Abstract

High visibility on-chip quantum interference among indistinguishable single-photons from multiples sources is a key prerequisite for integrated linear optical quantum computing. Resonant enhancement in micro-ring resonators naturally enables brighter, purer and more indistinguishable single-photon production without any tight spectral filtering. The indistinguisha-bility of heralded single-photons from multiple micro-ring resonators has not been measured in any photonic platform. Here, we report on-chip indistinguishability measurements of heralded single-photons generated from independent micro-ring resonators by using an on-chip Mach-Zehnder interferometer and spectral demultiplexer. We measured the raw heralded two-photon interference fringe visibility as 72 ± 3%. This result agrees with our model, which includes device imperfections, spectral impurity and multi-pair emissions. We identify multi-pair emissions as the main factor limiting the nonclassical interference visibility, and show a route towards achieving near unity visibility in future experiments.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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2017 (8)

S. Paesani, A. A. Gentile, R. Santagati, J. Wang, N. Wiebe, D. P. Tew, J. L. O’Brien, and M. G. Thompson, “Experimental Bayesian quantum phase estimation on a silicon photonic chip,” Phys. Rev. Lett. 118, 100503 (2017).
[Crossref]

J. Iles-Smith, D. P. S. McCutcheon, A. Nazir, and J. Mørk, “Phonon scattering inhibits simultaneous near-unity efficiency and indistinguishability in semiconductor single-photon sources,” Nat. Photonics 11, 521–526 (2017).
[Crossref]

J. C. Loredo, M. A. Broome, P. Hilaire, O. Gazzano, I. Sagnes, A. Lemaitre, M. P. Almeida, P. Senellart, and A. G. White, “Boson sampling with single-photon fock states from a bright solid-state source,” Phys. Rev. Lett. 118, 130503 (2017).
[Crossref] [PubMed]

H. Wang, Y. He, Y.-H. Li, Z.-E. Su, B. Li, H.-L. Huang, Xi. Ding, M.-C. Chen, C. Liu, J. Qin, J.-P. Li, Y.-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. Höfling, and C.-Y. Lu, “High-efficiency multiphoton boson sampling,” Nat. Photonics 11(6), 361–365 (2017).
[Crossref]

J. B. Spring, P. L. Mennea, B. J. Metcalf, P. C. Humphreys, J. C. Gates, H. L. Rogers, C. Söller, B. J. Smith, W. Steven Kolthammer, P. G. R. Smith, and I. A. Walmsley, “Chip-based array of near-identical, pure, heralded single-photon sources,” Optica 4(1), 90 (2017).
[Crossref]

J. Wang, S. Paesani, R. Santagati, S. Knauer, A. A. Gentile, N. Wiebe, M. Petruzzella, J. L. O’Brien, J. G. Rarity, A. Laing, and M. G. Thompson, “Experimental quantum Hamiltonian learning,” Nat. Phys. 13, 551–555 (2017).
[Crossref]

Z. Vernon, M. Menotti, C. C. Tison, J. A. Steidle, M. L. Fanto, P. M. Thomas, S. F. Preble, A. M. Smith, P. M. Alsing, M. Liscidini, and J. E. Sipe, “Truly unentangled photon pairs without spectral filtering,” Opt. Lett. 42(18), 3638–3641 (2017).
[Crossref] [PubMed]

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
[Crossref] [PubMed]

2016 (8)

Z. Vernon, M. Liscidini, and J. E. Sipe, “No free lunch: the trade-off between heralding rate and efficiency in microresonator-based heralded single photon sources,” Opt. Lett. 4(4), 788–791 (2016).
[Crossref]

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y 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).
[Crossref] [PubMed]

M. Savanier, R. Kumar, and S. Mookherjea, “Photon pair generation from compact silicon microring resonators using microwatt-level pump powers,” Opt. Express 24(4), 3313–3328 (2016).
[Crossref] [PubMed]

X. Zhang, R. Jiang, B. Bell, D.-Y. Choi, C. Chae, and C. Xiong, “Interfering heralded single photons from two separate silicon nanowires pumped at different wavelengths,” Technologies 4(3), 25 (2016).
[Crossref]

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(6), 870–894 (2016).
[Crossref]

T. Komljenovic, M. Davenport, J. Hulme, A. Y Liu, C. T Santis, A. Spott, S. Srinivasan, E. J Stanton, C. Zhang, and J. E Bowers, “Heterogeneous silicon photonic integrated circuits,” J. Lightwave Technol. 34(1), 20–35 (2016).
[Crossref]

N. Somaschi, V. Giesz, L. De Santis, J C. Loredo, M P. Almeida, G. Hornecker, S L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

X. Ding, Y. He, Z. C. Duan, N. Gregersen, M. C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116, 020401 (2016).
[Crossref] [PubMed]

2015 (5)

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(12), 1065 (2015).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
[Crossref] [PubMed]

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. Commun.  6, 7948 (2015).
[Crossref] [PubMed]

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. Applied 4, 021001 (2015).
[Crossref]

Z. Vernon and J. E. Sipe, “Spontaneous four-wave mixing in lossy microring resonators,” Phys. Rev. A 91(5), 053802 (2015).
[Crossref]

2014 (4)

Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with -0.58 db coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014).
[Crossref]

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(10), 103601 (2014).
[Crossref] [PubMed]

P. Gold, A. Thoma, S. Maier, S. Reitzenstein, C. Schneider, S. Höfling, and M. Kamp, “Two-photon interference from remote quantum dots with inhomogeneously broadened linewidths,” Phys. Rev. B 89, 035313 (2014).
[Crossref]

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(3), L42–L46 (2014).
[Crossref]

2013 (3)

Y. He, Y.-M. He, Y.-J. Wei, X. Jiang, M.-C. Chen, F.-L. Xiong, Y. Zhao, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “Indistinguishable photons emitted by spin-flip raman transitions in InGaAs quantum dots,” Phys. Rev. Lett. 111, 237403 (2013).
[Crossref]

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(2), 104–108 (2013).
[Crossref]

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).
[Crossref] [PubMed]

2012 (1)

M. Davanaço, 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(26), 261104 (2012).
[Crossref]

2011 (3)

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(6), 065005 (2011).
[Crossref]

G. D. Marshall, T. Gaebel, J. C. F. Matthews, J. Enderlein, J. L. O’Brien, and J. R. Rabeau, “Coherence properties of a single dipole emitter in diamond,” New J. Phys.  13, 055016 (2011).
[Crossref]

A. Christ, K. Laiho, A. Eckstein, K. N. Cassemiro, and C. Silberhorn, “Probing multimode squeezing with correlation functions,” New J. Phys.  13, 033027 (2011)
[Crossref]

2010 (2)

L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, “Spontaneous four-wave mixing in microring resonators,” Opt. Lett. 35(18), 3006–3008 (2010).
[Crossref] [PubMed]

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801 (2010).
[Crossref]

2008 (1)

M. Varnava, D. E. Browne, and T. Rudolph, “How good must single photon sources and detectors be for efficient linear optical quantum computation?” Phys. Rev. Lett. 100, 060502 (2008).
[Crossref] [PubMed]

2007 (1)

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).
[Crossref]

2006 (1)

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
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2004 (1)

E. Jeffrey, N. A. Peters, and P. G. Kwiat, “Towards a periodic deterministic source of arbitrary single-photon states,” New J. Phys.  6, 100 (2004).
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2003 (1)

U. Leonhardt, “Quantum physics of simple optical instruments,” Rep. Prog. Phys.  66(7), 1207 (2003).
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2002 (1)

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).
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2000 (1)

P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61(4), 042304 (2000).
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1999 (1)

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, “Photon bunching and multiphoton interference in parametric down-conversion,” Phys. Rev. A 60, 593 (1999).
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1990 (1)

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044 (1987).
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Aboussouan, P.

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801 (2010).
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Agha, I.

M. Davanaço, 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(26), 261104 (2012).
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Alibart, O.

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(3), L42–L46 (2014).
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P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801 (2010).
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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).
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Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
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Almeida, M P.

N. Somaschi, V. Giesz, L. De Santis, J C. Loredo, M P. Almeida, G. Hornecker, S L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
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Almeida, M. P.

J. C. Loredo, M. A. Broome, P. Hilaire, O. Gazzano, I. Sagnes, A. Lemaitre, M. P. Almeida, P. Senellart, and A. G. White, “Boson sampling with single-photon fock states from a bright solid-state source,” Phys. Rev. Lett. 118, 130503 (2017).
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Z. Vernon, M. Menotti, C. C. Tison, J. A. Steidle, M. L. Fanto, P. M. Thomas, S. F. Preble, A. M. Smith, P. M. Alsing, M. Liscidini, and J. E. Sipe, “Truly unentangled photon pairs without spectral filtering,” Opt. Lett. 42(18), 3638–3641 (2017).
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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. Applied 4, 021001 (2015).
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Antón, C.

N. Somaschi, V. Giesz, L. De Santis, J C. Loredo, M P. Almeida, G. Hornecker, S L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
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Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
[Crossref] [PubMed]

Aspelmeyer, M.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
[Crossref] [PubMed]

Assefa, S.

M. Davanaço, 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(26), 261104 (2012).
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Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
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Auffeves, A.

N. Somaschi, V. Giesz, L. De Santis, J C. Loredo, M P. Almeida, G. Hornecker, S L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
[Crossref] [PubMed]

Baldi, P.

P. Aboussouan, O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A 81, 021801 (2010).
[Crossref]

Bell, B.

X. Zhang, R. Jiang, B. Bell, D.-Y. Choi, C. Chae, and C. Xiong, “Interfering heralded single photons from two separate silicon nanowires pumped at different wavelengths,” Technologies 4(3), 25 (2016).
[Crossref]

Blauensteiner, B.

R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. 96, 240502 (2006).
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Bonneau, D.

M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “High-extinction ratio integrated photonic filters for silicon quantum photonics,” Opt. Lett. 42(4), 815–818 (2017).
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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. Commun.  6, 7948 (2015).
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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(2), 104–108 (2013).
[Crossref]

Bowers, J. E

Branning, D.

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).
[Crossref]

Braunstein, S. L.

P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61(4), 042304 (2000).
[Crossref]

Broome, M. A.

J. C. Loredo, M. A. Broome, P. Hilaire, O. Gazzano, I. Sagnes, A. Lemaitre, M. P. Almeida, P. Senellart, and A. G. White, “Boson sampling with single-photon fock states from a bright solid-state source,” Phys. Rev. Lett. 118, 130503 (2017).
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Browne, D. E.

M. Varnava, D. E. Browne, and T. Rudolph, “How good must single photon sources and detectors be for efficient linear optical quantum computation?” Phys. Rev. Lett. 100, 060502 (2008).
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Campos, R. A.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, “Two-photon interference in a Mach-Zehnder interferometer,” Phys. Rev. Lett. 65, 1348–1351 (1990).

Cassemiro, K. N.

A. Christ, K. Laiho, A. Eckstein, K. N. Cassemiro, and C. Silberhorn, “Probing multimode squeezing with correlation functions,” New J. Phys.  13, 033027 (2011)
[Crossref]

Castelletto, S.

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).
[Crossref]

Chae, C.

X. Zhang, R. Jiang, B. Bell, D.-Y. Choi, C. Chae, and C. Xiong, “Interfering heralded single photons from two separate silicon nanowires pumped at different wavelengths,” Technologies 4(3), 25 (2016).
[Crossref]

Chae, C. J.

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y 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).
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Chen, M. C.

X. Ding, Y. He, Z. C. Duan, N. Gregersen, M. C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116, 020401 (2016).
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Chen, M.-C.

H. Wang, Y. He, Y.-H. Li, Z.-E. Su, B. Li, H.-L. Huang, Xi. Ding, M.-C. Chen, C. Liu, J. Qin, J.-P. Li, Y.-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. Höfling, and C.-Y. Lu, “High-efficiency multiphoton boson sampling,” Nat. Photonics 11(6), 361–365 (2017).
[Crossref]

Y. He, Y.-M. He, Y.-J. Wei, X. Jiang, M.-C. Chen, F.-L. Xiong, Y. Zhao, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “Indistinguishable photons emitted by spin-flip raman transitions in InGaAs quantum dots,” Phys. Rev. Lett. 111, 237403 (2013).
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Chen, Y.-H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
[Crossref] [PubMed]

Choi, D.-Y.

X. Zhang, R. Jiang, B. Bell, D.-Y. Choi, C. Chae, and C. Xiong, “Interfering heralded single photons from two separate silicon nanowires pumped at different wavelengths,” Technologies 4(3), 25 (2016).
[Crossref]

Christ, A.

A. Christ, K. Laiho, A. Eckstein, K. N. Cassemiro, and C. Silberhorn, “Probing multimode squeezing with correlation functions,” New J. Phys.  13, 033027 (2011)
[Crossref]

Clark, A. S.

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(3), L42–L46 (2014).
[Crossref]

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).
[Crossref] [PubMed]

Collins, M. J.

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y 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).
[Crossref] [PubMed]

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(3), L42–L46 (2014).
[Crossref]

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).
[Crossref] [PubMed]

Cook, H. M.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528 (7583), 534–538 (2015).
[Crossref] [PubMed]

Davanaço, M.

M. Davanaço, 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(26), 261104 (2012).
[Crossref]

Davenport, M.

De Santis, L.

N. Somaschi, V. Giesz, L. De Santis, J C. Loredo, M P. Almeida, G. Hornecker, S L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

Demory, J.

N. Somaschi, V. Giesz, L. De Santis, J C. Loredo, M P. Almeida, G. Hornecker, S L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A G. White, L. Lanco, and P. Senellart, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10(5), 340–345 (2016).
[Crossref]

Dietrich, C. P.

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(6), 870–894 (2016).
[Crossref]

Ding, X.

X. Ding, Y. He, Z. C. Duan, N. Gregersen, M. C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116, 020401 (2016).
[Crossref] [PubMed]

Ding, Xi.

H. Wang, Y. He, Y.-H. Li, Z.-E. Su, B. Li, H.-L. Huang, Xi. Ding, M.-C. Chen, C. Liu, J. Qin, J.-P. Li, Y.-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. Höfling, and C.-Y. Lu, “High-efficiency multiphoton boson sampling,” Nat. Photonics 11(6), 361–365 (2017).
[Crossref]

Ding, Y.

Duan, Z. C.

X. Ding, Y. He, Z. C. Duan, N. Gregersen, M. C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, “On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar,” Phys. Rev. Lett. 116, 020401 (2016).
[Crossref] [PubMed]

D-Y Choi, D.-Y

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y 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).
[Crossref] [PubMed]

Dyer, S. D.

Eckstein, A.

A. Christ, K. Laiho, A. Eckstein, K. N. Cassemiro, and C. Silberhorn, “Probing multimode squeezing with correlation functions,” New J. Phys.  13, 033027 (2011)
[Crossref]

Eggleton, B. J.

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y 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).
[Crossref] [PubMed]

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(3), L42–L46 (2014).
[Crossref]

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).
[Crossref] [PubMed]

Enderlein, J.

G. D. Marshall, T. Gaebel, J. C. F. Matthews, J. Enderlein, J. L. O’Brien, and J. R. Rabeau, “Coherence properties of a single dipole emitter in diamond,” New J. Phys.  13, 055016 (2011).
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Ezaki, M.

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(2), 104–108 (2013).
[Crossref]

Fanto, M. L.

Z. Vernon, M. Menotti, C. C. Tison, J. A. Steidle, M. L. Fanto, P. M. Thomas, S. F. Preble, A. M. Smith, P. M. Alsing, M. Liscidini, and J. E. Sipe, “Truly unentangled photon pairs without spectral filtering,” Opt. Lett. 42(18), 3638–3641 (2017).
[Crossref] [PubMed]

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. Applied 4, 021001 (2015).
[Crossref]

Fiore, A.

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(6), 870–894 (2016).
[Crossref]

Fujiwara, M.

Fukuda, H.

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(6), 065005 (2011).
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Fulconis, J.

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).
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Gaebel, T.

G. D. Marshall, T. Gaebel, J. C. F. Matthews, J. Enderlein, J. L. O’Brien, and J. R. Rabeau, “Coherence properties of a single dipole emitter in diamond,” New J. Phys.  13, 055016 (2011).
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Gates, J. C.

Gazzano, O.

J. C. Loredo, M. A. Broome, P. Hilaire, O. Gazzano, I. Sagnes, A. Lemaitre, M. P. Almeida, P. Senellart, and A. G. White, “Boson sampling with single-photon fock states from a bright solid-state source,” Phys. Rev. Lett. 118, 130503 (2017).
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Gentile, A. A.

J. Wang, S. Paesani, R. Santagati, S. Knauer, A. A. Gentile, N. Wiebe, M. Petruzzella, J. L. O’Brien, J. G. Rarity, A. Laing, and M. G. Thompson, “Experimental quantum Hamiltonian learning,” Nat. Phys. 13, 551–555 (2017).
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S. Paesani, A. A. Gentile, R. Santagati, J. Wang, N. Wiebe, D. P. Tew, J. L. O’Brien, and M. G. Thompson, “Experimental Bayesian quantum phase estimation on a silicon photonic chip,” Phys. Rev. Lett. 118, 100503 (2017).
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X. Zhang, R. Jiang, B. Bell, D.-Y. Choi, C. Chae, and C. Xiong, “Interfering heralded single photons from two separate silicon nanowires pumped at different wavelengths,” Technologies 4(3), 25 (2016).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) shows the experimental setup. A pulsed laser passes through a broadband filter (BF) and a tunable filter (TF) to suppress broadband background emission and to match the bandwidth of the laser to the micro-ring resonator sources. A polarisation controller (PC) is used to optimise transmission onto the chip via a grating coupler. The photonic circuit consists of a directional coupler (DC1), micro-ring resonator sources (S1 and S2), micro-ring resonator filters (F1, F2), and an MZI composed of directional couplers (DC2, DC3) and a thermal phase-shifter (ΦMZI). Photon-pairs generated by the sources are coupled off-chip and filtered (BF1 to BF4) and collected by single-photon detectors (D1 to D4) connected to a time-tagger (TT). Analysis of four-fold coincidences is done in postprocessing. (b) The electric field intensity of the fundamental transverse electric (TE) mode of the silicon nanowire waveguide used in the chip is calculated with Lumerical Mode Solver. Waveguide dimensions were 500 nm × 220 nm and the group index was estimated as ng = 4:16 at the wavelength 1550 nm. (c) Spectral profiles of the source micro-ring resonators S1 and S2. Both sources are seen to be largely spectrally indistinguishable, with linewidths of 33 pm and 31 pm (Q-factor ~ 5 × 104). (d) Due the sensitivity of the high Q-factor sources, the resonance shifts when the heater of the MZI dissipates heat. In this figure, the resonance of the source S2 shifts 43 pm, when the MZI dissipates 60mW heat (2π phase) from its off position. Counteracting this thermal crosstalk is essential to perform the experiment and explained in detail in Appendix A.
Fig. 2
Fig. 2 4-fold coincidences as a function of the MZI phase. (a) The experimentally measured 4-fold coincidence fringes, demonstrating a fitted visibility of 72% for indistinguishable photons. The reduced visibility compared to the ideal case arises due to several factors which are included in the fit: contributions from higher photon-number terms; spectral impurity of the heralded photons and potentially the spectral distinguishability of the sources. These are discussed in the Results and Analysis section. (b) Theoretical 4-fold coincidence probability assuming ideal sources and MZI. The MZI fringe visibility (defined by Eq. (1)) has a maximum of 100% for indistinguishable photons and 33% for distinguishable photons. When the phase, ϕMZI, is adjusted to π/2 the MZI has a 50:50 splitting ratio (R = T = 0.5, where R and T are the reflection and transmission coefficients of the MZI). (c) Theoretical 4-fold coincidence probability assuming ideal sources, but an imperfect MZI. The MZI is assumed to be constructed from two non-ideal directional couplers (see DC2 and DC3 of Fig. 1) that have a 35:65 splitting ratio, as was the case for our fabricated chip. It is seen that the shape of the fringe changes as a result of the imperfect splitting ratio of the directional couplers. However, the global maximum and minimum probabilities achieved for both distinguishable and indistinguishable fringes remains the same. The main effect of the non-balanced splitting ratio of the directional couplers is to reduce the effective transmitivity of the MZI at the fringe peak where ϕMZI = π (T< 1). This does not reduce the fringe peak at ϕMZI = 0 (R=1) and so will not limit the fringe visibility. The details of the theoretical models and the full fittings that includes spectral impurity and multi-pair (upto 10 photon-pairs) emissions are in Appendix B.
Fig. 3
Fig. 3 (a) Simulation of the joint spectral amplitude (JSA) of the micro-ring resonators used for this experiment shows a spectral purity of 92%. (b) Visibility of the MZI fringe as a function of the source brightness, n ¯ including multi-mode and multi-pair emissions. Identical sources with a purity of 0.92 are considered which which can be modelled well by two effective Schmidt modes. A total 10 photon-pairs generated from both of the sources at a time are considered to include the multi-pair effects. In our experiment we determined an average source brightness of 0.110 ± 0.012 photons produced from each source per pump pulse. From the experiment, the MZI fringe visibility is found as 72 ± 3%. The simulated graph (blue solid line) goes through the intersection of these error margins, showing the agreement between the simulation and the experiment.
Fig. 4
Fig. 4 Spectral response of the device by adding the two output ports of the MZI (PMi: power-meter value of the ith port). (a) Without any spectral alignments, all the resonators S1, S2, F1, F2 are in spectrally distinguishable. (b) Using the thermal phase-shifter to align S1, S2 to match the the resonances with the DWDMs’ ITU grid channels 47, 39 and 31 for idler, pump and signal spectra respectively.
Fig. 5
Fig. 5 Wavelength stability of micro-ring resonator sources. (a) Thermal cross-talk between the MZI heater and source S1. In this test, the position of source S1 is measured, while the MZI heater power is adjusted over its full range. A large thermal crosstalk is observed between the MZI heater and source S1, which needs to be compensated for. This is achieved, by reducing the heater power supplied directly to S1 in proportion to the thermal crosstalk from the MZI heater. In this way, the resonance position of S1 can be held constant. The same technique is applied between S2, F1 and F2 and the MZI heater to ensure stability of both sources and on-chip filters. (b) Measured position of the micro-ring resonator source S1 over a period of 1100 minutes, which is equal to the time required for the acquisition of a complete fringe. The shaded area represents the FWHM of the resonance and the black trace represents a series of 111 measured resonance peak positions. The measured resonance positions have a standard deviation of 1.0 pm, compared to the FWHM of 33 pm for Source 1 (relative drift: 7.1%).
Fig. 6
Fig. 6 Spurious four wave mixing in the input waveguide (LWG ~ 730 μm) is substantial over the whole bandwidth of the DWDM channels. As shown in the inset, a CW pump laser (λp) is scanned over Ch 39 of the ITU grid, while signal-idler photon-pairs are collected as 2-fold coincidences for each pump wavelength λp from Ch 47 and Ch 31. The filter resonators F1 and F2 are detuned off the pump channel for this experiment. The plot shows the background photon-pair generated by the waveguide in shaded green, and by the resonators by shaded blue. If the accumulated source and background photons are CS1, CS2, and CBg, then (CS1 + CS2)/CBg ≈ 1.05.
Fig. 7
Fig. 7 Brightness for source S1 and S2. Signal and idler singles counts for S1 (a) and S2 (c). Signal-idler coincidence counts and the corresponding coincidence to accidental ratio (CAR) for S1 (b) and S2 (c).

Tables (1)

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Table 1 Average photon number per pulse estimation

Equations (21)

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V MZI = ( P 4 f ) max ( P 4 f ) min ( P 4 f ) max + ( P 4 f ) min .
( c ^ d ^ ) = 1 2 ( 1 1 1 1 ) ( e i ϕ MZI 0 0 1 ) ( 1 1 1 1 ) ( a ^ b ^ ) ,
( c ^ d ^ ) = e i ϕ MZI ( 1 0 0 i ) ( cos ( ϕ MZI / 2 ) sin ( ϕ MZI / 2 ) sin ( ϕ MZI / 2 ) cos ( ϕ MZI / 2 ) ) ( 1 0 0 i ) ( a ^ b ^ ) .
P 4 f ind ( ϕ MZI ) = | ψ out | c ^ d ^ | vac | 2 = | ψ out | ( R T ) a ^ b ^ | vac | 2 = 1 2 [ 1 + cos ( 2 ϕ MZI ) ] ,
P 4 f dist ( ϕ MZI ) = | ψ out | c ^ d ^ | vac | 2 + | ψ out | c ^ d ^ | vac | 2 = 1 2 + 1 4 [ 1 + cos ( 2 ϕ MZI ) ] .
( c ^ d ^ ) = ( sin θ cos θ cos θ sin θ ) ( e i ϕ MZI 0 0 1 ) ( sin θ cos θ cos θ sin θ ) ( a ^ b ^ ) ,
( c ^ d ^ ) = e i ϕ MZI / 2 ( e i Φ / 2 0 0 e i Φ / 2 ) ( i cos ( η / 2 ) sin ( η / 2 ) sin ( η / 2 ) i cos ( η / 2 ) ) ( i e i Φ / 2 0 0 i e i Φ / 2 ) ( a ^ b ^ ) .
P 4 f ind ( ϕ MZI ) = | ψ out | c ^ d ^ | vac | 2 = | ψ out | ( R T ) a ^ b ^ | vac | 2 = [ 2 sin 2 ( ϕ MZI / 2 ) sin 2 ( 2 θ ) 1 ] 2 ,
R = sin 2 ( η / 2 ) = sin 2 ( ϕ MZI / 2 ) sin 2 ( 2 θ )
T = cos 2 ( η / 2 ) = | cos ( ϕ MZI / 2 ) i sin ( ϕ MZI / 2 ) ( sin 2 θ cos 2 θ ) | 2
P 4 f dist = | sin 2 ( ϕ M Z I / 2 ) sin 2 ( 2 θ ) | 2 + | 1 sin 2 ( ϕ M Z I / 2 ) sin 2 ( 2 θ ) | 2 .
| Ψ = k 1 x k n k = 0 x n k | n k , n k
ρ ^ s = N n 1 , n k = 0 n 1 + n k 1 P i ( n 1 + n k ) n 1 | n k | ρ ^ | n k | n 1
a ^ 11 U 11 c ^ 11 + U 12 d ^ 11 ; a ^ 12 U 11 c ^ 12 + U 12 d ^ 12
a ^ 21 U 21 c ^ 21 + U 22 d ^ 21 ; a ^ 22 U 21 c ^ 22 + U 22 d ^ 22
P 4 f = N 1 N 2 n c 1 , n c k = 0 n c 1 + n c k 1 n d 1 , n d k = 0 n d 1 + n d k 1 P s ( n c 1 + n c k ) P s ( n d 1 + n d k ) n c 1 | n d 1 | n c k | n d k | ρ ^ | n c 1 | n d 1 | n c k | n d k
V MZI = ( P 4 f ) max ( P 4 f ) min ( P 4 f ) max + ( P 4 f ) min .
C ( s ) = ( η s γ e f f ) P i n 2 + β s P i n + D C s
C ( i ) = ( η i γ e f f ) P i n 2 + β i P i n + D C i
C C ( s , i ) = ( η i η s γ e f f ) P i n 2 + A C C
A C C = C ( s ) C ( i ) τ

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