Abstract

We experimentally demonstrate the generation of multi-photon Fock states with up to three photons in well-defined spatial-temporal modes synchronized with a classical clock. The states are characterized using quantum optical homodyne tomography to ensure mode selectivity. The three-photon Fock states are probabilistically generated by pulsed spontaneous parametric down conversion at a rate of one per second, enabling complete characterization in 12 hours.

© 2013 OSA

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  1. M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett.71, 1355–1358 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature403, 515–519 (2000).
    [CrossRef] [PubMed]
  4. M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A65, 032323 (2002).
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  5. J. K. Asbóth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett.94, 173602 (2005).
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  6. K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
    [CrossRef]
  7. E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
    [CrossRef]
  8. T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. A. Zavatta, V. Parigi, and M. Bellini, “Toward quantum frequency combs: boosting the generation of highly nonclassical light states by cavity-enhanced parametric down-conversion at high repetition rates,” Phys. Rev. A78, 033809 (2008).
    [CrossRef]
  15. K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett.88, 113601 (2002).
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  16. A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett.88, 250401 (2002).
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    [CrossRef]
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  19. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
    [CrossRef]
  23. T. Aichele, A. Lvovsky, and S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” EPJ. D18, 237–245 (2002).
    [CrossRef]
  24. C. Kim, R.-D. Li, and P. Kumar, “Deamplification response of a traveling-wave phase-sensitive optical parametric amplifier,” Opt. Lett.19, 132–134 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. F. Grosshans and P. Grangier, “Effective quantum efficiency in the pulsed homodyne detection of a n-photon state,” EPJ. D14, 119–125 (2001).
    [CrossRef]
  27. A. I. Lvovsky, “Iterative maximum-likelihood reconstruction in quantum homodyne tomography,” J. Opt. B: Quantum Semiclass. Opt. 6, S556–S559 (2004).
    [CrossRef]

2012 (1)

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

2011 (1)

P. van Loock, “Optical hybrid approaches to quantum information,” Laser Photon. Rev.5, 167–200 (2011).
[CrossRef]

2010 (1)

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
[CrossRef]

2009 (2)

2008 (2)

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
[CrossRef] [PubMed]

A. Zavatta, V. Parigi, and M. Bellini, “Toward quantum frequency combs: boosting the generation of highly nonclassical light states by cavity-enhanced parametric down-conversion at high repetition rates,” Phys. Rev. A78, 033809 (2008).
[CrossRef]

2007 (2)

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature448, 784–786 (2007).
[CrossRef] [PubMed]

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
[CrossRef]

2006 (2)

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

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]

2005 (2)

2004 (2)

A. I. Lvovsky, “Iterative maximum-likelihood reconstruction in quantum homodyne tomography,” J. Opt. B: Quantum Semiclass. Opt. 6, S556–S559 (2004).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A70, 053821 (2004).
[CrossRef]

2003 (1)

2002 (4)

T. Aichele, A. Lvovsky, and S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” EPJ. D18, 237–245 (2002).
[CrossRef]

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett.88, 113601 (2002).
[CrossRef] [PubMed]

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett.88, 250401 (2002).
[CrossRef] [PubMed]

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A65, 032323 (2002).
[CrossRef]

2001 (2)

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]

F. Grosshans and P. Grangier, “Effective quantum efficiency in the pulsed homodyne detection of a n-photon state,” EPJ. D14, 119–125 (2001).
[CrossRef]

2000 (1)

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature403, 515–519 (2000).
[CrossRef] [PubMed]

1997 (1)

K. Banaszek and P. L. Knight, “Quantum interference in three-photon down-conversion,” Phys. Rev. A55, 2368–2375 (1997).
[CrossRef]

1994 (1)

1993 (1)

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett.71, 1355–1358 (1993).
[CrossRef] [PubMed]

Achilles, D.

Aichele, T.

T. Aichele, A. Lvovsky, and S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” EPJ. D18, 237–245 (2002).
[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]

Asbóth, J. K.

J. K. Asbóth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett.94, 173602 (2005).
[CrossRef] [PubMed]

Babichev, S. A.

Banaszek, K.

Barbieri, M.

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

Bartley, T. J.

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

Bellini, M.

A. Zavatta, V. Parigi, and M. Bellini, “Toward quantum frequency combs: boosting the generation of highly nonclassical light states by cavity-enhanced parametric down-conversion at high repetition rates,” Phys. Rev. A78, 033809 (2008).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A70, 053821 (2004).
[CrossRef]

Bencheikh, K.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
[CrossRef]

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]

Bimbard, E.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
[CrossRef]

Boulanger, B.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
[CrossRef]

Bouwmeester, D.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature403, 515–519 (2000).
[CrossRef] [PubMed]

Burnett, K.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett.71, 1355–1358 (1993).
[CrossRef] [PubMed]

Bužek, V.

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A65, 032323 (2002).
[CrossRef]

Calsamiglia, J.

J. K. Asbóth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett.94, 173602 (2005).
[CrossRef] [PubMed]

Cooper, M.

M. Cooper, C. Söller, and B. J. Smith, “High-stability time-domain balanced homodyne detector for ultrafast optical pulse applications,” arXiv :1112.0875 [quant-ph] (2011).

Daniell, M.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature403, 515–519 (2000).
[CrossRef] [PubMed]

Datta, A.

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

Donati, G.

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

Douady, J.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
[CrossRef]

Grangier, P.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature448, 784–786 (2007).
[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]

F. Grosshans and P. Grangier, “Effective quantum efficiency in the pulsed homodyne detection of a n-photon state,” EPJ. D14, 119–125 (2001).
[CrossRef]

Gravier, F.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
[CrossRef]

Grice, W. P.

Grosse, N. B.

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

Grosshans, F.

F. Grosshans and P. Grangier, “Effective quantum efficiency in the pulsed homodyne detection of a n-photon state,” EPJ. D14, 119–125 (2001).
[CrossRef]

Hadfield, R.

R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics3, 696–705 (2009).
[CrossRef]

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]

Holland, M. J.

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett.71, 1355–1358 (1993).
[CrossRef] [PubMed]

Huisman, S. R.

Jain, N.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
[CrossRef]

S. R. Huisman, N. Jain, S. A. Babichev, F. Vewinger, A. N. Zhang, S. H. Youn, and A. I. Lvovsky, “Instant single-photon fock state tomography,” Opt. Lett.34, 2739–2741 (2009).
[CrossRef] [PubMed]

Jeong, H.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature448, 784–786 (2007).
[CrossRef] [PubMed]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

Jin, X.-M.

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

Kim, C.

Kim, M. S.

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A65, 032323 (2002).
[CrossRef]

Kim, Y.-H.

Knight, P. L.

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A65, 032323 (2002).
[CrossRef]

K. Banaszek and P. L. Knight, “Quantum interference in three-photon down-conversion,” Phys. Rev. A55, 2368–2375 (1997).
[CrossRef]

Kumar, P.

Lam, P. K.

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

Lance, A. M.

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

Levenson, A.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
[CrossRef]

Li, R.-D.

Lundeen, J. S.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
[CrossRef] [PubMed]

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett.88, 113601 (2002).
[CrossRef] [PubMed]

Lvovsky, A.

T. Aichele, A. Lvovsky, and S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” EPJ. D18, 237–245 (2002).
[CrossRef]

Lvovsky, A. I.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
[CrossRef]

S. R. Huisman, N. Jain, S. A. Babichev, F. Vewinger, A. N. Zhang, S. H. Youn, and A. I. Lvovsky, “Instant single-photon fock state tomography,” Opt. Lett.34, 2739–2741 (2009).
[CrossRef] [PubMed]

A. I. Lvovsky, “Iterative maximum-likelihood reconstruction in quantum homodyne tomography,” J. Opt. B: Quantum Semiclass. Opt. 6, S556–S559 (2004).
[CrossRef]

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett.88, 250401 (2002).
[CrossRef] [PubMed]

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]

MacRae, A.

E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
[CrossRef]

Mlynek, J.

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett.88, 250401 (2002).
[CrossRef] [PubMed]

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]

Mosley, P. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
[CrossRef] [PubMed]

Ourjoumtsev, A.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature448, 784–786 (2007).
[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]

Pan, J.-W.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature403, 515–519 (2000).
[CrossRef] [PubMed]

Parigi, V.

A. Zavatta, V. Parigi, and M. Bellini, “Toward quantum frequency combs: boosting the generation of highly nonclassical light states by cavity-enhanced parametric down-conversion at high repetition rates,” Phys. Rev. A78, 033809 (2008).
[CrossRef]

Ralph, T. C.

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

Resch, K. J.

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett.88, 113601 (2002).
[CrossRef] [PubMed]

Ritsch, H.

J. K. Asbóth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett.94, 173602 (2005).
[CrossRef] [PubMed]

Schiller, S.

T. Aichele, A. Lvovsky, and S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” EPJ. D18, 237–245 (2002).
[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]

Silberhorn, C.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
[CrossRef] [PubMed]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett.28, 2387–2389 (2003).
[CrossRef] [PubMed]

Sliwa, C.

Smith, B. J.

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
[CrossRef] [PubMed]

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M. Cooper, C. Söller, and B. J. Smith, “High-stability time-domain balanced homodyne detector for ultrafast optical pulse applications,” arXiv :1112.0875 [quant-ph] (2011).

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T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
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P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
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A. Zavatta, S. Viciani, and M. Bellini, “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A70, 053821 (2004).
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T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett.100, 133601 (2008).
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K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” Comptes Rendus Physique8, 206–220 (2007).
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A. I. Lvovsky, “Iterative maximum-likelihood reconstruction in quantum homodyne tomography,” J. Opt. B: Quantum Semiclass. Opt. 6, S556–S559 (2004).
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P. van Loock, “Optical hybrid approaches to quantum information,” Laser Photon. Rev.5, 167–200 (2011).
[CrossRef]

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E. Bimbard, N. Jain, A. MacRae, and A. I. Lvovsky, “Quantum-optical state engineering up to the two-photon level,” Nat. Photonics4, 243–247 (2010).
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Nature (2)

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature403, 515–519 (2000).
[CrossRef] [PubMed]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature448, 784–786 (2007).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (6)

A. Zavatta, V. Parigi, and M. Bellini, “Toward quantum frequency combs: boosting the generation of highly nonclassical light states by cavity-enhanced parametric down-conversion at high repetition rates,” Phys. Rev. A78, 033809 (2008).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection,” Phys. Rev. A70, 053821 (2004).
[CrossRef]

A. M. Lance, H. Jeong, N. B. Grosse, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum-state engineering with continuous-variable postselection,” Phys. Rev. A73, 041801 (2006).
[CrossRef]

M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A65, 032323 (2002).
[CrossRef]

K. Banaszek and P. L. Knight, “Quantum interference in three-photon down-conversion,” Phys. Rev. A55, 2368–2375 (1997).
[CrossRef]

T. J. Bartley, G. Donati, J. B. Spring, X.-M. Jin, M. Barbieri, A. Datta, B. J. Smith, and I. A. Walmsley, “Multi-photon state engineering by heralded interference between single photons and coherent states,” Phys. Rev. A86, 043820 (2012).
[CrossRef]

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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).
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[CrossRef] [PubMed]

K. J. Resch, J. S. Lundeen, and A. M. Steinberg, “Quantum state preparation and conditional coherence,” Phys. Rev. Lett.88, 113601 (2002).
[CrossRef] [PubMed]

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett.88, 250401 (2002).
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Other (1)

M. Cooper, C. Söller, and B. J. Smith, “High-stability time-domain balanced homodyne detector for ultrafast optical pulse applications,” arXiv :1112.0875 [quant-ph] (2011).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup for heralded Fock state tomography. BBO: beta barium borate crystal, KDP: potassium dihydrogen phosphate crystal, PBS: polarizing beam splitter, HT: highly-transmitting beam splitter, DM: dichroic mirror, SMD: spatially multiplexed detector, FBS: fiber beam splitter, MSO: mixed-signal oscilloscope, BHD: balanced homodyne detector, SMF: single-mode fiber, PM-SMF: polarization-maintaining single-mode fiber, IF: interference filter, 50/50: 50/50 beam splitter, APD: avalanche photodiode.

Fig. 2
Fig. 2

(a) LO (blue) and signal (red) spectral amplitudes, the calculated spectral overlap is 0.97. (b) Joint spectral intensity distribution for the collected signal and trigger modes from KDP crystal. The colour scale indicates the number of recorded coincidence counts for each spectral bin in the 2D scan. The calculated spectral purity of the state is 0.95.

Fig. 3
Fig. 3

Marginal distributions P(X) of the heralded (a) single- and (d) two-photon states, showing clear non-Gaussian profiles. Photon number statistics P(n): raw (blue) and corrected for the detector efficiency ηbhd (red) for (b) single- and (e) two-photon states. Wigner functions W(X, P) of the reconstructed (c) single- and (f) two-photon states, both corrected for the detector efficiency ηbhd.

Fig. 4
Fig. 4

(a) Predicted (red line) and measured (black dots) marginal distribution P(X) with error bars for the three-photon state. (b) Photon number statistics P(n) for predicted (green) and reconstructed (red) state, both corrected for detector efficiency ηbhd.

Fig. 5
Fig. 5

(a) Wigner function W(X,P) of the reconstructed three-photon state corrected for detector efficiency ηbhd, showing negativity around the origin of phase space. (b) Cross-section of Wigner function in P = 0 plane: reconstructed state (solid red line), predicted state (solid green line) and perfect three-photon state (dashed gray line).

Equations (4)

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| ψ 1 λ 2 ( | 0 , 0 + λ | 1 , 1 + λ 2 | 2 , 2 + λ 3 | 3 , 3 + O ( λ 4 ) ) ,
η he = R C η apd R trigger ,
ρ ^ meas = ( 1 η ) | 0 0 | + η | 1 1 | ,
F = Tr [ ( ρ ^ m ρ ^ p ρ ^ m ) 1 / 2 ] ,

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