Abstract

We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.

© 2016 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2015 (1)

2014 (2)

J. Sperling, W. Vogel, and G.S. Agarwal, “Quantum state engineering by click counting,” Phys. Rev. A 89, 043829 (2014).
[Crossref]

R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B 31(10), 8–13 (2014).
[Crossref]

2013 (2)

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

M. Cooper, L.J. Wright, C. Söller, and B.J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21(5), 5309–5317 (2013).
[Crossref] [PubMed]

2012 (1)

J. Sperling, W. Vogel, and G.S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85, 023820 (2012).
[Crossref]

2010 (2)

M. Avenhaus, K. Laiho, M.V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Agata M. Brańczyk, T.C. Ralph, Wolfram Helwig, and Christine Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12, 063001 (2010).
[Crossref]

2009 (2)

2008 (3)

M.N. O’Sullivan, K.W.C. Chan, V. Lakshminarayanan, and R.W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[Crossref]

Hiroki Takesue, Hiroshi Fukuda, Tai Tsuchizawa, Toshifumi Watanabe, Koji Yamada, Yashurio Tokura, and Seiichi Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express 16(8) 5721–5727 (2008).
[Crossref] [PubMed]

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

2007 (3)

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 75023803 (2007).
[Crossref]

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, “Photon number projection using non-number-resolving detectors,” New J. Phys. 9, 233 (2007).
[Crossref]

S.V. Polyakov and A. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15(4) 1390–1407 (2007).
[Crossref] [PubMed]

2006 (5)

2005 (1)

2004 (3)

D. Achilles, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51(9–10) 1499–1515 (2004).
[Crossref]

M. Ware and A. Migdall, “Single-photon detector characterization using correlated photons: the march from feasibility to metrology,” J. Mod. Opt. 51(9–10), 1549–1557 (2004).
[Crossref]

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(16), 3737–3744 (2004).
[Crossref] [PubMed]

2003 (4)

M.J. Fitch, B.C. Jacobs, T.B. Pittman, and J.D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[Crossref]

J. Řeháček, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67061801 (2003).
[Crossref]

K. Banaszek and I.A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003).
[Crossref] [PubMed]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I.A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 282387–2389 (2003).
[Crossref] [PubMed]

2001 (1)

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

2000 (1)

T Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61032302 (2000).
[Crossref]

1995 (1)

M. Munroe, D. Boggavarapu, M.E. Anderson, and M.G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52(2), R924–R927 (1995).
[Crossref] [PubMed]

1980 (1)

D.N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detections,” Sov. J. Quantum Electron. 10(9) 1112(1980).
[Crossref]

Achilles, D.

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, Los-Tolerant Characterization of Nonclassical Photon Statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[Crossref]

D. Achilles, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51(9–10) 1499–1515 (2004).
[Crossref]

D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, and I.A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 282387–2389 (2003).
[Crossref] [PubMed]

Agarwal, G.S.

J. Sperling, W. Vogel, and G.S. Agarwal, “Quantum state engineering by click counting,” Phys. Rev. A 89, 043829 (2014).
[Crossref]

J. Sperling, W. Vogel, and G.S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85, 023820 (2012).
[Crossref]

Agrawal, G.P.

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 75023803 (2007).
[Crossref]

Q. Lin, F. Yaman, and G.P. Agrawal, “Photon-pair generation by four-wave mixing in optical fibers,” Opt. Lett. 31(9) 1286–1288 (2006).
[Crossref] [PubMed]

Aichele, T.

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

Anderson, M.E.

M. Munroe, D. Boggavarapu, M.E. Anderson, and M.G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52(2), R924–R927 (1995).
[Crossref] [PubMed]

Avenhaus, M.

M. Avenhaus, K. Laiho, M.V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Banaszek, K.

Barbieri, M.

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

Bartley, T.J

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

Benson, O.

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

Boggavarapu, D.

M. Munroe, D. Boggavarapu, M.E. Anderson, and M.G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52(2), R924–R927 (1995).
[Crossref] [PubMed]

Boyd, R.W.

M.N. O’Sullivan, K.W.C. Chan, V. Lakshminarayanan, and R.W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[Crossref]

Branczyk, Agata M.

Agata M. Brańczyk, T.C. Ralph, Wolfram Helwig, and Christine Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12, 063001 (2010).
[Crossref]

Chae, C.J.

Chan, K.W.C.

M.N. O’Sullivan, K.W.C. Chan, V. Lakshminarayanan, and R.W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[Crossref]

Chekhova, M.V.

M. Avenhaus, K. Laiho, M.V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Chen, J.

Choi, D.-Y.

Chrapkiewicz, R.

R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B 31(10), 8–13 (2014).
[Crossref]

Clark, A.S.

Cohen, O.

Cooper, M.

Datta, A.

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

Donati, G.

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

Eggleton, B.J.

Eisaman, M.D.

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

Fan, J.

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

Fitch, M.J.

M.J. Fitch, B.C. Jacobs, T.B. Pittman, and J.D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[Crossref]

Foster, M. A.

Franson, J.D.

M.J. Fitch, B.C. Jacobs, T.B. Pittman, and J.D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[Crossref]

Fukuda, Hiroshi

Fulconis, J.

Gaeta, A. L.

Goldschmidt, E.A.

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

Grangier, P.

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

Halder, M.

Hansen, H.

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

He, J.

Helwig, Wolfram

Agata M. Brańczyk, T.C. Ralph, Wolfram Helwig, and Christine Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12, 063001 (2010).
[Crossref]

Huntington, E. H.

P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, “Photon number projection using non-number-resolving detectors,” New J. Phys. 9, 233 (2007).
[Crossref]

Inoue, K.

Itabashi, Seiichi

Jacobs, B.C.

M.J. Fitch, B.C. Jacobs, T.B. Pittman, and J.D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[Crossref]

Jin, X.-M.

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

Jizan, I.

Klyshko, D.N.

D.N. Klyshko, “Use of two-photon light for absolute calibration of photoelectric detections,” Sov. J. Quantum Electron. 10(9) 1112(1980).
[Crossref]

Kumar, P.

Kurizki, G.

T Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61032302 (2000).
[Crossref]

Laiho, K.

M. Avenhaus, K. Laiho, M.V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Lakshminarayanan, V.

M.N. O’Sullivan, K.W.C. Chan, V. Lakshminarayanan, and R.W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[Crossref]

Lee, K. F.

Li, X.

Liang, C.

Lin, Q.

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 75023803 (2007).
[Crossref]

Q. Lin, F. Yaman, and G.P. Agrawal, “Photon-pair generation by four-wave mixing in optical fibers,” Opt. Lett. 31(9) 1286–1288 (2006).
[Crossref] [PubMed]

Lipson, M.

Lundeen, J.S.

Lvovsky, A.I.

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

Mahou, P.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum OpticsCambridge University Press (1995).
[Crossref]

McMillan, A.R.

Migdall, A.

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

S.V. Polyakov and A. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15(4) 1390–1407 (2007).
[Crossref] [PubMed]

M. Ware and A. Migdall, “Single-photon detector characterization using correlated photons: the march from feasibility to metrology,” J. Mod. Opt. 51(9–10), 1549–1557 (2004).
[Crossref]

Mlynek, J.

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

Munroe, M.

M. Munroe, D. Boggavarapu, M.E. Anderson, and M.G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52(2), R924–R927 (1995).
[Crossref] [PubMed]

O’Sullivan, M.N.

M.N. O’Sullivan, K.W.C. Chan, V. Lakshminarayanan, and R.W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
[Crossref]

Opatrný, T

T Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61032302 (2000).
[Crossref]

Ourjoumtsev, A.

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

Pittman, T.B.

M.J. Fitch, B.C. Jacobs, T.B. Pittman, and J.D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[Crossref]

Polyakov, S.V.

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

S.V. Polyakov and A. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15(4) 1390–1407 (2007).
[Crossref] [PubMed]

Ralph, T. C.

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Raymer, M.G.

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Agata M. Brańczyk, T.C. Ralph, Wolfram Helwig, and Christine Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12, 063001 (2010).
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D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, Los-Tolerant Characterization of Nonclassical Photon Statistics,” Phys. Rev. Lett. 97, 043602 (2006).
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Q. Lin, F. Yaman, and G.P. Agrawal, “Photon-pair generation by four-wave mixing in optical fibers,” Opt. Lett. 31(9) 1286–1288 (2006).
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J. Mod. Opt. (2)

D. Achilles, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51(9–10) 1499–1515 (2004).
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R. Chrapkiewicz, “Photon counts statistics of squeezed and multimode thermal states of light on multiplexed on-off detectors,” J. Opt. Soc. Am. B 31(10), 8–13 (2014).
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Agata M. Brańczyk, T.C. Ralph, Wolfram Helwig, and Christine Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12, 063001 (2010).
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P. P. Rohde, J. G. Webb, E. H. Huntington, and T. C. Ralph, “Photon number projection using non-number-resolving detectors,” New J. Phys. 9, 233 (2007).
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M. Cooper, L.J. Wright, C. Söller, and B.J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21(5), 5309–5317 (2013).
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Hiroki Takesue, Hiroshi Fukuda, Tai Tsuchizawa, Toshifumi Watanabe, Koji Yamada, Yashurio Tokura, and Seiichi Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express 16(8) 5721–5727 (2008).
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A.R. McMillan, J. Fulconis, M. Halder, C. Xiong, J.G. Rarity, and W.J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570nm,” Opt. Express 17(8), 6156–6165 (2009).
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H. Takesue and K. Inoue, “1.5-μ m band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13(20), 7832–7839 (2005).
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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(16), 3737–3744 (2004).
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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(25), 12388–12393 (2006).
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B.J. Smith, P. Mahou, O. Cohen, J.S. Lundeen, and I.A. Walmsley, “Photon pair generation in birefringent optical fibers,” Opt. Express 17(26) 23589–23602 (2009).
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Opt. Lett. (5)

Phys. Rev. A (9)

J. Sperling, W. Vogel, and G.S. Agarwal, “True photocounting statistics of multiple on-off detectors,” Phys. Rev. A 85, 023820 (2012).
[Crossref]

M. Munroe, D. Boggavarapu, M.E. Anderson, and M.G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52(2), R924–R927 (1995).
[Crossref] [PubMed]

E.A. Goldschmidt, M.D. Eisaman, J. Fan, S.V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008).
[Crossref]

T Opatrný, G. Kurizki, and D.-G. Welsch, “Improvement on teleportation of continuous variables by photon subtraction via conditional measurement,” Phys. Rev. A 61032302 (2000).
[Crossref]

M.N. O’Sullivan, K.W.C. Chan, V. Lakshminarayanan, and R.W. Boyd, “Conditional preparation of states containing a definite number of photons,” Phys. Rev. A 77, 023804 (2008).
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J. Sperling, W. Vogel, and G.S. Agarwal, “Quantum state engineering by click counting,” Phys. Rev. A 89, 043829 (2014).
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M.J. Fitch, B.C. Jacobs, T.B. Pittman, and J.D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68, 043814 (2003).
[Crossref]

J. Řeháček, “Multiple-photon resolving fiber-loop detector,” Phys. Rev. A 67061801 (2003).
[Crossref]

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 75023803 (2007).
[Crossref]

Phys. Rev. Lett. (5)

D. Achilles, C. Silberhorn, and I. A. Walmsley, “Direct, Los-Tolerant Characterization of Nonclassical Photon Statistics,” Phys. Rev. Lett. 97, 043602 (2006).
[Crossref]

A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001)
[Crossref] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon fock state,” Phys. Rev. Lett. 96, 213601 (2006).
[Crossref] [PubMed]

T.J Bartley, G. Donati, X.-M. Jin, A. Datta, M. Barbieri, and I. A. Walmsley, “Direct Observation of Sub-Binomial Light,” Phys. Rev. Lett. 110, 173602 (2013).
[Crossref] [PubMed]

M. Avenhaus, K. Laiho, M.V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

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[Crossref]

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum OpticsCambridge University Press (1995).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Spatially multiplexed detector setup with three detectors to approximate a number-resolving detector. Each detector receives a fraction Ri of the light from the original state and has an efficiency of ηi of detecting an incident photon.

Fig. 2
Fig. 2

Experimental setup for measuring conditionally prepared number states. The multiplexed detectors are located within the dashed box. The two heralding detectors and the three signal detectors are connected to an FPGA and a computer for storing data. HWP denotes a halfwave plate; DM denotes a dichroic mirror; BS denotes a beamsplitter; PBS denotes a polarizing beamsplitter.

Fig. 3
Fig. 3

Photon-number probabilities measured without conditional detection of herald photons. The vacuum component is outlined with a dashed line. Error bars are present and are smaller than the markers.

Fig. 4
Fig. 4

Photon-number probabilities measured with single herald conditional preparation. The vacuum component is suppressed while the p1 component is high, showing a dominant one-photon-number component.

Fig. 5
Fig. 5

Photon-number probabilities of double-heralded states. The one-photon contribution is large relative to the two-photon contribution, in contrast to the desired outcome of a pure two-photon state. The large uncertainty bounds are due primarily to the large systematic error in measuring the efficiency in the signal channel by a classical field with a center wavelength close to the SFWM signal field.

Fig. 6
Fig. 6

Meausred Klyshko heralding efficiencies for different average pump powers and fiber lengths with the fits to Eq. (12) denoted by the dashed lines. There are three points presented for each pump power and fiber length representing the Klyshko heralding efficiency for each signal detector. Some points overlap where values are nearly identical.

Fig. 7
Fig. 7

Inferred noise-free photon-number distributions with double-heralded conditional preparation using the Klyshko heralding efficiencies in the inversion algorithm. The measured values show the photon-number probabilities of the two-photon state that would be observed in the absence of false heralding from independent noise processes. Error bars are present for all three powers and are attributed primarily to statistical error in the measurement of the Klyshko heralding efficiencies.

Equations (18)

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( q 1 q 2 q 3 ) = ( P ( 1 | 1 ) P ( 1 | 2 ) P ( 1 | 3 ) 0 P ( 2 | 2 ) P ( 2 | 3 ) 0 0 P ( 3 | 3 ) ) ( p 1 p 2 p 3 )
p 0 = 1 ( p 1 + p 2 + p 3 )
P ¯ s r ( n s | n r ) = P ¯ r s ( n s , n r ) n s = 0 P ¯ r s ( n s , n r ) = P ¯ r s ( n s , n r ) P ¯ r ( n r )
p ( m | k ) = ( k m ) η r m ( 1 η r ) k m
P ( n s | k r ) = m = 0 k r P ¯ s r ( n s | m ) p ( m | k r ) = m = 0 k r ( k r m ) η r m ( 1 η r ) k r m P ¯ s r ( n s | m )
P S ( n | k ) = m = 1 n ( k m ) ( 1 ρ L o s s ) m ( ρ L o s s ) k m P ¯ s r ( m | k )
η K = P ( H , S ) P ( H )
N H S = η H η S γ
N H = η H γ
η K = P ( H , S ) P ( H ) = N H S N H = η S η H γ η H γ = η S
η K = η S η H γ η H γ + η H σ = η S γ γ + σ
η K = η S × P 2 L P 2 L + β P L + α P
P ( 1 | n ) = P ( A | n ) + P ( B | n ) + P ( C | n ) 2 ( P ( A B | n ) + P ( A C | n ) + P ( B C | n ) ) + 3 P ( A B C | n )
P ( 2 | n ) = P ( A B | n ) + P ( A C | n ) + P ( B C | n ) 3 P ( A B C | n )
P ( 3 | n ) = P ( A B C | n )
P ( i | n ) = 1 ( 1 R i η i ) n
P ( i j | n ) = 1 ( 1 R i η i ) n ( 1 R j η j ) n + ( 1 R i η i R j η j ) n
P ( i j k | n ) = 1 ( 1 R i η i ) n ( 1 R j η j ) n ( 1 R k η k ) n + ( 1 R i η i R j η j ) n + ( 1 R i η i R k η k ) n + ( 1 R j η j R k η k ) n ( 1 R i η i R j η j R k η k ) n

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