
Y.-H.
Lin
,
B.-J.
Huang
,
H.-Y.
Wang
,
C.-T.
Tsai
,
C.-I.
Wu
, and
Y.-C.
Chi
, “
Si-rich SiNx based Kerr switch enables optical data conversion up to 12 Gbit/s
,”
Sci. Rep.
5
,
9611
(
2015
).
49.
D.
Ahn
,
C-y.
Hong
,
J.
Liu
,
W.
Giziewicz
,
M.
Beals
,
L. C.
Kimerling
,
J.
Michel
,
J.
Chen
, and
F. X.
Kärtner
, “
High performance, waveguide integrated Ge photodetectors
,”
Opt. Express
15
,
3916
3921
(
2007
).
50.
M.
Dinu
,
F.
Quochi
, and
H.
Garcia
, “
Third-order nonlinearities in silicon at telecom wavelengths
,”
Appl. Phys. Lett.
82
,
2954
2956
(
2003
).
51.
G.
Li
,
J.
Yao
,
H.
Thacker
,
A.
Mekis
,
X.
Zheng
,
I.
Shubin
,
Y.
Luo
,
J-h.
Lee
,
K.
Raj
,
J. E.
Cunningham
, and
A. V.
Krishnamoorthy
, “
Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects
,”
Opt. Express
20
,
12035
12039
(
2012
).
52.
I.
Shoji
,
T.
Kondo
, and
R.
Ito
, “
Second-order nonlinear susceptibilities of various dielectric and semiconductor materials
,”
Opt. Quantum Electron.
34
,
797
833
(
2002
).
53.
Y.
Sugimoto
,
Y.
Tanaka
,
N.
Ikeda
,
Y.
Nakamura
,
K.
Asakawa
, and
K.
Inoue
, “
Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length
,”
Opt. Express
12
,
1090
1096
(
2004
).
54.
Y.
Fujii
,
S.
Yoshida
,
S.
Misawa
,
S.
Maekawa
, and
T.
Sakudo
, “
Nonlinear optical susceptibilities of AlN film
,”
Appl. Phys. Lett.
31
,
815
816
(
1977
).
55.
H.
Jung
,
C.
Xiong
,
K. Y.
Fong
,
X.
Zhang
, and
H. X.
Tang
, “
Optical frequency comb generation from aluminum nitride microring resonator
,”
Opt. Letters
38
,
2810
2813
(
2013
).
56.
C.
Xiong
,
W. H. P.
Pernice
,
X.
Sun
,
C.
Schuck
,
K. Y.
Fong
, and
H. X.
Tang
, “
Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics
,”
New J. Phys.
14
,
095014
(
2012
).
57.
R.
DeSalvo
,
A. A.
Said
,
D. J.
Hagan
,
E. W.
Van Stryland
, and
M.
Sheik-Bahae
, “
Infrared to ultraviolet measurements of two-photon absorption and n/sub 2/ in wide bandgap solids
,”
IEEE J. Quantum Electron.
32
,
1324
1333
(
1996
).
58.
H. T.
Bookey
,
R. R.
Thomson
,
N. D.
Psaila
,
A. K.
Kar
,
N.
Chiodo
,
R.
Osellame
, and
G.
Cerullo
, “
Femtosecond laser inscription of low insertion loss waveguides in z-cut lithium niobate
,”
IEEE Photonics Technol. Lett.
19
,
892
894
(
2007
).
59.
D.
Milam
, “
Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica
,”
Appl. Optics
37
,
546
550
(
1998
).
60.
D. J.
Moss
,
R.
Morandotti
,
A. L.
Gaeta
, and
M.
Lipson
, “
New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics
,”
Nat. Photonics
7
,
597
607
(
2013
).
61.
C. P.
Dietrich
,
A.
Fiore
,
M. G.
Thompson
,
M.
Kamp
, and
S.
Höfling
, “
GaAs integrated quantum photonics: Towards compact and multi-functional quantum photonic integrated circuits
,”
Laser Photonics Rev.
10
,
870
894
(
2016
).
62.
R. G.
Walker
, “
High-speed III-V semiconductor intensity modulators
,”
IEEE J. Quantum Electron.
27
,
654
667
(
1991
).
63.
A.
Orieux
,
A.
Eckstein
,
A.
Lemaître
,
P.
Filloux
,
I.
Favero
,
G.
Leo
,
T.
Coudreau
,
A.
Keller
,
P.
Milman
, and
S.
Ducci
, “
Direct Bell states generation on a III-V semiconductor chip at room temperature
,”
Phys. Rev. Lett.
110
,
160502
(
2013
).
64.
P.
Kultavewuti
,
E. Y.
Zhu
,
X.
Xing
,
L.
Qian
,
V.
Pusino
,
M.
Sorel
, and
J. S.
Aitchison
, “
Polarization-entangled photon pair sources based on spontaneous four wave mixing assisted by polarization mode dispersion
,”
Sci. Rep.
7
(
1
),
5785
(
2017
).
65.
F.
Boitier
,
A.
Orieux
,
C.
Autebert
,
A.
Lemaître
,
E.
Galopin
,
C.
Manquest
,
C.
Sirtori
,
I.
Favero
,
G.
Leo
, and
S.
Ducci
, “
Electrically injected photon-pair source at room temperature
,”
Phys. Rev. Lett.
112
,
183901
(
2014
).
66.
X.
Guo
,
C-l.
Zou
,
C.
Schuck
,
H.
Jung
,
R.
Cheng
, and
H. X.
Tang
, “
Parametric down-conversion photon-pair source on a nanophotonic chip
,”
Light: Sci. Appl.
6
,
e16249
e16249
(
2017
).
67.
K. D.
Jöns
,
L.
Schweickert
,
M. A.
Versteegh
,
D.
Dalacu
,
P. J.
Poole
,
A.
Gulinatti
,
A.
Giudice
,
V.
Zwiller
, and
M. E.
Reimer
, “
Bright nanoscale source of deterministic entangled photon pairs violating Bell's inequality
,”
Sci. Rep.
7
,
7751
(
2017
).
68.
L.
Arizmendi
, “
Photonic applications of lithium niobate crystals
,”
physica status solidi (a)
201
,
253
283
(
2004
).
69.
R. R.
Gattass
and
E.
Mazur
, “
Femtosecond laser micromachining in transparent materials
,”
Nat. Photonics
2
,
219
225
(
2008
).
70.
M.
Armenise
, “
Fabrication techniques of lithium niobate waveguides
,”
IEE Proc. J (Optoelectron.)
135
,
85
91
(
1988
).
71.
O.
Alibart
,
V.
D'Auria
,
M. D.
Micheli
,
F.
Doutre
,
F.
Kaiser
,
L.
Labonté
,
T.
Lunghi
,
É.
Picholle
, and
S.
Tanzilli
, “
Quantum photonics at telecom wavelengths based on lithium niobate waveguides
,”
J. Opt. (United Kingdom)
18
,
104001
(
2016
).
72.
C.
Schuck
,
W. H.
Pernice
, and
H. X.
Tang
, “
Waveguide integrated low noise NbTiN nanowire single-photon detectors with milli-Hz dark count rate
,”
Sci. reports
3
,
1893
(
2013
).
73.
A. A.
Sayem
,
R.
Cheng
,
S.
Wang
, and
H. X.
Tang
, “
Lithium-niobate-on-insulator waveguide-integrated superconducting nanowire single-photon detectors
,”
Appl. Phys. Lett.
116
,
151102
(
2020
).
74.
G.
Poberaj
,
H.
Hu
,
W.
Sohler
, and
P.
Günter
, “
Lithium niobate on insulator (LNOI) for micro-photonic devices
,”
Laser Photonics Rev.
6
,
488
503
(
2012
).
75.
M.
Bazzan
and
C.
Sada
, “
Optical waveguides in lithium niobate: Recent developments and applications
,”
Appl. Phys. Rev.
2
,
040603
(
2015
).
76.
C.
Xiong
,
G. D.
Marshall
,
A.
Peruzzo
,
M.
Lobino
,
A. S.
Clark
,
D.-Y.
Choi
,
S. J.
Madden
,
C. M.
Natarajan
,
M. G.
Tanner
,
R. H.
Hadfield
,
S. N.
Dorenbos
,
T.
Zijlstra
,
V.
Zwiller
,
M. G.
Thompson
,
J. G.
Rarity
,
M. J.
Steel
,
B.
Luther-Davies
,
B. J.
Eggleton
, and
J. L.
O'Brien
, “
Generation of correlated photon pairs in a chalcogenide As2S3 waveguide
,”
Appl. Phys. Lett.
98
,
051101
(
2011
).
77.
J. S.
Sanghera
,
L. B.
Shaw
, and
I. D.
Aggarwal
, “
Chalcogenide glass-fiber-based mid-IR sources and applications
,”
IEEE J. Sel. Top. Quantum Electron.
15
,
114
119
(
2009
).
78.
C. R.
Petersen
,
U.
Møller
,
I.
Kubat
,
B.
Zhou
,
S.
Dupont
,
J.
Ramsay
,
T.
Benson
,
S.
Sujecki
,
N.
Abdel-Moneim
,
Z.
Tang
,
D.
Furniss
,
A.
Seddon
, and
O.
Bang
, “
Mid-infrared supercontinuum covering the 1.4–13.3 μm molecular fingerprint region using ultra-high NA chalcogenide step-index fibre
,”
Nat. Photonics
8
,
830
834
(
2014
).
79.
S. O.
Leonov
,
Y.
Wang
,
V. S.
Shiryaev
,
G. E.
Snopatin
,
B. S.
Stepanov
,
V. G.
Plotnichenko
,
E.
Vicentini
,
A.
Gambetta
,
N.
Coluccelli
,
C.
Svelto
,
P.
Laporta
, and
G.
Galzerano
, “
Coherent mid-infrared supercontinuum generation in tapered suspended-core As39Se61 fibers pumped by a few-optical-cycle Cr:ZnSe laser
,”
Opt. Lett.
45
,
1346
1349
(
2020
).
80.
M.
Fox
,
Quantum Optics: An Introduction
, Vol.
15
(
OUP
,
Oxford
,
2006
).
81.
L.-T.
Feng
,
G.-C.
Guo
, and
X.-F.
Ren
, “
Progress on integrated quantum photonic sources with silicon
,”
Adv. Quantum Technol.
3
,
1900058
(
2020
).
82.
K.
Harada
,
H.
Takesue
,
H.
Fukuda
,
T.
Tsuchizawa
,
T.
Watanabe
,
K.
Yamada
,
Y.
Tokura
, and
S.
Itabashi
, “
Frequency and polarization characteristics of correlated photon-pair generation using a silicon wire waveguide
,”
IEEE J. Sel. Top. Quantum Electron.
16
,
325
331
(
2010
).
83.
O.
Alibart
,
J.
Fulconis
,
G. K. L.
Wong
,
S. G.
Murdoch
,
W. J.
Wadsworth
, and
J. G.
Rarity
, “
Photon pair generation using four-wave mixing in a microstructured fibre: Theory versus experiment
,”
New J. Phys.
8
,
67
(
2006
).
84.
C. K.
Hong
,
Z. Y.
Ou
, and
L.
Mandel
, “
Measurement of subpicosecond time intervals between two photons by interference
,”
Phys. Rev. Lett.
59
,
2044
2046
(
1987
).
85.
J. D.
Franson
, “
Bell inequality for position and time
,”
Phys. Rev. Lett.
62
,
2205
(
1989
).
86.
J. F.
Clauser
,
M. A.
Horne
,
A.
Shimony
, and
R. A.
Holt
, “
Proposed experiment to test local hidden-variable theories
,”
Phys. Rev. Lett.
23
,
880
(
1969
).
87.
S.
Aerts
,
P.
Kwiat
,
J.-Å.
Larsson
, and
M.
Żukowski
, “
Two-photon franson-type experiments and local realism
,”
Phys. Rev. Lett.
83
,
2872
2875
(
1999
).
88.
K.
Zielnicki
,
K.
Garay-Palmett
,
D.
Cruz-Delgado
,
H.
Cruz-Ramirez
,
M. F.
O'Boyle
,
B.
Fang
,
V. O.
Lorenz
,
A. B.
U'Ren
, and
P. G.
Kwiat
, “
Joint spectral characterization of photon-pair sources
,”
J. Mod. Opt.
65
,
1141
1160
(
2018
).
89.
B.
Brecht
,
D. V.
Reddy
,
C.
Silberhorn
, and
M. G.
Raymer
, “
Photon temporal modes: A complete framework for quantum information science
,”
Phys. Rev. X
5
,
041017
(
2015
).
90.
J. B.
Spring
,
P. S.
Salter
,
B. J.
Metcalf
,
P. C.
Humphreys
,
M.
Moore
,
N.
Thomas-Peter
,
M.
Barbieri
,
X.-M.
Jin
,
N. K.
Langford
,
W. S.
Kolthammer
,
M. J.
Booth
, and
I. A.
Walmsley
, “
On-chip low loss heralded source of pure single photons
,”
Opt. Express
21
,
13522
13532
(
2013
).
91.
G.
Harder
,
V.
Ansari
,
B.
Brecht
,
T.
Dirmeier
,
C.
Marquardt
, and
C.
Silberhorn
, “
An optimized photon pair source for quantum circuits
,”
Opt. Express
21
,
13975
13985
(
2013
).
92.
X-s.
Ma
,
S.
Zotter
,
J.
Kofler
,
T.
Jennewein
, and
A.
Zeilinger
, “
Experimental generation of single photons via active multiplexing
,”
Phys. Rev. A
83
,
043814
(
2011
).
93.
A. L.
Migdall
,
D.
Branning
, and
S.
Castelletto
, “
Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source
,”
Phys. Rev. A
66
,
053805
(
2002
).
94.
M.
Avenhaus
,
H. B.
Coldenstrodt-Ronge
,
K.
Laiho
,
W.
Mauerer
,
I. A.
Walmsley
, and
C.
Silberhorn
, “
Photon number statistics of multimode parametric down-conversion
,”
Phys. Rev. Lett.
101
,
053601
(
2008
).
95.
I.
Aharonovich
,
D.
Englund
, and
M.
Toth
, “
Solid-state single-photon emitters
,”
Nat. Photonics
10
,
631
(
2016
).
96.
M. J.
Collins
,
C.
Xiong
,
I. H.
Rey
,
T. D.
Vo
,
J.
He
,
S.
Shahnia
,
C.
Reardon
,
T. F.
Krauss
,
M. J.
Steel
,
A. S.
Clark
, and
B. J.
Eggleton
, “
Integrated spatial multiplexing of heralded single-photon sources
,”
Nat. Commun.
4
,
2582
(
2013
).
97.
F.
Kaneda
and
P. G.
Kwiat
, “
High-efficiency single-photon generation via large-scale active time multiplexing
,”
Sci. Adv.
5
,
eaaw8586
(
2019
).
98.
A.
Christ
and
C.
Silberhorn
, “
Limits on the deterministic creation of pure single-photon states using parametric down-conversion
,”
Phys. Rev. A
85
,
023829
(
2012
).
99.
D. C.
Burnham
and
D. L.
Weinberg
, “
Observation of simultaneity in parametric production of optical photon pairs
,”
Phys. Rev. Lett.
25
,
84
87
(
1970
).
100.
B. Y.
Zel'dovich
and
D. N.
Klyshko
, “
Field Statistics in Parametric Luminescence
,”
JETP Letters
9
,
40
(
1969
), available at http://www.jetpletters.ac.ru/ps/1639/article_25275.shtml.
101.
M.
Fiorentino
,
P. L.
Voss
,
J. E.
Sharping
, and
P.
Kumar
, “
All-fiber photon-pair source for quantum communications
,”
IEEE Photonics Technol. Lett.
14
,
983
985
(
2002
).
102.
K.
Inoue
and
K.
Shimizu
, “
Generation of quantum-correlated photon pairs in optical fiber: Influence of spontaneous Raman scattering
,”
Japanese J. Appl. Phys.
43
,
8048
(
2004
).
103.
X.
Li
,
J.
Chen
,
P.
Voss
,
J.
Sharping
, and
P.
Kumar
, “
All-fiber photon-pair source for quantum communications: Improved generation of correlated photons
,”
Opt. Express
12
,
3737
3744
(
2004
).
104.
H.
Takesue
and
K.
Inoue
, “
1.5-μm band quantum-correlated photon pair generation in dispersion-shifted fiber: Suppression of noise photons by cooling fiber
,”
Opt. Express
13
,
7832
7839
(
2005
).
105.
S. D.
Dyer
,
B.
Baek
, and
S. W.
Nam
, “
High-brightness, low-noise, all-fiber photon pair source
,”
Opt. Express
17
,
10290
10297
(
2009
).
106.
J. E.
Sharping
,
M.
Fiorentino
, and
P.
Kumar
, “
Observation of twin-beam-type quantum correlation in optical fiber
,”
Opt. Lett.
26
,
367
(
2001
).
107.
H.
Takesue
and
K.
Inoue
, “
Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop
,”
Phys. Rev. A
70
,
031802
(
2004
).
108.
H.
Takesue
and
K.
Inoue
, “
Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar light-wave circuit interferometers
,”
Phys. Rev. A
72
,
041804(R)
(
2005
).
109.
X.
Li
,
P. L.
Voss
,
J. E.
Sharping
, and
P.
Kumar
, “
Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band
,”
Phys. Rev. Lett.
94
,
053601
(
2005
).
110.
A.
Clark
,
B.
Bell
,
J.
Fulconis
,
M. M.
Halder
,
B.
Cemlyn
,
O.
Alibart
,
C.
Xiong
,
W. J.
Wadsworth
, and
J. G.
Rarity
, “
Intrinsically narrowband pair photon generation in microstructured fibres
,”
New J. Phys.
13
,
065009
(
2011
).
111.
J. E.
Sharping
,
J.
Chen
,
X.
Li
,
P.
Kumar
, and
R. S.
Windeler
, “
Quantum-correlated twin photons from microstructure fiber
,”
Opt. Express
12
,
3086
(
2004
).
112.
J. G.
Rarity
,
J.
Fulconis
,
J.
Duligall
,
W. J.
Wadsworth
, and
P. S. J.
Russell
, “
Photonic crystal fiber source of correlated photon pairs
,”
Opt. Express
13
,
534
544
(
2005
).
113.
J.
Fulconis
,
O.
Alibart
,
W. J.
Wadsworth
,
P. S.
Russell
, and
J. G.
Rarity
, “
High brightness single mode source of correlated photon pairs using a photonic crystal fiber
,”
Opt. Express
13
,
7572
7582
(
2005
).
114.
J.
Fan
,
A.
Migdall
, and
L. J.
Wang
, “
Efficient generation of correlated photon pairs in a microstructure fiber
,”
Opt. Lett.
30
,
3368
3370
(
2005
).
115.
J.
Fulconis
,
O.
Alibart
,
W. J.
Wadsworth
, and
J. G.
Rarity
, “
Quantum interference with photon pairs using two micro-structured fibres
,”
New J. Phys.
9
,
276
(
2007
).
116.
M.
Halder
,
J.
Fulconis
,
B.
Cemlyn
,
A.
Clark
,
C.
Xiong
,
W. J.
Wadsworth
, and
J. G.
Rarity
, “
Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources
,”
Opt. Express
17
,
4670
(
2009
).
117.
J.
Fan
,
M. D.
Eisaman
, and
A.
Migdall
, “
Bright phase-stable broadband fiber-based source of polarization-entangled photon pairs
,”
Phys. Rev. A
76
,
1
4
(
2007
).
118.
J.
Fulconis
,
O.
Alibart
,
J. L.
O'Brien
,
W. J.
Wadsworth
, and
J. G.
Rarity
, “
Nonclassical interference and entanglement generation using a photonic crystal fiber pair photon source
,”
Phys. Rev. Lett.
99
,
120501
(
2007
).
119.
G.
Bonfrate
,
V.
Pruneri
,
P. G.
Kazansky
,
P.
Tapster
, and
J. G.
Rarity
, “
Parametric fluorescence in periodically poled silica fibers
,”
Appl. Phys. Lett.
75
,
2356
2358
(
1999
).
120.
K. P.
Huy
,
A. T.
Nguyen
,
E.
Brainis
,
M.
Haelterman
,
P.
Emplit
,
C.
Corbari
,
A.
Canagasabey
,
M.
Ibsen
,
P. G.
Kazansky
,
O.
Deparis
,
A. A.
Fotiadi
,
P.
Mégret
, and
S.
Massar
, “
Photon pair source based on parametric fluorescence in periodically poled twin-hole silica fiber
,”
Opt. Express
15
,
4419
4426
(
2007
).
121.
E. Y.
Zhu
,
Z.
Tang
,
L.
Qian
,
L. G.
Helt
,
M.
Liscidini
,
J. E.
Sipe
,
C.
Corbari
,
A.
Canagasabey
,
M.
Ibsen
, and
P. G.
Kazansky
, “
Poled-fiber source of broadband polarization-entangled photon pairs
,”
Opt. letters
38
,
4397
4400
(
2013
).
122.
E. Y.
Zhu
,
Z.
Tang
,
L.
Qian
,
L. G.
Helt
,
M.
Liscidini
,
J. E.
Sipe
,
C.
Corbari
,
A.
Canagasabey
,
M.
Ibsen
, and
P. G.
Kazansky
, “
Direct generation of polarization-entangled photon pairs in a poled fiber
,”
Phys. Rev. Lett.
108
,
213902
(
2012
).
123.
K.
Guo
,
E. N.
Christensen
,
J. B.
Christensen
,
J. G.
Koefoed
,
D.
Bacco
,
Y.
Ding
,
H.
Ou
, and
K.
Rottwitt
, “
High coincidence-to-accidental ratio continuous-wave photon-pair generation in a grating-coupled silicon strip waveguide
,”
Appl. Phys. Express
10
,
062801
(
2017
).
124.
C.
Jie-Rong
,
Z.
Wei
,
Z.
Qiang
,
F.
Xue
,
H.
Yi-Dong
, and
P.
Jiang-De
, “
Correlated photon pair generation in silicon wire waveguides at 1.5 μm
,”
Chin. Phys. Lett.
27
,
124208
(
2010
).
125.
K-i.
Harada
,
H.
Takesue
,
H.
Fukuda
,
T.
Tsuchizawa
,
T.
Watanabe
,
K.
Yamada
,
Y.
Tokura
, and
S-i
Itabashi
, “
Indistinguishable photon pair generation using two independent silicon wire waveguides
,”
New J. Phys.
13
,
065005
(
2011
).
126.
J. W.
Silverstone
,
D.
Bonneau
,
K.
Ohira
,
N.
Suzuki
,
H.
Yoshida
,
N.
Iizuka
,
M.
Ezaki
,
C. M.
Natarajan
,
M. G.
Tanner
,
R. H.
Hadfield
,
V.
Zwiller
,
G. D.
Marshall
,
J. G.
Rarity
,
J. L.
O'Brien
, and
M. G.
Thompson
, “
On-chip quantum interference between silicon photon-pair sources
,”
Nat. Photonics
8
,
104
(
2014
).
127.
J. E.
Sharping
,
K. F.
Lee
,
M. A.
Foster
,
A. C.
Turner
,
B. S.
Schmidt
,
M.
Lipson
,
A. L.
Gaeta
, and
P.
Kumar
, “
Generation of correlated photons in nanoscale silicon waveguides
,”
Opt. Express
14
,
12388
12393
(
2006
).
128.
H.
Takesue
,
H.
Fukuda
,
T.
Tsuchizawa
,
T.
Watanabe
,
K.
Yamada
,
Y.
Tokura
, and
S-i.
Itabashi
, “
Generation of polarization entangled photon pairs using silicon wire waveguide
,”
Opt. Express
16
,
5721
5727
(
2008
).
129.
K-i.
Harada
,
H.
Takesue
,
H.
Fukuda
,
T.
Tsuchizawa
,
T.
Watanabe
,
K.
Yamada
,
Y.
Tokura
, and
S-i.
Itabashi
, “
Generation of high-purity entangled photon pairs using silicon wire waveguide
,”
Opt. Express
16
,
20368
20373
(
2008
).
130.
S.
Clemmen
,
K. P.
Huy
,
W.
Bogaerts
,
R. G.
Baets
,
P.
Emplit
, and
S.
Massar
, “
Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators
,”
Opt. Express
17
,
16558
16570
(
2009
).
131.
M.
Zhang
,
L.-T.
Feng
,
Z.-Y.
Zhou
,
Y.
Chen
,
H.
Wu
,
M.
Li
,
S.-M.
Gao
,
G.-P.
Guo
,
G.-C.
Guo
,
D.-X.
Dai
, and
X.-F.
Ren
, “
Generation of multiphoton quantum states on silicon
,”
Light: Sci. Appl.
8
(
1
),
41
(
2019
).
132.
S.
Paesani
,
M.
Borghi
,
S.
Signorini
,
A.
Maïnos
,
L.
Pavesi
, and
A.
Laing
, “
Near-ideal spontaneous photon sources in silicon quantum photonics
,”
Nat. communications
11
(
1
),
2505
(
2020
).
133.
L.-T.
Feng
,
M.
Zhang
,
X.
Xiong
,
Y.
Chen
,
H.
Wu
,
M.
Li
,
G.-P.
Guo
,
G.-C.
Guo
,
D.-X.
Dai
, and
X.-F.
Ren
, “
On-chip transverse-mode entangled photon pair source
,”
NPJ Quantum Inf.
5
(
1
),
2
(
2019
).
134.
N.
Matsuda
,
H. L.
Jeannic
,
H.
Fukuda
,
T.
Tsuchizawa
,
W. J.
Munro
,
K.
Shimizu
,
K.
Yamada
,
Y.
Tokura
, and
H.
Takesue
, “
A monolithically integrated polarization entangled photon pair source on a silicon chip
,”
Sci. Rep.
2
,
817
(
2012
).
135.
L.
Olislager
,
J.
Safioui
,
S.
Clemmen
,
K. P.
Huy
,
W.
Bogaerts
,
R.
Baets
,
P.
Emplit
, and
S.
Massar
, “
Silicon-on-insulator integrated source of polarization-entangled photons
,”
Opt. Lett.
38
,
1960
1962
(
2013
).
136.
N.
Lv
,
W.
Zhang
,
Y.
Guo
,
Q.
Zhou
,
Y.
Huang
, and
J.
Peng
, “
1.5 μm polarization entanglement generation based on birefringence in silicon wire waveguides
,”
Opt. Lett.
38
,
2873
2876
(
2013
).
137.
M.
Savanier
,
R.
Kumar
, and
S.
Mookherjea
, “
Optimizing photon-pair generation electronically using a p-i-n diode incorporated in a silicon microring resonator
,”
Appl. Phys. Lett.
107
,
131101
(
2015
).
138.
S.
Azzini
,
D.
Grassani
,
M. J.
Strain
,
M.
Sorel
,
L. G.
Helt
,
J. E.
Sipe
,
M.
Liscidini
,
M.
Galli
, and
D.
Bajoni
, “
Ultra-low power generation of twin photons in a compact silicon ring resonator
,”
Opt. Express
20
,
23100
23107
(
2012
).
139.
E.
Engin
,
D.
Bonneau
,
C. M.
Natarajan
,
A. S.
Clark
,
M. G.
Tanner
,
R. H.
Hadfield
,
S. N.
Dorenbos
,
V.
Zwiller
,
K.
Ohira
,
N.
Suzuki
,
H.
Yoshida
,
N.
Iizuka
,
M.
Ezaki
,
J. L.
O'Brien
, and
M. G.
Thompson
, “
Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement
,”
Opt. Express
21
,
27826
27834
(
2013
).
140.
W. C.
Jiang
,
X.
Lu
,
J.
Zhang
,
O.
Painter
, and
Q.
Lin
, “
Silicon-chip source of bright photon pairs
,”
Opt. Express
23
,
20884
20904
(
2015
).
141.
M.
Savanier
,
R.
Kumar
, and
S.
Mookherjea
, “
Photon pair generation from compact silicon microring resonators using microwatt-level pump powers
,”
Opt. Express
24
,
3313
3328
(
2016
).
142.
C. M.
Gentry
,
J. M.
Shainline
,
M. T.
Wade
,
M. J.
Stevens
,
S. D.
Dyer
,
X.
Zeng
,
F.
Pavanello
,
T.
Gerrits
,
S. W.
Nam
,
R. P.
Mirin
, and
M. A.
Popović
, “
Quantum-correlated photon pairs generated in a commercial 45 nm complementary metal-oxide semiconductor microelectronic chip
,”
Optica
2
,
1065
1071
(
2015
).
143.
X.
Lu
,
S.
Rogers
,
T.
Gerrits
,
W. C.
Jiang
,
S. W.
Nam
, and
Q.
Lin
, “
Heralding single photons from a high-Q silicon microdisk
,”
Optica
3
,
1331
1338
(
2016
).
144.
C.
Ma
,
X.
Wang
, and
S.
Mookherjea
, “
Progress towards a widely usable integrated silicon photonic photon-pair source
,”
OSA Continuum
3
,
1398
(
2020
).
145.
X.
Shi
,
K.
Guo
,
J. B.
Christensen
,
M. A.
Castaneda
,
X.
Liu
,
H.
Ou
, and
K.
Rottwitt
, “
Multichannel photon-pair generation with strong and uniform spectral correlation in a silicon microring resonator
,”
Phys. Rev. Appl.
12
,
034053
(
2019
).
146.
N. C.
Harris
,
D.
Grassani
,
A.
Simbula
,
M.
Pant
,
M.
Galli
,
T.
Baehr-Jones
,
M.
Hochberg
,
D.
Englund
,
D.
Bajoni
, and
C.
Galland
, “
Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems
,”
Phys. Rev. X
4
,
041047
(
2014
).
147.
J. W.
Silverstone
,
R.
Santagati
,
D.
Bonneau
,
M. J.
Strain
,
M.
Sorel
,
J. L.
O'Brien
, and
M. G.
Thompson
, “
Qubit entanglement between ring-resonator photon-pair sources on a silicon chip
,”
Nat. communications
6
(
1
),
7948
(
2015
).
148.
R.
Wakabayashi
,
M.
Fujiwara
,
K-i.
Yoshino
,
Y.
Nambu
,
M.
Sasaki
, and
T.
Aoki
, “
Time-bin entangled photon pair generation from Si micro-ring resonator
,”
Opt. Express
23
,
1103
1113
(
2015
).
149.
F.
Mazeas
,
M.
Traetta
,
M.
Bentivegna
,
F.
Kaiser
,
D.
Aktas
,
W.
Zhang
,
C. A.
Ramos
,
L. A.
Ngah
,
T.
Lunghi
,
E.
Picholle
,
N.
Belabas-Plougonven
,
X. L.
Roux
,
E.
Cassan
,
D.
Marris-Morini
,
L.
Vivien
,
G.
Sauder
,
L.
Labonté
, and
S.
Tanzilli
, “
High-quality photonic entanglement for wavelength-multiplexed quantum communication based on a silicon chip
,”
Opt. Express
24
,
28731
28738
(
2016
).
150.
M.
Fujiwara
,
R.
Wakabayashi
,
M.
Sasaki
, and
M.
Takeoka
, “
Wavelength division multiplexed and double-port pumped time-bin entangled photon pair generation using Si ring resonator
,”
Opt. Express
25
,
3445
3453
(
2017
).
151.
C.
Ma
,
X.
Wang
,
V.
Anant
,
A. D.
Beyer
,
M. D.
Shaw
, and
S.
Mookherjea
, “
Silicon photonic entangled photon-pair and heralded single photon generation with CAR > 12,000 and g(2)(0) < 0.006
,”
Opt. Express
25
,
32995
33006
(
2017
).
152.
I. I.
Faruque
,
G. F.
Sinclair
,
D.
Bonneau
,
J. G.
Rarity
, and
M. G.
Thompson
, “
On-chip quantum interference with heralded photons from two independent micro-ring resonator sources in silicon photonics
,”
Opt. Express
26
,
20379
20395
(
2018
).
153.
D.
Grassani
,
S.
Azzini
,
M.
Liscidini
,
M.
Galli
,
M. J.
Strain
,
M.
Sorel
,
J. E.
Sipe
, and
D.
Bajoni
, “
Micrometer-scale integrated silicon source of time-energy entangled photons
,”
Optica
2
,
88
94
(
2015
).
154.
S. F.
Preble
,
M. L.
Fanto
,
J. A.
Steidle
,
C. C.
Tison
,
G. A.
Howland
,
Z.
Wang
, and
P. M.
Alsing
, “
On-chip quantum interference from a single silicon ring-resonator source
,”
Phys. Rev. Appl.
4
,
021001
(
2015
).
155.
D.
Grassani
,
A.
Simbula
,
S.
Pirotta
,
M.
Galli
,
M.
Menotti
,
N. C.
Harris
,
T.
Baehr-Jones
,
M.
Hochberg
,
C.
Galland
,
M.
Liscidini
, and
D.
Bajoni
, “
Energy correlations of photon pairs generated by a silicon microring resonator probed by Stimulated Four Wave Mixing
,”
Sci. Rep.
6
,
23564
(
2016
).
156.
M.
Davanço
,
J. R.
Ong
,
A. B.
Shehata
,
A.
Tosi
,
I.
Agha
,
S.
Assefa
,
F.
Xia
,
W. M. J.
Green
,
S.
Mookherjea
, and
K.
Srinivasan
, “
Telecommunications-band heralded single photons from a silicon nanophotonic chip
,”
Appl. Phys. Lett.
100
,
261104
(
2012
).
157.
S.
Azzini
,
D.
Grassani
,
M.
Galli
,
D.
Gerace
,
M.
Patrini
,
M.
Liscidini
,
P.
Velha
, and
D.
Bajoni
, “
Stimulated and spontaneous four-wave mixing in silicon-on-insulator coupled photonic wire nano-cavities
,”
Appl. Phys. Lett.
103
,
031117
(
2013
).
158.
N.
Matsuda
,
H.
Takesue
,
K.
Shimizu
,
Y.
Tokura
,
E.
Kuramochi
, and
M.
Notomi
, “
Slow light enhanced correlated photon pair generation in photonic-crystal coupled-resonator optical waveguides
,”
Opt. Express
21
,
8596
8604
(
2013
).
159.
C.
Xiong
,
C.
Monat
,
A. S.
Clark
,
C.
Grillet
,
G. D.
Marshall
,
M. J.
Steel
,
J.
Li
,
L.
O'Faolain
,
T. F.
Krauss
,
J. G.
Rarity
, and
B. J.
Eggleton
, “
Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide
,”
Opt. Lett.
36
,
3413
3415
(
2011
).
160.
R.
Kumar
,
J. R.
Ong
,
J.
Recchio
,
K.
Srinivasan
, and
S.
Mookherjea
, “
Spectrally multiplexed and tunable-wavelength photon pairs at 1.55 μm from a silicon coupled-resonator optical waveguide
,”
Opt. Lett.
38
,
2969
2971
(
2013
).
161.
J.
He
,
A. S.
Clark
,
M. J.
Collins
,
J.
Li
,
T. F.
Krauss
,
B. J.
Eggleton
, and
C.
Xiong
, “
Degenerate photon-pair generation in an ultracompact silicon photonic crystal waveguide
,”
Opt. Lett.
39
,
3575
3578
(
2014
).
162.
H.
Takesue
,
N.
Matsuda
,
E.
Kuramochi
, and
M.
Notomi
, “
Entangled photons from on-chip slow light
,”
Sci. Rep.
4
,
3913
(
2014
).
163.
J. W.
Choi
,
B.-U.
Sohn
,
G. F. R.
Chen
,
D. K. T.
Ng
, and
D. T. H.
Tan
, “
Correlated photon pair generation in ultra-silicon-rich nitride waveguide
,”
Opt. Commun.
463
,
125351
(
2020
).
164.
X.
Zhang
,
Y.
Zhang
,
C.
Xiong
, and
B. J.
Eggleton
, “
Correlated photon pair generation in low-loss double-stripe silicon nitride waveguides
,”
J. Opt.
18
,
074016
(
2016
).
165.
F.
Samara
,
A.
Martin
,
C.
Autebert
,
M.
Karpov
,
T. J.
Kippenberg
,
H.
Zbinden
, and
R.
Thew
, “
High-rate photon pairs and sequential Time-Bin entanglement with Si3N4 microring resonators
,”
Opt. Express
27
,
19309
19318
(
2019
).
166.
P.
Imany
,
J. A.
Jaramillo-Villegas
,
O. D.
Odele
,
K.
Han
,
D. E.
Leaird
,
J. M.
Lukens
,
P.
Lougovski
,
M.
Qi
, and
A. M.
Weiner
, “
50-GHz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator
,”
Opt. Express
26
,
1825
1840
(
2018
).
167.
J. A.
Jaramillo-Villegas
,
P.
Imany
,
O. D.
Odele
,
D. E.
Leaird
,
Z.-Y.
Ou
,
M.
Qi
, and
A. M.
Weiner
, “
Persistent energy–time entanglement covering multiple resonances of an on-chip biphoton frequency comb
,”
Optica
4
,
655
658
(
2017
).
168.
X.
Lu
,
Q.
Li
,
D. A.
Westly
,
G.
Moille
,
A.
Singh
,
V.
Anant
, and
K.
Srinivasan
, “
Chip-integrated visible–telecom entangled photon pair source for quantum communication
,”
Nat. Physics
15
,
373
381
(
2019
).
169.
S.
Tanzilli
,
W.
Tittel
,
H.
De Riedmatten
,
H.
Zbinden
,
P.
Baldi
,
M.
DeMicheli
,
D. B.
Ostrowsky
, and
N.
Gisin
, “
PPLN waveguide for quantum communication
,”
Eur. Phys. J. D
18
,
155
160
(
2002
).
170.
O.
Alibart
,
D. B.
Ostrowsky
,
P.
Baldi
, and
S.
Tanzilli
, “
High-performance guided-wave asynchronous heralded single-photon source
,”
Opt. Lett.
30
,
1539
1541
(
2005
).
171.
F.
Setzpfandt
,
A. S.
Solntsev
,
J.
Titchener
,
C. W.
Wu
,
C.
Xiong
,
R.
Schiek
,
T.
Pertsch
,
D. N.
Neshev
, and
A. A.
Sukhorukov
, “
Tunable generation of entangled photons in a nonlinear directional coupler
,”
Laser Photonics Rev.
10
,
131
136
(
2016
).
172.
A.
Martin
,
A.
Issautier
,
H.
Herrmann
,
W.
Sohler
,
D. B.
Ostrowsky
,
O.
Alibart
, and
S.
Tanzilli
, “
A polarization entangled photon-pair source based on a type-II PPLN waveguide emitting at a telecom wavelength
,”
New J. Phys.
12
,
103005
(
2010
).
173.
C.
Schaeff
,
R.
Polster
,
R.
Lapkiewicz
,
R.
Fickler
,
S.
Ramelow
, and
A.
Zeilinger
, “
Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits
,”
Opt. Express
20
,
16145
16153
(
2012
).
174.
H.
Takesue
,
K.
Inoue
,
O.
Tadanaga
,
Y.
Nishida
, and
M.
Asobe
, “
Generation of pulsed polarization-entangled photon pairs in a 1.55-μm band with a periodically poled lithium niobate waveguide and an orthogonal polarization delay circuit
,”
Opt. Lett.
30
,
293
295
(
2005
).
175.
M.
Hunault
,
H.
Takesue
,
O.
Tadanaga
,
Y.
Nishida
, and
M.
Asobe
, “
Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO3 waveguide
,”
Opt. Lett.
35
,
1239
1241
(
2010
).
176.
R.
Kruse
,
L.
Sansoni
,
S.
Brauner
,
R.
Ricken
,
C. S.
Hamilton
,
I.
Jex
, and
C.
Silberhorn
, “
Dual-path source engineering in integrated quantum optics
,”
Phys. Rev. A
92
,
053841
(
2015
).
177.
H.
Jin
,
F. M.
Liu
,
P.
Xu
,
J. L.
Xia
,
M. L.
Zhong
,
Y.
Yuan
,
J. W.
Zhou
,
Y. X.
Gong
,
W.
Wang
, and
S. N.
Zhu
, “
On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits
,”
Phys. Rev. Lett.
113
,
103601
(
2014
).
178.
L.
Sansoni
,
K. H.
Luo
,
C.
Eigner
,
R.
Ricken
,
V.
Quiring
,
H.
Herrmann
, and
C.
Silberhorn
, “
A two-channel, spectrally degenerate polarization entangled source on chip
,”
NPJ Quantum Inf.
3
(
1
),
5
(
2017
).
179.
Y. M.
Sua
,
H.
Fan
,
A.
Shahverdi
,
J.-Y.
Chen
, and
Y.-P.
Huang
, “
Direct generation and detection of quantum correlated photons with 3.2 um wavelength spacing
,”
Sci. Rep.
7
,
17494
(
2017
).
180.
P.
Vergyris
,
T.
Meany
,
T.
Lunghi
,
G.
Sauder
,
J.
Downes
,
M. J.
Steel
,
M. J.
Withford
,
O.
Alibart
, and
S.
Tanzilli
, “
On-chip generation of heralded photon-number states
,”
Sci. Rep.
6
,
35975
(
2016
).
181.
R.
Ikuta
,
R.
Tani
,
M.
Ishizaki
,
S.
Miki
,
M.
Yabuno
,
H.
Terai
,
N.
Imoto
, and
T.
Yamamoto
, “
Frequency-multiplexed photon pairs over 1000 modes from a quadratic nonlinear optical waveguide resonator with a singly resonant configuration
,”
Phys. Rev. Lett.
123
,
193603
(
2019
).
182.
E.
Pomarico
,
B.
Sanguinetti
,
N.
Gisin
,
R.
Thew
,
H.
Zbinden
,
G.
Schreiber
,
A.
Thomas
, and
W.
Sohler
, “
Waveguide-based OPO source of entangled photon pairs
,”
New J. Phys.
11
,
113042
(
2009
).
183.
E.
Pomarico
,
B.
Sanguinetti
,
C. I.
Osorio
,
H.
Herrmann
, and
R. T.
Thew
, “
Engineering integrated pure narrow-band photon sources
,”
New J. Phys.
14
,
033008
(
2012
).
184.
J.
Zhao
,
C.
Ma
,
M.
Rüsing
, and
S.
Mookherjea
, “
High quality entangled photon pair generation in periodically poled thin-film lithium niobate waveguides
,”
Phys. Rev. Lett.
124
,
163603
(
2020
).
185.
A.
Yoshizawa
,
R.
Kaji
, and
H.
Tsuchida
, “
Generation of polarisation-entangled photon pairs at 1550 nm using two PPLN waveguides
,”
Electron. Lett.
39
,
621
622
(
2003
).
186.
H.
Chen
,
S.
Auchter
,
M.
Prilmüller
,
A.
Schlager
,
T.
Kauten
,
K.
Laiho
,
B.
Pressl
,
H.
Suchomel
,
M.
Kamp
,
S.
Höfling
, and
C.
Schneider
, “
Invited article: Time-bin entangled photon pairs from Bragg-reflection waveguides
,”
APL Photonics
3
,
080804
(
2018
).
187.
J.
Belhassen
,
F.
Baboux
,
Q.
Yao
,
M.
Amanti
,
I.
Favero
,
A.
Lemaître
,
W. S.
Kolthammer
,
I. A.
Walmsley
, and
S.
Ducci
, “
On-chip III-V monolithic integration of heralded single photon sources and beamsplitters
,”
Appl. Phys. Lett.
112
,
071105
(
2018
).
188.
R.
Horn
,
P.
Abolghasem
,
B. J.
Bijlani
,
D.
Kang
,
A. S.
Helmy
, and
G.
Weihs
, “
Monolithic source of photon pairs
,”
Phys. Rev. Lett.
108
,
153605
(
2012
).
189.
P.
Sarrafi
,
E. Y.
Zhu
,
B. M.
Holmes
,
D. C.
Hutchings
,
S.
Aitchison
, and
L.
Qian
, “
High-visibility two-photon interference of frequency–time entangled photons generated in a quasi-phase-matched AlGaAs waveguide
,”
Opt. Lett.
39
,
5188
5191
(
2014
).
190.
C.
Autebert
,
N.
Bruno
,
A.
Martin
,
A.
Lemaitre
,
C. G.
Carbonell
,
I.
Favero
,
G.
Leo
,
H.
Zbinden
, and
S.
Ducci
, “
Integrated AlGaAs source of highly indistinguishable and energy-time entangled photons
,”
Optica
3
,
143
146
(
2016
).
191.
C.
Autebert
,
G.
Boucher
,
F.
Boitier
,
A.
Eckstein
,
I.
Favero
,
G.
Leo
, and
S.
Ducci
, “
Photon pair sources in AlGaAs: From electrical injection to quantum state engineering
,”
J. Mod. Opt.
62
,
1739
1745
(
2015
).
192.
R. T.
Horn
,
P.
Kolenderski
,
D.
Kang
,
P.
Abolghasem
,
C.
Scarcella
,
A.
Della Frera
,
A.
Tosi
,
L. G.
Helt
,
S. V.
Zhukovsky
,
J. E.
Sipe
,
G.
Weihs
,
A. S.
Helmy
, and
T.
Jennewein
, “
Inherent polarization entanglement generated from a monolithic semiconductor chip
,”
Sci. Rep.
3
,
02314
(
2013
).
193.
D.
Kang
,
M.
Kim
,
H.
He
, and
A. S.
Helmy
, “
Two polarization-entangled sources from the same semiconductor chip
,”
Phys. Rev. A
92
,
013821
(
2015
).
194.
A.
Vallés
,
M.
Hendrych
,
J.
Svozilík
,
R.
Machulka
,
P.
Abolghasem
,
D.
Kang
,
B. J.
Bijlani
,
A. S.
Helmy
, and
J. P.
Torres
, “
Generation of polarization-entangled photon pairs in a Bragg reflection waveguide
,”
Opt. Express
21
,
10841
10849
(
2013
).
195.
S. V.
Zhukovsky
,
L. G.
Helt
,
D.
Kang
,
P.
Abolghasem
,
A. S.
Helmy
, and
J.
Sipe
, “
Generation of maximally-polarization-entangled photons on a chip
,”
Phys. Rev. A
85
,
013838
(
2012
).
196.
P.
Kultavewuti
,
E. Y.
Zhu
,
L.
Qian
,
V.
Pusino
,
M.
Sorel
, and
J. S.
Aitchison
, “
Correlated photon pair generation in AlGaAs nanowaveguides via spontaneous four-wave mixing
,”
Opt. Express
24
,
3365
3376
(
2016
).
197.
R. R.
Kumar
,
M.
Raevskaia
,
V.
Pogoretskii
,
Y.
Jiao
, and
H. K.
Tsang
, “
Entangled photon pair generation from an InP membrane micro-ring resonator
,”
Appl. Phys. Lett.
114
,
021104
(
2019
).
198.
C.
Reimer
,
M.
Kues
,
P.
Roztocki
,
B.
Wetzel
,
F.
Grazioso
,
B. E.
Little
,
S. T.
Chu
,
T.
Johnston
,
Y.
Bromberg
,
L.
Caspani
,
D. J.
Moss
, and
R.
Morandotti
, “
Generation of multiphoton entangled quantum states by means of integrated frequency combs
,”
Science
351
,
1176
1180
(
2016
).
199.
M.
Kues
,
C.
Reimer
,
P.
Roztocki
,
L. R.
Cortés
,
S.
Sciara
,
B.
Wetzel
,
Y.
Zhang
,
A.
Cino
,
S. T.
Chu
,
B. E.
Little
,
D. J.
Moss
,
L.
Caspani
,
J.
Azaña
, and
R.
Morandotti
, “
On-chip generation of high-dimensional entangled quantum states and their coherent control
,”
Nature
546
,
622
626
(
2017
).
200.
C.
Reimer
,
M.
Kues
,
L.
Caspani
,
B.
Wetzel
,
P.
Roztocki
,
M.
Clerici
,
Y.
Jestin
,
M.
Ferrera
,
M.
Peccianti
,
A.
Pasquazi
,
B. E.
Little
,
S. T.
Chu
,
D. J.
Moss
, and
R.
Morandotti
, “
Cross-polarized photon-pair generation and bi-chromatically pumped optical parametric oscillation on a chip
,”
Nat. Commun.
6
(
1
),
8236
(
2015
).
201.
C.
Reimer
,
L.
Caspani
,
M.
Clerici
,
M.
Ferrera
,
M.
Kues
,
M.
Peccianti
,
A.
Pasquazi
,
L.
Razzari
,
B. E.
Little
,
S. T.
Chu
,
D. J.
Moss
, and
R.
Morandotti
, “
Integrated frequency comb source of heralded single photons
,”
Opt. Express
22
,
6535
6546
(
2014
).
202.
C.
Xiong
,
L. G.
Helt
,
A. C.
Judge
,
G. D.
Marshall
,
M. J.
Steel
,
J. E.
Sipe
, and
B. J.
Eggleton
, “
Quantum-correlated photon pair generation in chalcogenide As2S3 waveguides
,”
Opt. Express
18
,
16206
16216
(
2010
).
203.
J. B.
Spring
,
P. L.
Mennea
,
B. J.
Metcalf
,
P. C.
Humphreys
,
J. C.
Gates
,
H. L.
Rogers
,
C.
Söller
,
B. J.
Smith
,
W. S.
Kolthammer
,
P. G. R.
Smith
, and
I. A.
Walmsley
, “
Chip-based array of near-identical, pure, heralded single-photon sources
,”
Optica
4
,
90
96
(
2017
).
204.
S.
Clemmen
,
A.
Perret
,
S. K.
Selvaraja
,
W.
Bogaerts
,
D.
Van Thourhout
,
R.
Baets
,
P.
Emplit
, and
S.
Massar
, “
Generation of correlated photons in hydrogenated amorphous-silicon waveguides
,”
Opt. Lett.
35
,
3483
3485
(
2010
).
205.
E.
Hemsley
,
D.
Bonneau
,
J.
Pelc
,
R.
Beausoleil
,
J. L.
O'Brien
, and
M. G.
Thompson
, “
Photon pair generation in hydrogenated amorphous silicon microring resonators
,”
Sci. Rep.
6
,
38908
(
2016
).
206.
J.
Chen
,
X.
Li
, and
P.
Kumar
, “
Two-photon-state generation via four-wave mixing in optical fibers
,”
Phys. Rev. A
72
,
033801
(
2005
).
207.
P.
Russell
, “
Photonic crystal fibers
,”
Science
299
,
358
362
(
2003
).
208.
D.
Cruz-Delgado
,
R.
Ramirez-Alarcon
,
E.
Ortiz-Ricardo
,
J.
Monroy-Ruz
,
F.
Dominguez-Serna
,
H.
Cruz-Ramirez
,
K.
Garay-Palmett
, and
A. B.
U'Ren
, “
Fiber-based photon-pair source capable of hybrid entanglement in frequency and transverse mode, controllably scalable to higher dimensions
,”
Sci. Rep.
6
,
27377
(
2016
).
209.
C. Guo, J. Su, Z. Zhang, L Cui, and X Li, Optics letters 44(2), 235–238 (2019); available at https://www.osapublishing.org/ol/abstract.cfm?uri=ol-44-2-235.
210.
Y.
Zhang
,
R.
Spiniolas
,
K.
Shinbrough
,
B.
Fang
,
O.
Cohen
, and
V. O.
Lorenz
, “
Dual-pump approach to photon-pair generation: Demonstration of enhanced characterization and engineering capabilities
,”
Opt. Express
27
,
19050
(
2019
).
211.
B.
Fang
,
O.
Cohen
,
J. B.
Moreno
, and
V. O.
Lorenz
, “
State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing
,”
Opt. Express
21
,
2707
2717
(
2013
).
212.
P. G.
Kazansky
,
P. S. J.
Russell
, and
H.
Takebe
, “
Glass fiber poling and applications
,”
J. Lightwave Technol.
15
,
1484
1493
(
1997
).
213.
G. P.
Agrawal
,
Applications of Nonlinear Fiber Optics
(
Elsevier
,
2001
).
214.
Y. M.
Sua
,
J.
Malowicki
,
M.
Hirano
, and
K. F.
Lee
, “
Generation of high-purity entangled photon pair in a short highly nonlinear fiber
,”
Opt. Lett.
38
,
73
75
(
2013
).
215.
Q.
Zhou
,
W.
Zhang
,
J-r.
Cheng
,
Y-d.
Huang
, and
J-d.
Peng
, “
Noise performance comparison of 1.5 μm correlated photon pair generation in different fibers
,”
Opt. Express
18
,
17114
17123
(
2010
).
216.
Q.
Lin
and
G. P.
Agrawal
, “
Silicon waveguides for creating quantum-correlated photon pairs
,”
Opt. Lett.
31
,
3140
3142
(
2006
).
217.
P.
Sarrafi
,
E. Y.
Zhu
,
K.
Dolgaleva
,
B. M.
Holmes
,
D. C.
Hutchings
,
J. S.
Aitchison
, and
L.
Qian
, “
Continuous-wave quasi-phase-matched waveguide correlated photon pair source on a III–V chip
,”
Appl. Phys. Lett.
103
,
251115
(
2013
).
218.
A. W.
Elshaari
,
I. E.
Zadeh
,
A.
Fognini
,
M. E.
Reimer
,
D.
Dalacu
,
P. J.
Poole
,
V.
Zwiller
, and
K. D.
Jöns
, “
On-chip single photon filtering and multiplexing in hybrid quantum photonic circuits
,”
Nat. Commun.
8
(
1
),
379
(
2017
).
219.
W.
Bogaerts
,
P.
De Heyn
,
T.
Van Vaerenbergh
,
K.
De Vos
,
S.
Kumar Selvaraja
,
T.
Claes
,
P.
Dumon
,
P.
Bienstman
,
D.
Van Thourhout
, and
R.
Baets
, “
Silicon microring resonators
,”
Laser Photon. Rev.
6
,
47
73
(
2012
).
220.
T. J.
Kippenberg
,
R.
Holzwarth
, and
S. A.
Diddams
, “
Microresonator-based optical frequency combs
,”
Science
332
,
555
559
(
2011
).
221.
N.
Matsuda
,
T.
Kato
,
K-i.
Harada
,
H.
Takesue
,
E.
Kuramochi
,
H.
Taniyama
, and
M.
Notomi
, “
Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide
,”
Opt. Express
19
,
19861
19874
(
2011
).
222.
S.
Saravi
,
T.
Pertsch
, and
F.
Setzpfandt
, “
Generation of counterpropagating path-entangled photon pairs in a single periodic waveguide
,”
Phys. Rev. Lett.
118
,
183603
(
2017
).
223.
C.
Errando-Herranz
,
E.
Schöll
,
M.
Laini
,
S.
Gyger
,
A. W.
Elshaari
,
A.
Branny
,
U.
Wennberg
,
S.
Barbat
,
T.
Renaud
,
M.
Brotons-Gisbert
,
C.
Bonato
,
B. D.
Gerardot
,
V.
Zwiller
, and
K. D.
Jöns
, “
On-chip single photon emission from a waveguide-coupled two-dimensional semiconductor
,” arXiv:2002.07657 (
2020
).
224.
F.
Lenzini
,
N.
Gruhler
,
N.
Walter
, and
W. H. P.
Pernice
, “
Diamond as a platform for integrated quantum photonics
,”
Adv. Quantum Technol.
1
,
1800061
(
2018
).
225.
V.
Bharadwaj
,
O.
Jedrkiewicz
,
J. P.
Hadden
,
B.
Sotillo
,
M. R.
Vázquez
,
P.
Dentella
,
T. T.
Fernandez
,
A.
Chiappini
,
A. N.
Giakoumaki
,
T. L.
Phu
,
M.
Bollani
,
M.
Ferrari
,
R.
Ramponi
,
P. E.
Barclay
, and
S. M.
Eaton
, “
Femtosecond laser written photonic and microfluidic circuits in diamond
,”
J. Phys.: Photonics
1
,
022001
(
2019
).
226.
B. J. M.
Hausmann
,
I.
Bulu
,
V.
Venkataraman
,
P.
Deotare
, and
M.
Lončar
, “
Diamond nonlinear photonics
,”
Nat. Photonics
8
,
369
374
(
2014
).
227.
V.
Bharadwaj
,
Y.
Wang
,
T. T.
Fernandez
,
R.
Ramponi
,
S. M.
Eaton
, and
G.
Galzerano
, “
Femtosecond laser written diamond waveguides: A step towards integrated photonics in the far infrared
,”
Opt. Mater.
85
,
183
185
(
2018
).