Abstract

Multi-mode interference (MMI) devices fabricated in silicon oxynitride (SiON) with a refractive index contrast of 2.4% provide a highly compact and stable platform for multi-photon non-classical interference. MMI devices can introduce which-path information for photons propagating in the multi-mode section which can result in degradation of this non-classical interference. We theoretically derive the visibility of quantum interference of two photons injected in a MMI device and predict near unity visibility for compact SiON devices. We complement the theoretical results by experimentally demonstrating visibilities of up to 97.7% in 2×2 MMI devices without the requirement of narrow-band photons.

© 2013 OSA

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2012 (2)

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

E. Poem, Y. Gilead, and Y. Silberberg, “Two-Photon Path-Entangled States in Multimode Waveguides,” Phys. Rev. Lett.108, 153602 (2012).
[CrossRef] [PubMed]

2011 (1)

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

2010 (3)

S. D. Barrett and T. M. Stace, “Fault Tolerant Quantum Computation with Very High Threshold for Loss Errors,” Phys. Rev. Lett.105, 200502 (2010).
[CrossRef]

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

2009 (1)

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

2008 (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon Waveguide Quantum Circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

2007 (2)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics1, 165–171 (2007).
[CrossRef]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007).
[CrossRef] [PubMed]

2004 (1)

Z. Jin and G.-D. Peng, “Optimal design of N× N silica multimode interference couplers — an improved approach,” Opt. Commun.241, 299–308 (2004).
[CrossRef]

1999 (1)

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging:principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

1994 (1)

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

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, 2044–2046 (1987).
[CrossRef] [PubMed]

1982 (1)

R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys.21, 467–488 (1982).
[CrossRef]

1973 (1)

Bachmann, M.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

Barrett, S. D.

S. D. Barrett and T. M. Stace, “Fault Tolerant Quantum Computation with Very High Threshold for Loss Errors,” Phys. Rev. Lett.105, 200502 (2010).
[CrossRef]

Besse, P. A.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

Bonneau, D.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Bryngdahl, O.

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon Waveguide Quantum Circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Dorenbos, S. N.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Engin, E.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Ezaki, M.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Feynman, R. P.

R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys.21, 467–488 (1982).
[CrossRef]

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

Gilead, Y.

E. Poem, Y. Gilead, and Y. Silberberg, “Two-Photon Path-Entangled States in Multimode Waveguides,” Phys. Rev. Lett.108, 153602 (2012).
[CrossRef] [PubMed]

Gisin, N.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics1, 165–171 (2007).
[CrossRef]

Grattan, K. T. V.

Hadfield, R. H.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Halder, M.

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Hong, C. K.

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).
[CrossRef] [PubMed]

Iizuka, N.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Jelezko, F.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

Jin, Z.

Z. Jin and G.-D. Peng, “Optimal design of N× N silica multimode interference couplers — an improved approach,” Opt. Commun.241, 299–308 (2004).
[CrossRef]

Ladd, T. D.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

Laflamme, R.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

Laing, A.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Mandel, L.

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).
[CrossRef] [PubMed]

Melchior, H.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

Monroe, C.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

Nagata, T.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007).
[CrossRef] [PubMed]

Nakamura, Y.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

Natarajan, C. M.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

O’Brien, J. L.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature (London)464, 45–53 (2010).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon Waveguide Quantum Circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007).
[CrossRef] [PubMed]

Ohira, K.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Okamoto, R.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007).
[CrossRef] [PubMed]

Ou, Z. Y.

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).
[CrossRef] [PubMed]

Peng, G.-D.

Z. Jin and G.-D. Peng, “Optimal design of N× N silica multimode interference couplers — an improved approach,” Opt. Commun.241, 299–308 (2004).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging:principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

Peruzzo, A.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Poem, E.

E. Poem, Y. Gilead, and Y. Silberberg, “Two-Photon Path-Entangled States in Multimode Waveguides,” Phys. Rev. Lett.108, 153602 (2012).
[CrossRef] [PubMed]

Politi, A.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon Waveguide Quantum Circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Rahman, B. M. A.

Rajarajan, M.

Ralph, T. C.

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon Waveguide Quantum Circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Rudolph, T.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

Sasaki, K.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007).
[CrossRef] [PubMed]

Silberberg, Y.

E. Poem, Y. Gilead, and Y. Silberberg, “Two-Photon Path-Entangled States in Multimode Waveguides,” Phys. Rev. Lett.108, 153602 (2012).
[CrossRef] [PubMed]

Smit, M. K.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging:principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

Stace, T. M.

S. D. Barrett and T. M. Stace, “Fault Tolerant Quantum Computation with Very High Threshold for Loss Errors,” Phys. Rev. Lett.105, 200502 (2010).
[CrossRef]

Suzuki, N.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Takeuchi, S.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science316, 726–729 (2007).
[CrossRef] [PubMed]

Tanner, M. G.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Thew, R.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics1, 165–171 (2007).
[CrossRef]

Thompson, M. G.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Verde, M. R.

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3, 687–695 (2009).
[CrossRef]

Yoshida, H.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon Waveguide Quantum Circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Zwiller, V.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O’Brien, “High-fidelity operation of quantum photonic circuits,” Appl. Phys. Lett.97, 211109 (2010).
[CrossRef]

Int. J. Theor. Phys. (1)

R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys.21, 467–488 (1982).
[CrossRef]

J. Lightwave Technol. (3)

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” J. Lightwave Technol.12, 1004–1009 (1994).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging:principles and applications,” J. Lightwave Technol.13, 615–627 (1995).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

A schematic of the experimental setup and of a 2×2 MMI device (not to scale). Single mode input (labelled 1 and 2) and output (3 and 4) waveguides connected to the multimode waveguide region.

Fig. 2
Fig. 2

Theoretical graph of the maximum visibility against number of identical concatenated MMI devices for 0.5 nm, 3.1 nm and 5 nm bandwidth photons. This simulated device has a width of 8 μm and a length of 305 μm, equivalent to one of the measured MMI devices, a theoretical loss of 0.15 dB and a zero dispersion visibility of 99.9%.

Fig. 3
Fig. 3

A characteristic HOM dip for MMI device with W = 8μm and L = 320μm measured, with Vexp = 97.69 ± 0.53%. The green data points represent the accidental coincidence counts.

Fig. 4
Fig. 4

A plot summarizing the results from the different MMI devices tested in this work. The blue, dotted lines connect results for the experimental visibility Vexp from the Hong-Ou-Mandel type experiments, the green dashed line is for the maximum expected visibilities Vmax calculated from single photon ratio counts as described in the main text and the red solid lines is for the ratio of visibilities Vexp/Vmax. The different MMI devices are grouped according to their widths, as indicated in the figure legend.

Equations (5)

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U 2 × 2 = ( r i t i t r )
T 2 × 2 = ( r 1 e i φ t 2 e i φ t 1 r 2 )
V g m ( r 1 , r 2 , t 1 , t 2 , φ , Δ ω , δ τ ) = 2 t 1 t 2 r 1 r 2 cos ( 2 φ ) e ( Δ ω δ τ ) 2 t 1 t 2 + r 1 r 2
| 1 ( y , z ) = j = 0 N 1 p j e i ( β 0 β j ) z | 1 j ( y )
V t h = i , j = 1 N p i p j V g m ( r 1 , r 2 , t 1 , t 2 , φ , Δ ω , δ τ i , j )

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