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.
References
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.
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.
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.
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.
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
).228.
C.
Okoth
, A.
Cavanna
, T.
Santiago-Cruz
, and M. V.
Chekhova
, “Microscale generation of entangled photons without momentum conservation
,” Phys. Rev. Lett.
123
, 263602
(2019
).229.
I.
Chung
and M. G.
Kanatzidis
, “Metal chalcogenides: A rich source of nonlinear optical materials
,” Chem. Mater.
26
, 849
–869
(2014
).230.
K. F.
Lee
, Y.
Tian
, H.
Yang
, K.
Mustonen
, A.
Martinez
, Q.
Dai
, E. I.
Kauppinen
, J.
Malowicki
, P.
Kumar
, and Z.
Sun
, “Photon-pair generation with a 100 nm thick carbon nanotube film
,” Adv. Mater.
29
, 1605978
(2017
).231.
H.
Mäntynen
, N.
Anttu
, Z.
Sun
, and H.
Lipsanen
, “Single-photon sources with quantum dots in III–V nanowires
,” Nanophotonics
8
, 747
–769
(2019
).232.
A.
Autere
, H.
Jussila
, Y.
Dai
, Y.
Wang
, H.
Lipsanen
, and Z.
Sun
, “Nonlinear optics with 2D layered materials
,” Adv. Mater.
30
, 1705963
(2018
).233.
H. D.
Saleh
, S.
Vezzoli
, L.
Caspani
, A.
Branny
, S.
Kumar
, B. D.
Gerardot
, and D.
Faccio
, “Towards spontaneous parametric down conversion from monolayer mos 2
,” Sci. Rep.
8
(1
), 3862
(2018
).234.
L.
Marini
, L.
Helt
, Y.
Lu
, B. J.
Eggleton
, and S.
Palomba
, “Constraints on downconversion in atomically thick films
,” JOSA B
35
, 672
–679
(2018
).235.
Y.
Wang
, M.
Ghotbi
, S.
Das
, Y.
Dai
, S.
Li
, X.
Hu
, X.
Gan
, J.
Zhao
, and Z.
Sun
, “Difference frequency generation in monolayer MoS2
,” Nanoscale
12
, 19638
(2020
).236.
Y.
Dai
, Y.
Wang
, S.
Das
, H.
Xue
, X.
Bai
, E.
Hulkko
, G.
Zhang
, X.
Yang
, Q.
Dai
, and Z.
Sun
, “Electrical control of interband resonant nonlinear optics in monolayer MoS2
,” ACS Nano
14
, 8442
–8448
(2020
).237.
Y.
Zhang
, J.
Wu
, Y.
Yang
, Y.
Qu
, L.
Jia
, T.
Moein
, B.
Jia
, and D. J.
Moss
, “Enhanced nonlinear optical figure-of-merit at 1550 nm for silicon nanowires integrated with graphene oxide layered films
,” arXiv:2004.08043 (2020
).238.
A.
Ishizawa
, R.
Kou
, T.
Goto
, T.
Tsuchizawa
, N.
Matsuda
, K.
Hitachi
, T.
Nishikawa
, K.
Yamada
, T.
Sogawa
, and H.
Gotoh
, “Optical nonlinearity enhancement with graphene-decorated silicon waveguides
,” Sci. Rep.
7
, 45520
(2017
).239.
Q.
Feng
, H.
Cong
, B.
Zhang
, W.
Wei
, Y.
Liang
, S.
Fang
, T.
Wang
, and J.
Zhang
, “Enhanced optical Kerr nonlinearity of graphene/Si hybrid waveguide
,” Appl. Phys. Lett.
114
, 071104
(2019
).240.
N.
Vermeulen
, D.
Castelló-Lurbe
, M.
Khoder
, I.
Pasternak
, A.
Krajewska
, T.
Ciuk
, W.
Strupinski
, J.
Cheng
, H.
Thienpont
, and J.
Van Erps
, “Graphene's nonlinear-optical physics revealed through exponentially growing self-phase modulation
,” Nat. Commun.
9
, 2675
(2018
).241.
K.
Chen
, X.
Zhou
, X.
Cheng
, R.
Qiao
, Y.
Cheng
, C.
Liu
, Y.
Xie
, W.
Yu
, F.
Yao
, Z.
Sun
, F.
Wang
, K.
Liu
, and L.
Zhongfan
, “Graphene photonic crystal fibre with strong and tunable light–matter interaction
,” Nat. Photonics
13
, 754
–759
(2019
).242.
Y.
Zuo
, W.
Yu
, C.
Liu
, X.
Cheng
, R.
Qiao
, J.
Liang
, X.
Zhou
, J.
Wang
, M.
Wu
, Y.
Zhao
, P.
Gao
, S.
Wu
, Z.
Sun
, K.
Liu
, X.
Bai
, and Z.
Liu
, “Optical fibres with embedded two-dimensional materials for ultrahigh nonlinearity
,” Nat. Nanotechnol.
15
, 987
–991
(2020
).243.
Y.
Yonezu
, R.
Kou
, H.
Nishi
, T.
Tsuchizawa
, K.
Yamada
, T.
Aoki
, A.
Ishizawa
, and N.
Matsuda
, “Evaluation of graphene optical nonlinearity with photon-pair generation in graphene-on-silicon waveguides
,” Opt. Express
27
, 30262
–30271
(2019
).244.
Z.
Sun
, A.
Martinez
, and F.
Wang
, “Optical modulators with 2D layered materials
,” Nat. Photonics
10
, 227
–238
(2016
).245.
M.
Long
, P.
Wang
, H.
Fang
, and W.
Hu
, “Progress, challenges, and opportunities for 2D material based photodetectors
,” Adv. Funct. Mater.
29
, 1803807
(2019
).246.
D.
Armani
, T.
Kippenberg
, S.
Spillane
, and D. K.
Vahala
, “Ultra-high-Q toroid microcavity on a chip
,” Nature
421
, 925
–928
(2003
).247.
J.
Fürst
, D.
Strekalov
, D.
Elser
, A.
Aiello
, U. L.
Andersen
, C.
Marquardt
, and G.
Leuchs
, “Quantum light from a whispering-gallery-mode disk resonator
,” Phys. Rev. Lett.
106
, 113901
(2011
).248.
M.
Förtsch
, G.
Schunk
, J. U.
Fürst
, D.
Strekalov
, T.
Gerrits
, M. J.
Stevens
, F.
Sedlmeir
, H. G. L.
Schwefel
, S. W.
Nam
, G.
Leuchs
, and C.
Marquardt
, “Highly efficient generation of single-mode photon pairs from a crystalline whispering-gallery-mode resonator source
,” Phys. Rev. A
91
, 23812
(2015
).249.
L.
Li
, Z.
Liu
, X.
Ren
, S.
Wang
, V.-C.
Su
, M.-K.
Chen
, C. H.
Chu
, H. Y.
Kuo
, B.
Liu
, W.
Zang
, G.
Guo
, L.
Zhang
, Z.
Wang
, S.
Zhu
, and D. P.
Tsai
, “Metalens-array–based high-dimensional and multiphoton quantum source
,” Science
368
, 1487
–1490
(2020
).250.
A. N.
Poddubny
, I. V.
Iorsh
, and A. A.
Sukhorukov
, “Generation of photon-plasmon quantum states in nonlinear hyperbolic metamaterials
,” Phys. Rev. Lett.
117
, 123901
(2016
).251.
M. S.
Tame
, K.
McEnery
, Ş.
Özdemir
, J.
Lee
, S. A.
Maier
, and M.
Kim
, “Quantum plasmonics
,” Nat. Phys.
9
, 329
–340
(2013
).252.
G.
Marino
, A. S.
Solntsev
, L.
Xu
, V. F.
Gili
, L.
Carletti
, A. N.
Poddubny
, M.
Rahmani
, D. A.
Smirnova
, H.
Chen
, A.
Lemaître
, G.
Zhang
, A. V.
Zayats
, C.
De Angelis
, G.
Leo
, A. A.
Sukhorukov
, and D. N.
Neshev
, “Spontaneous photon-pair generation from a dielectric nanoantenna
,” Optica
6
, 1416
–1422
(2019
).253.
G.
Laurent
, N.
Chauvet
, G.
Nogues
, A.
Drezet
, and G.
Bachelier
, “Photon-pair production at the nanoscale with hybrid nonlinear/plasmonic antennas
,” arXiv:1806.08702 (2018
).254.
A.
Davoyan
and H.
Atwater
, “Quantum nonlinear light emission in metamaterials: Broadband purcell enhancement of parametric downconversion
,” Optica
5
, 608
–611
(2018
).255.
M.
Müller
, S.
Bounouar
, K. D.
Jöns
, M.
Glässl
, and P.
Michler
, “On-demand generation of indistinguishable polarization-entangled photon pairs
,” Nat. Photonics
8
, 224
–228
(2014
).256.
F.
Kaneda
, B. G.
Christensen
, J. J.
Wong
, H. S.
Park
, K. T.
McCusker
, and P. G.
Kwiat
, “Time-multiplexed heralded single-photon source
,” Optica
2
, 1010
–1013
(2015
).257.
C.
Xiong
, X.
Zhang
, Z.
Liu
, M. J.
Collins
, A.
Mahendra
, L. G.
Helt
, M. J.
Steel
, D.-Y.
Choi
, C. J.
Chae
, P. H. W.
Leong
, and B. J.
Eggleton
, “Active temporal multiplexing of indistinguishable heralded single photons
,” Nat. Commun.
7
, 10853
(2016
).258.
Y.-H.
Li
, Z.-Y.
Zhou
, L.-T.
Feng
, W.-T.
Fang
, S-l.
Liu
, S.-K.
Liu
, K.
Wang
, X.-F.
Ren
, D.-S.
Ding
, L.-X.
Xu
, and B.-S.
Shi
, “On-chip multiplexed multiple entanglement sources in a single silicon nanowire
,” Phys. Rev. Appl.
7
, 064005
(2017
).259.
T.
Meany
, L. A.
Ngah
, M. J.
Collins
, A. S.
Clark
, R. J.
Williams
, B. J.
Eggleton
, M. J.
Steel
, M. J.
Withford
, O.
Alibart
, and S.
Tanzilli
, “Hybrid photonic circuit for multiplexed heralded single photons
,” Laser Photonics Rev.
8
, L42
–L46
(2014
).260.
C.
Joshi
, A.
Farsi
, S.
Clemmen
, S.
Ramelow
, and A. L.
Gaeta
, “Frequency multiplexing for quasi-deterministic heralded single-photon sources
,” Nat. Commun.
9
, 847
(2018
).261.
T. J.
Seok
, K.
Kwon
, J.
Henriksson
, J.
Luo
, and, and M. C.
Wu
, “240 × 240 wafer-scale silicon photonic switches
,” Optical Fiber Communication Conference and Exhibition
, San Diego, CA (IEEE
, 2019
), pp. 1–3.262.
J.
Wang
, S.
Paesani
, Y.
Ding
, R.
Santagati
, P.
Skrzypczyk
, A.
Salavrakos
, J.
Tura
, R.
Augusiak
, L.
Mančinska
, D.
Bacco
, D.
Bonneau
, J. W.
Silverstone
, Q.
Gong
, A.
Acín
, K.
Rottwitt
, L. K.
Oxenløwe
, J. L.
O'Brien
, A.
Laing
, and M. G.
Thompson
, “Multidimensional quantum entanglement with large-scale integrated optics
,” Science
360
, 285
–291
(2018
).263.
J. F.
Bauters
, M. J. R.
Heck
, D. D.
John
, J. S.
Barton
, C. M.
Bruinink
, A.
Leinse
, R. G.
Heideman
, D. J.
Blumenthal
, and J. E.
Bowers
, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding
,” Opt. Express
19
, 24090
–24101
(2011
).264.
Z.
Xie
, T.
Zhong
, S.
Shrestha
, X.
Xu
, J.
Liang
, Y.-X.
Gong
, J. C.
Bienfang
, A.
Restelli
, J. H.
Shapiro
, F. N.
Wong
, and C. W.
Wong
, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb
,” Nat. Photonics
9
, 536
–542
(2015
).265.
G.
Maltese
, M.
Amanti
, F.
Appas
, G.
Sinnl
, A.
Lemaitre
, P.
Milman
, F.
Baboux
, and S.
Ducci
, “Generation and symmetry control of quantum frequency combs
,” NPJ Quantum Inf.
6
(1
), 13
(2020
).266.
M.
Kues
, C.
Reimer
, J. M.
Lukens
, W. J.
Munro
, A. M.
Weiner
, D. J.
Moss
, and R.
Morandotti
, “Quantum optical microcombs
,” Nat. Photonics
13
, 170
–179
(2019
).267.
I. M.
Georgescu
, S.
Ashhab
, and F.
Nori
, “Quantum simulation
,” Rev. Mod. Phys.
86
, 153
(2014
).268.
A. M.
Childs
, “Universal computation by quantum walk
,” Phys. Rev. Lett.
102
, 180501
(2009
).269.
M.
Tillmann
, B.
Dakić
, R.
Heilmann
, S.
Nolte
, A.
Szameit
, and P.
Walther
, “Experimental boson sampling
,” Nat. Photonics
7
, 540
–544
(2013
).270.
J. B.
Spring
, B. J.
Metcalf
, P. C.
Humphreys
, W. S.
Kolthammer
, X.-M.
Jin
, M.
Barbieri
, A.
Datta
, N.
Thomas-Peter
, N. K.
Langford
, D.
Kundys
, J. C.
Gates
, B. J.
Smith
, P. G. R.
Smith
, and I. A.
Walmsley
, “Boson sampling on a photonic chip
,” Science
339
, 798
–801
(2013
).271.
H.
Wang
, J.
Qin
, X.
Ding
, M.-C.
Chen
, S.
Chen
, X.
You
, Y.-M.
He
, X.
Jiang
, L.
You
, Z.
Wang
, C.
Schneider
, J. J.
Renema
, S.
Höfling
, C.-Y.
Lu
, and J.-W.
Pan
, “Boson sampling with 20 input photons and a 60-mode interferometer in a 1014-dimensional Hilbert space
,” Phys. Rev. Lett.
123
, 250503
(2019
).272.
E.
Knill
, R.
Laflamme
, and G. J.
Milburn
, “A scheme for efficient quantum computation with linear optics
,” Nature
409
, 46
–52
(2001
).273.
K.
Chen
, C.-M.
Li
, Q.
Zhang
, Y.-A.
Chen
, A.
Goebel
, S.
Chen
, A.
Mair
, and J.-W.
Pan
, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states
,” Phys. Rev. Lett.
99
, 120503
(2007
).274.
P.
Walther
, K. J.
Resch
, T.
Rudolph
, E.
Schenck
, H.
Weinfurter
, V.
Vedral
, M.
Aspelmeyer
, and A.
Zeilinger
, “Experimental one-way quantum computing
,” Nature
434
, 169
–176
(2005
).© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.