Abstract

An understanding of the phenomenon of light interference forms the kernel underlying the discovery of the nature of light from the viewpoints of both classical physics and quantum physics. Here we report on two-photon interference with temporally separated continuous-wave coherent photons by using a temporal post-selection method with an arbitrary time delay. Although the temporal separation of a day between the photons is considerably longer than the coherence time of the light source, we observe the Hong–Ou–Mandel (HOM) interference of the pairwise two-photon state. Furthermore, we experimentally demonstrate the HOM interference observed in one of the interferometer-output modes by using only one single-photon detector for a large temporal separation.

© 2020 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (3)

2016 (2)

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

H. Kim, S. M. Lee, and H. S. Moon, “Two-photon interference of temporally separated photons,” Sci. Rep. 6, 34805 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (1)

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

2012 (2)

P. Hong, J. Liu, and G. Zhang, “Two-photon superbunching of thermal light via multiple two-photon path interference,” Phys. Rev. A 86, 013807 (2012).
[Crossref]

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

2007 (2)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

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).
[Crossref]

2005 (2)

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. B 22, 493 (2005).
[Crossref]

2004 (1)

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801(R) (2004).
[Crossref]

2003 (1)

Y.-H. Kim, “Two-photon interference without bunching two photons,” Phys. Lett. A 315, 352 (2003).
[Crossref]

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

1999 (2)

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[Crossref]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, and Y. Shih, “Quantum interference by two temporally distinguishable pulses,” Phys. Rev. A 60, R37 (1999).
[Crossref]

1996 (1)

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

1993 (1)

1989 (1)

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]

Alibart, O.

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).
[Crossref]

Baba, M.

Cao, D.-Z.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801(R) (2004).
[Crossref]

Chekhova, M. V.

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, and Y. Shih, “Quantum interference by two temporally distinguishable pulses,” Phys. Rev. A 60, R37 (1999).
[Crossref]

Chen, H.

Chen, Z. B.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University, 1958).

Dowiling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Fulconis, J.

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).
[Crossref]

Gage, E. C.

Grice, W. P.

Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. B 22, 493 (2005).
[Crossref]

Hariharan, P.

P. Hariharan and B. C. Sanders, “Quantum phenomena in optical interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), pp. 49–128.

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]

Hong, P.

P. Hong, J. Liu, and G. Zhang, “Two-photon superbunching of thermal light via multiple two-photon path interference,” Phys. Rev. A 86, 013807 (2012).
[Crossref]

Huang, F.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

Jaeger, G.

G. Jaeger and A. V. Sergienko, “Multi-photon quantum interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2001), pp. 277–324.

Jiang, W. C.

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

Jung, T.

Kim, H.

Kim, Y.-H.

Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. B 22, 493 (2005).
[Crossref]

Y.-H. Kim, “Two-photon interference without bunching two photons,” Phys. Lett. A 315, 352 (2003).
[Crossref]

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, and Y. Shih, “Quantum interference by two temporally distinguishable pulses,” Phys. Rev. A 60, R37 (1999).
[Crossref]

Kim, Y.-S.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Kok, P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Kuga, T.

Kulik, S. P.

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, and Y. Shih, “Quantum interference by two temporally distinguishable pulses,” Phys. Rev. A 60, R37 (1999).
[Crossref]

Kuo, P. S.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Kwon, O.

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Lee, S. M.

Lee, Y.-S.

Li, F.-L.

Li, H.-G.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

Lin, Q.

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

Liu, J.

J. Liu, H. Zheng, H. Chen, Y. Zhou, F.-L. Li, and Z. Xu, “The first- and second-order temporal interference between thermal and laser light,” Opt. Express 23, 11868–11878 (2015).
[Crossref]

P. Hong, J. Liu, and G. Zhang, “Two-photon superbunching of thermal light via multiple two-photon path interference,” Phys. Rev. A 86, 013807 (2012).
[Crossref]

Lu, C. Y.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Lu, X.

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

Magill, B. E.

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
[Crossref]

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B 6, 100–103 (1989).
[Crossref]

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]

Matsuoka, M.

Migdall, A.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Miyamoto, Y.

Moon, H. S.

Mulkey, D.

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

Munro, W. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

O’Brien, J. L.

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).
[Crossref]

Ou, Z. Y.

Z. Y. Ou, E. C. Gage, B. E. Magill, and L. Mandel, “Fourth-order interference technique for determining the coherence time of a light beam,” J. Opt. Soc. Am. B 6, 100–103 (1989).
[Crossref]

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]

Pan, J. W.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Park, J.

Pittman, T. B.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

Ralph, T. C.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowiling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

Rarity, J. G.

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).
[Crossref]

Rogers, S.

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

Sanders, B. C.

P. Hariharan and B. C. Sanders, “Quantum phenomena in optical interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), pp. 49–128.

Sergienko, A. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

G. Jaeger and A. V. Sergienko, “Multi-photon quantum interferometry,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2001), pp. 277–324.

Shih, Y.

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, and Y. Shih, “Quantum interference by two temporally distinguishable pulses,” Phys. Rev. A 60, R37 (1999).
[Crossref]

Shih, Y. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

Slattery, O.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?” Phys. Rev. Lett. 77, 1917 (1996).
[Crossref]

Sun, X.-J.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

Tang, X.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Two-photon interference with continuous-wave multi-mode coherent light,” Opt. Express 22, 3611–3620 (2014).
[Crossref]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses,” Phys. Rev. A 87, 063843 (2013).
[Crossref]

Wadsworth, W. J.

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).
[Crossref]

Wang, K.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

K. Wang and D.-Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70, 041801(R) (2004).
[Crossref]

Weinfurter, H.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Xiong, J.

J. Xiong, D.-Z. Cao, F. Huang, H.-G. Li, X.-J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudo thermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
[Crossref]

Xu, Z.

Zeilinger, A.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Zhang, G.

P. Hong, J. Liu, and G. Zhang, “Two-photon superbunching of thermal light via multiple two-photon path interference,” Phys. Rev. A 86, 013807 (2012).
[Crossref]

Zheng, H.

Zhou, Y.

Zukowski, M.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

ACS Photon. (1)

S. Rogers, D. Mulkey, X. Lu, W. C. Jiang, and Q. Lin, “High visibility time-energy entangled photons from a silicon nanophotonic chip,” ACS Photon. 3, 1754–1761 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. B (1)

Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. B 22, 493 (2005).
[Crossref]

Nature (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optica (1)

Phys. Lett. A (1)

Y.-H. Kim, “Two-photon interference without bunching two photons,” Phys. Lett. A 315, 352 (2003).
[Crossref]

Phys. Rev. A (4)

Y.-H. Kim, M. V. Chekhova, S. P. Kulik, and Y. Shih, “Quantum interference by two temporally distinguishable pulses,” Phys. Rev. A 60, R37 (1999).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic depicting coincidence measurement of two temporally separated CW-mode coherent photons via temporal post-selection. (b) Feynman diagrams depicting indistinguishable events of the TSPT states at the output stage.
Fig. 2.
Fig. 2. Schematic of experimental setup for HOM interference with a weak CW laser via temporal post-selection with the use of a polarization-based Michelson interferometer (M, mirror; PBS, polarizing beam splitter; IF, interference filter; HWP, half-wave plate; QWP, quarter-wave plate; SPD, single-photon detector).
Fig. 3.
Fig. 3. (a) Schematic for time-delayed coincidence measurement between D1 and D2 at both output ports of the PBS. (b) Normalized coincidence in different spatial modes in the three cases of Δt=0, 40, and 254 ns.
Fig. 4.
Fig. 4. (a) Schematic for time-delayed coincidence measurement of two photons in identical spatial modes upon performing two consecutive measurements with one SPD (D2). (b) Normalized coincidence in the same spatial modes in the case of Δt=60ns.
Fig. 5.
Fig. 5. Analysis method for HOM fringe using photons temporally separated by the order of a day: one set (set A) of time-tagged data and another set (set B) are independently obtained after a long time delay ΔT, where D1 and D2 represent the time data of the detection events at D1 and D2, respectively, corresponding to the two spatial modes of the interferometer arms.
Fig. 6.
Fig. 6. HOM interference fringe of the TSPT state for ΔT=1 day. (a) HOM dip fringe (orange circles) of one-day-delayed coincidence counts between D1 data of set A and D2 data of set B; the red curve indicates the fitting of the HOM fringe with visibility of 50%±3%. (b) HOM peak fringe (blue circles) of one-day-delayed coincidence counts between D2 data of set A and D2 data of set B in the same spatial modes; the red curve indicates the fitting of the HOM peak fringe.

Equations (1)

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|ΨTSPT=12[a1a2(Δti)+a2a1(Δti)]|0,0,

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