Abstract

Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.

© 2017 Optical Society of America

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2016 (3)

J. B. Christensen, C. J. McKinstrie, and K. Rottwitt, “Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing,” Phys. Rev. A 94, 013819 (2016).
[Crossref]

N. Liu, Y. Liu, X. Guo, L. Yang, X. Li, and Z. Y. Ou, “Approaching single temporal mode operation in twin beams generated by pulse pumped high gain spontaneous four wave mixing,” Opt. Express 24, 1096–1108 (2016).
[Crossref] [PubMed]

G. F. Sinclair and M. G. Thompson, “Effect of self- and cross-phase modulation on photon pairs generated by spontaneous four-wave mixing in integrated optical waveguides,” Phys. Rev. A 94, 063855 (2016).
[Crossref]

2015 (5)

B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “On the effects of self- and cross-phase modulation on photon purity for four-wave mixing photon-pair sources,” Phys. Rev. A. 92, 053849 (2015).
[Crossref]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

I. A. Walmsley, “Quantum optics: Science and technology in a new light,” Science 348, 525–530 (2015).
[Crossref] [PubMed]

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

J. P. Dowling and K. P. Seshadreesan, “Quantum Optical Technologies for Metrology, Sensing, and Imaging,” J. Lightwave Technol. 33, 2359–2370 (2015).
[Crossref]

2014 (2)

2013 (4)

B. Fang, O. Cohen, J. B. Moreno, and V. O. Lorenz, “State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing,” Opt. Express 21, 2707–2717 (2013).
[Crossref] [PubMed]

C. J. McKinstrie and M. Karlsson, “Schmidt decompositions of parametric processes I: Basic theory and simple examples,” Opt. Express 21, 1374–1394 (2013).
[Crossref] [PubMed]

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal Multi-Photon Phase Sensing with a Single Interference Fringe,” Sci. Rep. 32684 (2013).
[Crossref] [PubMed]

M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21, 5311–5317 (2013).
[Crossref]

2012 (3)

2011 (1)

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
[Crossref] [PubMed]

2010 (2)

U. L. Andersen, G. Leuchs, and C. Silberhorn, “Continuous-variable quantum information processing,” Laser Photon. Rev. 4, 337–354 (2010).
[Crossref]

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref] [PubMed]

2009 (2)

M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009).
[Crossref] [PubMed]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

2008 (1)

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]

2007 (3)

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15, 14870–14886 (2007).
[Crossref] [PubMed]

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

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature 448, 784–786 (2007).
[Crossref] [PubMed]

2006 (1)

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

2005 (5)

D. Amans, E. Brainis, M. Haelterman, P. Emplit, and S. Massar, “Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime,” Opt. Lett. 30, 1051–1053 (2005).
[Crossref] [PubMed]

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A 71, 055801 (2005).
[Crossref]

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[Crossref] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

2004 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt. 51, 1739–1759 (2004).
[Crossref]

2002 (3)

A. C. Funk and M. G. Raymer, “Quantum key distribution using non-classical photon number correlations in macroscopic light pulses,” Phys. Rev. A 65, 042307 (2002).
[Crossref]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

2001 (2)

J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
[Crossref]

D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63, 022309 (2001).
[Crossref]

1998 (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

1995 (1)

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

1990 (4)

O. Aytur and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551–1554 (1990).
[Crossref] [PubMed]

C. J. McKinstrie and G. G. Luther, “The modulational instability of colinear waves,” Phys. Scripta 30, 31–40 (1990).
[Crossref]

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
[Crossref] [PubMed]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[Crossref]

1989 (1)

M. G. Raymer, Z. W. Li, and I. A. Walmsley, “Temporal quantum fluctuations in stimulated Raman scattering: Coherent-modes description,” Phys. Rev. Lett. 63, 1586–1589 (1989).
[Crossref] [PubMed]

1987 (2)

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]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

1986 (1)

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

1982 (1)

1981 (2)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

1970 (1)

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

1965 (1)

D. L. Bobroff, “Coupled-modes analysis of the photon-photon parametric backward-wave oscillator,” J. Appl. Phys. 36, 1760–1769 (1965).
[Crossref]

Amans, D.

Andersen, U. L.

U. L. Andersen, G. Leuchs, and C. Silberhorn, “Continuous-variable quantum information processing,” Laser Photon. Rev. 4, 337–354 (2010).
[Crossref]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Aytur, O.

O. Aytur and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551–1554 (1990).
[Crossref] [PubMed]

Bachor, H. A.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Banaszek, K.

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

Bell, B.

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B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

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C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Single-temporal-mode photon generation beyond the low-power regime,” Quantum Information and Measurement conference, Paris, France, 5–7 April 2017, paper QW3C.6. In the simulations, β1 = 10s/cm, β2 = 0.2 ps2/cm and l = 1.0 cm.

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M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
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Fuchs, C. A.

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N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
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A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
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Gerry, C. C.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005). Two-mode squeezed vacuum states are discussed in Sec. 7.7.

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R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
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A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature 448, 784–786 (2007).
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A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

Guo, X.

Haelterman, M.

Halder, M.

Harvey, J. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
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G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal Multi-Photon Phase Sensing with a Single Interference Fringe,” Sci. Rep. 32684 (2013).
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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).
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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

Huntington, E.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
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A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature 448, 784–786 (2007).
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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
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Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
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A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
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Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
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Knight, P. L.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005). Two-mode squeezed vacuum states are discussed in Sec. 7.7.

Kok, P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Downing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
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M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
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Lam, P. K.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
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M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Lee, N.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
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Leonhardt, R.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[Crossref]

Leuchs, G.

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

U. L. Andersen, G. Leuchs, and C. Silberhorn, “Continuous-variable quantum information processing,” Laser Photon. Rev. 4, 337–354 (2010).
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M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
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Li, Z. W.

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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
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Liu, Y.

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
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W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
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A. I. Lvovsky, “Squeezed light,” in Photonics: Scientific Foundations, Technology and Applications, Volume 1, edited by D. Andrews, ed. (Wiley, 2015), pp. 121–164.

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V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
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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).
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M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2007).
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Mavalvala, N.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref] [PubMed]

McCall, S. L.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

McClelland, D. E.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref] [PubMed]

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B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “On the effects of self- and cross-phase modulation on photon purity for four-wave mixing photon-pair sources,” Phys. Rev. A. 92, 053849 (2015).
[Crossref]

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McKinstrie, C. J.

J. B. Christensen, C. J. McKinstrie, and K. Rottwitt, “Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing,” Phys. Rev. A 94, 013819 (2016).
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C. J. McKinstrie and M. Karlsson, “Schmidt decompositions of parametric processes I: Basic theory and simple examples,” Opt. Express 21, 1374–1394 (2013).
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L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
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L. Mejling, D. S. Cargill, C. J. McKinstrie, K. Rottwitt, and R. O. Moore, “Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime,” Opt. Express 20, 27454–27475 (2012).
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K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15, 14870–14886 (2007).
[Crossref] [PubMed]

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

C. J. McKinstrie and G. G. Luther, “The modulational instability of colinear waves,” Phys. Scripta 30, 31–40 (1990).
[Crossref]

C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Single-temporal-mode photon generation beyond the low-power regime,” Quantum Information and Measurement conference, Paris, France, 5–7 April 2017, paper QW3C.6. In the simulations, β1 = 10s/cm, β2 = 0.2 ps2/cm and l = 1.0 cm.

McMillan, A.

B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “On the effects of self- and cross-phase modulation on photon purity for four-wave mixing photon-pair sources,” Phys. Rev. A. 92, 053849 (2015).
[Crossref]

Mejling, L.

Milburn, G. J.

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

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

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Ou, Z. Y.

N. Liu, Y. Liu, X. Guo, L. Yang, X. Li, and Z. Y. Ou, “Approaching single temporal mode operation in twin beams generated by pulse pumped high gain spontaneous four wave mixing,” Opt. Express 24, 1096–1108 (2016).
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F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

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]

Ourjoumtsev, A.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature 448, 784–786 (2007).
[Crossref] [PubMed]

Peng, K. C.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
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Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Polzik, E. S.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Preskill, J.

D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63, 022309 (2001).
[Crossref]

Pryde, G. J.

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal Multi-Photon Phase Sensing with a Single Interference Fringe,” Sci. Rep. 32684 (2013).
[Crossref] [PubMed]

Radic, S.

Radzewicz, C.

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

Ralph, T. C.

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

Rangel-Rojo, R.

Rarity, J.

B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “On the effects of self- and cross-phase modulation on photon purity for four-wave mixing photon-pair sources,” Phys. Rev. A. 92, 053849 (2015).
[Crossref]

Rarity, J. G.

Raymer, M. G.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
[Crossref] [PubMed]

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15, 14870–14886 (2007).
[Crossref] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[Crossref] [PubMed]

M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt. 51, 1739–1759 (2004).
[Crossref]

A. C. Funk and M. G. Raymer, “Quantum key distribution using non-classical photon number correlations in macroscopic light pulses,” Phys. Rev. A 65, 042307 (2002).
[Crossref]

M. G. Raymer, Z. W. Li, and I. A. Walmsley, “Temporal quantum fluctuations in stimulated Raman scattering: Coherent-modes description,” Phys. Rev. Lett. 63, 1586–1589 (1989).
[Crossref] [PubMed]

M. G. Raymer, K. Rzazewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[Crossref] [PubMed]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Single-temporal-mode photon generation beyond the low-power regime,” Quantum Information and Measurement conference, Paris, France, 5–7 April 2017, paper QW3C.6. In the simulations, β1 = 10s/cm, β2 = 0.2 ps2/cm and l = 1.0 cm.

Reddy, D. V.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

Reid, M. D.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Rothenberg, J. E.

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
[Crossref] [PubMed]

Rottwitt, K.

J. B. Christensen, C. J. McKinstrie, and K. Rottwitt, “Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing,” Phys. Rev. A 94, 013819 (2016).
[Crossref]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
[Crossref] [PubMed]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

L. Mejling, D. S. Cargill, C. J. McKinstrie, K. Rottwitt, and R. O. Moore, “Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime,” Opt. Express 20, 27454–27475 (2012).
[Crossref] [PubMed]

C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Single-temporal-mode photon generation beyond the low-power regime,” Quantum Information and Measurement conference, Paris, France, 5–7 April 2017, paper QW3C.6. In the simulations, β1 = 10s/cm, β2 = 0.2 ps2/cm and l = 1.0 cm.

Rzazewski, K.

Schnabel, R.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref] [PubMed]

Seshadreesan, K. P.

Sharping, J. E.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Observation of twin-beam-type quantum correlation in optical fiber,” Opt. Lett. 26, 367–369 (2001).
[Crossref]

Silberhorn, C.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

U. L. Andersen, G. Leuchs, and C. Silberhorn, “Continuous-variable quantum information processing,” Laser Photon. Rev. 4, 337–354 (2010).
[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]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

Sinclair, G. F.

G. F. Sinclair and M. G. Thompson, “Effect of self- and cross-phase modulation on photon pairs generated by spontaneous four-wave mixing in integrated optical waveguides,” Phys. Rev. A 94, 063855 (2016).
[Crossref]

Smith, B. J.

M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21, 5311–5317 (2013).
[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]

Söller, C.

M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21, 5311–5317 (2013).
[Crossref]

Sorensen, J. L.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Takeda, S.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
[Crossref] [PubMed]

Takeno, Y.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
[Crossref] [PubMed]

Thompson, M. G.

G. F. Sinclair and M. G. Thompson, “Effect of self- and cross-phase modulation on photon pairs generated by spontaneous four-wave mixing in integrated optical waveguides,” Phys. Rev. A 94, 063855 (2016).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Treps, N.

Tualle-Brouri, R.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature 448, 784–786 (2007).
[Crossref] [PubMed]

U’Ren, A. B.

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. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15, 14870–14886 (2007).
[Crossref] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

van Loock, P.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

Voss, P. L.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

Wadsworth, W. J.

Walmsley, I. A.

I. A. Walmsley, “Quantum optics: Science and technology in a new light,” Science 348, 525–530 (2015).
[Crossref] [PubMed]

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. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15, 14870–14886 (2007).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[Crossref] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

M. G. Raymer, Z. W. Li, and I. A. Walmsley, “Temporal quantum fluctuations in stimulated Raman scattering: Coherent-modes description,” Phys. Rev. Lett. 63, 1586–1589 (1989).
[Crossref] [PubMed]

Wasilewski, W.

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

Wasylczyk, P.

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]

Webb, J.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
[Crossref] [PubMed]

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Wright, L. J.

M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21, 5311–5317 (2013).
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M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

Xiang, G. Y.

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal Multi-Photon Phase Sensing with a Single Interference Fringe,” Sci. Rep. 32684 (2013).
[Crossref] [PubMed]

Xiao, M.

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

Xiong, C.

Yang, L.

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B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
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Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Zhang, W.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
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Zukowski, M.

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983–985 (2002).
[Crossref]

J. Appl. Phys. (1)

D. L. Bobroff, “Coupled-modes analysis of the photon-photon parametric backward-wave oscillator,” J. Appl. Phys. 36, 1760–1769 (1965).
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J. Lightwave Technol. (1)

J. Mod. Opt. (1)

M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt. 51, 1739–1759 (2004).
[Crossref]

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

Laser Photon. Rev. (1)

U. L. Andersen, G. Leuchs, and C. Silberhorn, “Continuous-variable quantum information processing,” Laser Photon. Rev. 4, 337–354 (2010).
[Crossref]

Laser Phys. (1)

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146–161 (2005).

Nat. Commun. (2)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref] [PubMed]

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref] [PubMed]

Nature (1)

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical Schrödinger cats from photon number states,” Nature 448, 784–786 (2007).
[Crossref] [PubMed]

Opt. Commun. (2)

M. Chekhova, G. Leuchs, and M. Zukowski, “Bright squeezed vacuum: Entanglement of macroscopic light beams,” Opt. Commun. 337, 27–43 (2015).
[Crossref]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[Crossref]

Opt. Express (8)

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15, 14870–14886 (2007).
[Crossref] [PubMed]

M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009).
[Crossref] [PubMed]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express 20, 8367–8396 (2012).
[Crossref] [PubMed]

L. Mejling, D. S. Cargill, C. J. McKinstrie, K. Rottwitt, and R. O. Moore, “Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime,” Opt. Express 20, 27454–27475 (2012).
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C. J. McKinstrie and M. Karlsson, “Schmidt decompositions of parametric processes I: Basic theory and simple examples,” Opt. Express 21, 1374–1394 (2013).
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N. Liu, Y. Liu, X. Guo, L. Yang, X. Li, and Z. Y. Ou, “Approaching single temporal mode operation in twin beams generated by pulse pumped high gain spontaneous four wave mixing,” Opt. Express 24, 1096–1108 (2016).
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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, 5311–5317 (2013).
[Crossref]

Opt. Lett. (3)

Phys. Plasmas (1)

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas 2, 4596–4605 (1995).
[Crossref]

Phys. Rev. A (10)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A 85, 053829 (2012).
[Crossref]

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42, 682–685 (1990).
[Crossref] [PubMed]

G. F. Sinclair and M. G. Thompson, “Effect of self- and cross-phase modulation on photon pairs generated by spontaneous four-wave mixing in integrated optical waveguides,” Phys. Rev. A 94, 063855 (2016).
[Crossref]

D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63, 022309 (2001).
[Crossref]

A. C. Funk and M. G. Raymer, “Quantum key distribution using non-classical photon number correlations in macroscopic light pulses,” Phys. Rev. A 65, 042307 (2002).
[Crossref]

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
[Crossref]

J. B. Christensen, C. J. McKinstrie, and K. Rottwitt, “Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing,” Phys. Rev. A 94, 013819 (2016).
[Crossref]

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A 71, 055801 (2005).
[Crossref]

W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006).
[Crossref]

Phys. Rev. A. (1)

B. Bell, A. McMillan, W. McCutcheon, and J. Rarity, “On the effects of self- and cross-phase modulation on photon purity for four-wave mixing photon-pair sources,” Phys. Rev. A. 92, 053849 (2015).
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Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Phys. Rev. Lett. (7)

M. G. Raymer, Z. W. Li, and I. A. Walmsley, “Temporal quantum fluctuations in stimulated Raman scattering: Coherent-modes description,” Phys. Rev. Lett. 63, 1586–1589 (1989).
[Crossref] [PubMed]

M. Xiao, L. A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[Crossref] [PubMed]

O. Aytur and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551–1554 (1990).
[Crossref] [PubMed]

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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Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
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D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Phys. Rev. X (1)

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

Phys. Scripta (1)

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Rev. Mod. Phys. (4)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Downing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
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M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Sci. Rep. (1)

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal Multi-Photon Phase Sensing with a Single Interference Fringe,” Sci. Rep. 32684 (2013).
[Crossref] [PubMed]

Science (5)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–332 (2011).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

I. A. Walmsley, “Quantum optics: Science and technology in a new light,” Science 348, 525–530 (2015).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[Crossref] [PubMed]

Other (7)

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2007).
[Crossref]

R. W. Boyd, Nonlinear Optics, 3rd Ed. (Academic, 2008).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

A. I. Lvovsky, “Squeezed light,” in Photonics: Scientific Foundations, Technology and Applications, Volume 1, edited by D. Andrews, ed. (Wiley, 2015), pp. 121–164.

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University, 2000).

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005). Two-mode squeezed vacuum states are discussed in Sec. 7.7.

C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Single-temporal-mode photon generation beyond the low-power regime,” Quantum Information and Measurement conference, Paris, France, 5–7 April 2017, paper QW3C.6. In the simulations, β1 = 10s/cm, β2 = 0.2 ps2/cm and l = 1.0 cm.

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Figures (13)

Fig. 1
Fig. 1 Contour plot of the Green function νrs for two cases in which the pump shapes are Gauss (HG0) functions. (a) βpl/τ = βrl/τ = 1 and βql/τ = βsl/τ = −1. (b) βpl/τ = 4 = − βql/τ and βrl/τ = 2 = − βsl/τ. Lighter shading represents higher values, whereas darker shading represents lower values. Time is measured in units of τ. The input and output times are correlated.
Fig. 2
Fig. 2 The normalized Schmidt coefficient is plotted as a function of mode number for two HG0 pumps. (a) βpl/τ = βrl/τ = 1 and βql/τ = βsl/τ = −1. (b) βpl/τ = 4 = − βql/τ and βrl/τ = 2 = − βsl/τ. Several coefficients are nonzero.
Fig. 3
Fig. 3 Frequency diagrams for vector four-wave mixing in a strongly-birefringent medium [44]. Points on the blue (red) curves denote waves that are aligned with the fast (slow) axes of the medium. The wavenumbers and slownesses (β1) are matched simultaneously for pump frequencies that are (a) degenerate and (b) nondegenerate. Notice that the copropagating waves have different polarizations. The pump and sideband frequencies can be interchanged (pr and qs). The displayed diagrams pertain to the anomalous dispersion regime and similar diagrams pertain to the normal dispersion regime.
Fig. 4
Fig. 4 Characteristic diagram for (a) idler generation and (b) signal generation. The horizontal axis is distance and the vertical axis is time. The interaction is limited to the region in which the pumps collide, which is the interior of the dashed diamond. The blue and red rays (arrows) represent parts of the signal and idler that interact strongly.
Fig. 5
Fig. 5 The first Schmidt coefficient is plotted as a function of the gain parameter γ ¯. In (a) the solid line is γ ¯ and the vertical scale is linear, whereas in (b) the solid curve is exp ( 2 γ ¯ ) / ( 16 π γ ¯ ) 1 / 2 and the scale is logarithmic. Filled circles denote results for two HG0 pumps, whereas empty circles denote results for one HG0 and one HG1 pump. The Schmidt coefficients do not depend on the pump shapes.
Fig. 6
Fig. 6 (a) The ratio of the second Schmidt coefficient to the first is plotted as a function of the gain parameter γ ¯. Filled circles denote results for two HG0 pumps, whereas empty circles denote results for one HG0 and one HG1 pump. The relative probability of the second mode, which is the square of the Schmidt ratio, never exceeds 1%. (b) The Schmidt ratio is plotted as a function of mode number for the worst case, in which γ ¯ = 1.76. The HG0-HG0 and HG0-HG1 results are indistinguishable.
Fig. 7
Fig. 7 Contour plots of the Green function νrs for the gain parameters (a) γ ¯ = 0.3 and (b) γ ¯ = 3.0. Both pump shapes are Gauss (HG0) functions. Lighter shading represents higher values, whereas darker shading represents lower values. High gain localizes the Green function near early input and output times.
Fig. 8
Fig. 8 The (common) signal and idler Schmidt function (dots) is plotted as a function of time for the gain parameters (a) γ ¯ = 0.3 and (b) γ ¯ = 3.0. Both pump shapes (solid curves) are Gauss (HG0) functions. In the low-gain regime the Schmidt function is approximately Gaussian, whereas in the high-gain regime it is a distorted Gaussian.
Fig. 9
Fig. 9 Contour plots of the Green function νrs for the gain parameters (a) γ ¯ = 0.3 and (b) γ ¯ = 3.0. The pump shapes are HG0 and HG1 functions. Lighter shading represents higher values, whereas darker shading represents lower values. High gain localizes the Green function near early input and output times.
Fig. 10
Fig. 10 The input signal (a) and output idler (b) Schmidt functions (dots) are plotted as functions of time for the gain parameter γ ¯ = 0.3. The pump shapes (solid curves) are HG0 and HG1 functions. In the low-gain regime both Schmidt functions are approximately HG functions.
Fig. 11
Fig. 11 The input signal (a) and output idler (b) Schmidt functions (dots) are plotted as functions of time for the gain parameter γ ¯ = 3.0. The pump shapes (solid curves) are HG0 and HG1 functions. In the high-gain regime both Schmidt functions are distorted HG functions.
Fig. 12
Fig. 12 The ratio of the second Schmidt coefficient to the first is plotted as a function of the gain parameter γ ¯ for two Gauss (HG0) pumps. The solid curve denotes semi-analytical results that omit nonlinear phase modulation, whereas crosses denote numerical results that include nonlinear phase modulation. The results are qualitatively similar and quantitatively comparable.
Fig. 13
Fig. 13 The amplitudes (blue curves) and phases (red curves) of the input signal (a) and output idler (b) Schmidt functions are plotted as functions of time for the gain parameter γ ¯ = 1.55. Both pump shapes are Gauss (HG0) functions. Nonlinear phase modulation imposes opposite chirps and frequency shifts on the signal and idler. The chirps are extremal near the peaks of the copropagating pumps, relative to which the signal and idler are skewed toward early times.

Equations (31)

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( z + β r t ) A r ( t , z ) = i γ p q ( t , z ) A s * ( t , z ) ,
( z + β s t ) A s ( t , z ) = i γ p q ( t , z ) A r * ( t , z ) ,
b r ( t ) = d t [ μ r r ( t , t ) a r ( t ) + ν r s ( t , t ) a s ( t ) ] ,
b s ( t ) = d t [ μ s s ( t , t ) a s ( t ) + ν s r ( t , t ) a r ( t ) ] ,
d t [ μ r r ( t 1 , t ) μ r r * ( t 2 , t ) ν r s ( t 1 , t ) ν r s * ( t 2 , t ) ] = δ ( t 1 t 2 ) ,
d t [ μ r r ( t 1 , t ) ν s r ( t 2 , t ) ν r s ( t 1 , t ) μ s s ( t 2 , t ) ] = 0 .
μ r r ( t , t ) = n ν r n ( t ) μ n μ r n * ( t ) , ν r s ( t , t ) = n ν r n ( t ) ν n u s n ( t ) ,
b r n = μ n a r n + ν n a s n , b s n = μ n a s n + ν n a r n ,
| ψ n = k ( ν n / μ n ) k | k , k / μ n ,
μ s s ( t , t ) = δ ( t t β s l ) , ν r s ( t , t ) = i γ p q ( t c , z c ) / β r s ,
t c = [ β r t β s ( t β r l ) ] / β r s , z c = [ t ( t β r l ) ] / β r s .
ν r s ( t r , t s β s l ) = ν s r ( t r β r l , t s ) .
t c β p z c = [ β r p t β s p ( t β r l ) ] / β r s
| ψ 1 = d t r d t s f ( t r , t s ) a r ( t r ) a s ( t s ) | vac ,
f ( t r , t s ) = d t μ s s ( t s , t ) ν r s ( t r , t ) = d t μ r r ( t r , t ) ν s r ( t s , t )
f ( t r , t s ) = n ν n ν r n ( t r ) ν s n ( t s ) ,
HG n ( s ) = H n ( s / τ ) exp ( s 2 / 2 τ 2 ) / π 1 / 4 ( 2 n n ! τ ) 1 / 2 ,
μ s s ( t , t ) = δ ( t t β s l ) + γ ¯ A q ( t β s l ) ( ξ / η ) 1 / 2 I 1 [ 2 γ ¯ ( ξ η ) 1 / 2 ] A q ( t ) × H ( t t β s l ) H ( t + β r l t ) ,
ν r s ( t , t ) = i γ ¯ A p ( t β r l ) I 0 [ 2 γ ¯ ( ξ η ) 1 / 2 ] A q ( t ) H ( t t β s l ) H ( t + β r l t ) ,
ξ ( t , t ) = t β r l t d s | A p ( s ) | 2 , η ( t , t ) = t t β s l d s | A q ( s ) | 2 .
k s ( t s , t s ) = d t r ν r s * ( t r , t s ) ν r s ( t r , t s ) ,
k r ( t r , t r ) = d t s ν r s ( t r , t s ) ν r s * ( t r , t s ) .
( z + β r t ) A r = i γ p q A s * + σ r δ ( z ) δ ( t ) , ( z + β s t ) A s = i γ p q A r * + σ s δ ( z ) δ ( t ) ,
y A r = i γ ¯ A p ( x ) A q ( y ) A s * + σ r δ ( x ) δ ( y ) , x A s = i γ ¯ A p ( x ) A q ( y ) A r * + σ s δ ( x ) δ ( y ) ,
η A r = i γ ¯ A s * + σ r A p * δ ( ξ ) δ ( η ) , ξ A s = i γ ¯ A r * + σ s A q * δ ( ξ ) δ ( η ) ,
G r s ( ξ , η ) = i γ ¯ I 0 [ 2 γ ¯ ( ξ η ) 1 / 2 ] H ( ξ ) H ( η ) ,
G s s ( ξ , η ) = γ ¯ ( ξ / η ) 1 / 2 I 1 [ 2 γ ¯ ( ξ η ) 1 / 2 ] H ( ξ ) H ( η ) + H ( ξ ) δ ( η ) ,
G r s ( ξ , η ) ~ γ ¯ exp [ 2 γ ¯ ξ 1 / 2 ( 1 η ) 1 / 2 ] ( 4 π γ ¯ ) 1 / 2 ~ γ ¯ exp [ 2 γ ¯ γ ¯ ( 1 ξ ) γ ¯ η ] ( 4 π γ ¯ ) 1 / 2 .
G r s ( t , t ) = γ ¯ A p ( t β r l ) I 0 [ 2 γ ¯ ( ξ η ) 1 / 2 ] A q ( t ) × H ( t t β s l ) H ( t + β r l t ) ,
G s s ( t , t ) = δ ( t t β s l ) + γ ¯ A p ( t β s l ) ( ξ / η ) 1 / 2 I 1 [ 2 γ ¯ ( ξ η ) 1 / 2 ] A q ( t ) × H ( t t β s l ) H ( t + β r l t ) ,
ξ ( t , t ) = t β r l t d s | A p ( s ) | 2 , η ( t , t ) = t t β s l d s | A q ( s ) | 2 .

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