Abstract

We develop the theory of frequency up-conversion of an arbitrary spatially-broadband quantum state (quantum image), deriving the analytical solutions for the cases of plane-wave pump and short crystal with arbitrary pump. By using an example of the quantum image imposed by the orbital angular momentum of the pump beam in spontaneous parametric down-conversion, we show that 99%-fidelity up-conversion of quantum images from an infrared wavelength to the visible wavelength can be obtained in periodically-poled lithium-niobate crystals at reasonable pump intensities well below the crystal damage threshold.

© 2012 OSA

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  1. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
    [CrossRef]
  2. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999).
    [CrossRef] [PubMed]
  3. D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys. 56, 281 (2001).
  4. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954 (1999).
    [CrossRef]
  5. R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
    [CrossRef]
  6. Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
    [CrossRef]
  7. M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71(5), 1539–1589 (1999).
    [CrossRef]
  8. S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83(10), 1938–1941 (1999).
    [CrossRef]
  9. K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. 5(4), S535–S544 (2003).
    [CrossRef]
  10. A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94(22), 223603 (2005).
    [CrossRef] [PubMed]
  11. E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” J. Sel. Top. Quantum Electron. 14(3), 635–647 (2008).
    [CrossRef]
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    [CrossRef]
  14. J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
    [CrossRef] [PubMed]
  15. H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105(9), 093604 (2010).
    [CrossRef] [PubMed]
  16. M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
    [CrossRef]
  17. A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
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  20. A. S. Chirkin and E. V. Makeev, “Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image,” J. Opt. B Quantum Semiclassical Opt. 7(12), S500–S506 (2005).
    [CrossRef]
  21. E. V. Makeev and A. S. Chirkin, “Quantum fluctuations of parametrically amplified and up-converted optical images in consecutive wave interactions,” J. Russ. Laser Res. 27(5), 466–474 (2006).
    [CrossRef]
  22. G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A 65(5), 053801 (2002).
    [CrossRef]
  23. A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. 94(12), 123601 (2005).
    [CrossRef] [PubMed]
  24. M. L. Marable, S.-K. Choi, and P. Kumar, “Measurement of quantum-noise correlations in parametric image amplification,” Opt. Express 2(3), 84–92 (1998).
    [CrossRef] [PubMed]
  25. O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
    [CrossRef] [PubMed]
  26. J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101(23), 233604 (2008).
    [CrossRef] [PubMed]
  27. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
    [CrossRef] [PubMed]
  28. A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
    [CrossRef]
  29. M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17(14), 11415–11425 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11415 .
    [CrossRef] [PubMed]
  30. M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009).
    [CrossRef]
  31. S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, “Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response,” J. Opt. Soc. Am. B 14(7), 1564 (1997).
    [CrossRef]
  32. C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
    [CrossRef]
  33. K. G. Köprülü and O. Aytür, “Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states,” Phys. Rev. A 60(5), 4122–4134 (1999).
    [CrossRef]
  34. K. G. Köprülü and O. Aytür, “Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers,” J. Opt. Soc. Am. B 18(6), 846 (2001).
    [CrossRef]
  35. M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010).
    [CrossRef]
  36. M. Annamalai, M. Vasilyev, N. Stelmakh, and P. Kumar, “Compact representation of spatial modes of phase-sensitive image amplifier,” the Conference on Lasers and Electro-Optics, Baltimore, MD, May 1–6, 2011, paper JThB77.
  37. K. G. Köprülü, Y.-P. Huang, G. A. Barbosa, and P. Kumar, “Lossless single-photon shaping via heralding,” Opt. Lett. 36(9), 1674–1676 (2011).
    [CrossRef] [PubMed]

2011 (2)

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

K. G. Köprülü, Y.-P. Huang, G. A. Barbosa, and P. Kumar, “Lossless single-photon shaping via heralding,” Opt. Lett. 36(9), 1674–1676 (2011).
[CrossRef] [PubMed]

2010 (5)

M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010).
[CrossRef]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105(9), 093604 (2010).
[CrossRef] [PubMed]

M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
[CrossRef]

2009 (2)

M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17(14), 11415–11425 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11415 .
[CrossRef] [PubMed]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009).
[CrossRef]

2008 (3)

J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101(23), 233604 (2008).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” J. Sel. Top. Quantum Electron. 14(3), 635–647 (2008).
[CrossRef]

2007 (1)

L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103(1), 62–66 (2007).
[CrossRef]

2006 (1)

E. V. Makeev and A. S. Chirkin, “Quantum fluctuations of parametrically amplified and up-converted optical images in consecutive wave interactions,” J. Russ. Laser Res. 27(5), 466–474 (2006).
[CrossRef]

2005 (3)

A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. 94(12), 123601 (2005).
[CrossRef] [PubMed]

A. S. Chirkin and E. V. Makeev, “Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image,” J. Opt. B Quantum Semiclassical Opt. 7(12), S500–S506 (2005).
[CrossRef]

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94(22), 223603 (2005).
[CrossRef] [PubMed]

2004 (1)

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
[CrossRef] [PubMed]

2003 (1)

K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. 5(4), S535–S544 (2003).
[CrossRef]

2002 (1)

G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A 65(5), 053801 (2002).
[CrossRef]

2001 (2)

K. G. Köprülü and O. Aytür, “Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers,” J. Opt. Soc. Am. B 18(6), 846 (2001).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys. 56, 281 (2001).

1999 (5)

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954 (1999).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999).
[CrossRef] [PubMed]

M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71(5), 1539–1589 (1999).
[CrossRef]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83(10), 1938–1941 (1999).
[CrossRef]

K. G. Köprülü and O. Aytür, “Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states,” Phys. Rev. A 60(5), 4122–4134 (1999).
[CrossRef]

1998 (2)

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
[CrossRef]

M. L. Marable, S.-K. Choi, and P. Kumar, “Measurement of quantum-noise correlations in parametric image amplification,” Opt. Express 2(3), 84–92 (1998).
[CrossRef] [PubMed]

1997 (1)

1992 (1)

J. M. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68(14), 2153–2156 (1992).
[CrossRef] [PubMed]

1987 (1)

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[CrossRef]

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
[CrossRef]

1968 (1)

J. E. Midwinter, “Image conversion from 1.6 μm to the visible in lithium niobate,” Appl. Phys. Lett. 12(3), 68–70 (1968).
[CrossRef]

Altman, A. R.

A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. 94(12), 123601 (2005).
[CrossRef] [PubMed]

Andrekson, P. A.

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Annamalai, M.

M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010).
[CrossRef]

Arnaut, H. H.

G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A 65(5), 053801 (2002).
[CrossRef]

Aytür, O.

K. G. Köprülü and O. Aytür, “Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers,” J. Opt. Soc. Am. B 18(6), 846 (2001).
[CrossRef]

K. G. Köprülü and O. Aytür, “Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states,” Phys. Rev. A 60(5), 4122–4134 (1999).
[CrossRef]

Bache, M.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
[CrossRef] [PubMed]

Barbosa, G. A.

K. G. Köprülü, Y.-P. Huang, G. A. Barbosa, and P. Kumar, “Lossless single-photon shaping via heralding,” Opt. Lett. 36(9), 1674–1676 (2011).
[CrossRef] [PubMed]

A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. 94(12), 123601 (2005).
[CrossRef] [PubMed]

G. A. Barbosa and H. H. Arnaut, “Twin photons with angular-momentum entanglement: phase matching,” Phys. Rev. A 65(5), 053801 (2002).
[CrossRef]

Blanchet, J. L.

J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101(23), 233604 (2008).
[CrossRef] [PubMed]

Blessing, D. J.

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Bogris, A.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Boyer, V.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Brambilla, E.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
[CrossRef] [PubMed]

Cardimona, D.

A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[CrossRef]

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982).
[CrossRef]

Chirkin, A. S.

E. V. Makeev and A. S. Chirkin, “Quantum fluctuations of parametrically amplified and up-converted optical images in consecutive wave interactions,” J. Russ. Laser Res. 27(5), 466–474 (2006).
[CrossRef]

A. S. Chirkin and E. V. Makeev, “Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image,” J. Opt. B Quantum Semiclassical Opt. 7(12), S500–S506 (2005).
[CrossRef]

Choi, S.-K.

Cohadon, P. F.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
[CrossRef]

Corndorf, E.

A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, “Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum,” Phys. Rev. Lett. 94(12), 123601 (2005).
[CrossRef] [PubMed]

Dasgupta, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Devaux, F.

E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” J. Sel. Top. Quantum Electron. 14(3), 635–647 (2008).
[CrossRef]

J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101(23), 233604 (2008).
[CrossRef] [PubMed]

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94(22), 223603 (2005).
[CrossRef] [PubMed]

Di Trapani, P.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
[CrossRef] [PubMed]

Dudin, Y. O.

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
[CrossRef]

Ellis, A. D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Fabre, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
[CrossRef]

Furfaro, L.

J. L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101(23), 233604 (2008).
[CrossRef] [PubMed]

Gatti, A.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
[CrossRef] [PubMed]

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R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
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Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
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M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17(14), 11415–11425 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11415 .
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M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009).
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A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
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D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys. 56, 281 (2001).

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999).
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Li, R.-D.

Lugiato, L.

K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. 5(4), S535–S544 (2003).
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Lugiato, L. A.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93(24), 243601 (2004).
[CrossRef] [PubMed]

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Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103(1), 62–66 (2007).
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Marino, A. M.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
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C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
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H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105(9), 093604 (2010).
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Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
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H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105(9), 093604 (2010).
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A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94(22), 223603 (2005).
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O'Gorman, J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Parmigiani, F.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

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A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. 62(7), 2640–2645 (1987).
[CrossRef]

Petropoulos, P.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Phelan, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

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V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Puttnam, B. J.

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

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H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105(9), 093604 (2010).
[CrossRef] [PubMed]

Radnaev, A. G.

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
[CrossRef]

Rakher, M. T.

M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Raymer, M. G.

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105(9), 093604 (2010).
[CrossRef] [PubMed]

Richardson, D. J.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Ritsch, H.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
[CrossRef]

Schwob, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998).
[CrossRef]

Sjodin, M.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Slattery, O. T.

M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Slavík, R.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Sokolov, I. V.

L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103(1), 62–66 (2007).
[CrossRef]

Srinivasan, K.

M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Stelmakh, N.

M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010).
[CrossRef]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009).
[CrossRef]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17(14), 11415–11425 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11415 .
[CrossRef] [PubMed]

Sygletos, S.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Syvridis, D.

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954 (1999).
[CrossRef]

Tang, X.

M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

Tipsuwannakul, E.

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Toda, H.

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Tong, Z.

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Vasilyev, M.

M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010).
[CrossRef]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009).
[CrossRef]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17(14), 11415–11425 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11415 .
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D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys. 56, 281 (2001).

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999).
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S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83(10), 1938–1941 (1999).
[CrossRef]

Wang, K.

K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. 5(4), S535–S544 (2003).
[CrossRef]

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R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
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W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954 (1999).
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K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. 5(4), S535–S544 (2003).
[CrossRef]

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A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
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M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave-pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009).
[CrossRef]

M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010).
[CrossRef]

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A. S. Chirkin and E. V. Makeev, “Simultaneous phase-sensitive parametric amplification and up-conversion of an optical image,” J. Opt. B Quantum Semiclassical Opt. 7(12), S500–S506 (2005).
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[CrossRef]

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D. Levandovsky, M. Vasilyev, and P. Kumar, ““Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–,” J. Phys. 56, 281 (2001).

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E. V. Makeev and A. S. Chirkin, “Quantum fluctuations of parametrically amplified and up-converted optical images in consecutive wave interactions,” J. Russ. Laser Res. 27(5), 466–474 (2006).
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M. T. Rakher, L. Ma, O. T. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4(11), 786–791 (2010).
[CrossRef]

R. Slavík, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010).
[CrossRef]

Z. Tong, C. Lundstrom, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Gruner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011).
[CrossRef]

Nat. Phys. (1)

A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6(11), 894–899 (2010).
[CrossRef]

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L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103(1), 62–66 (2007).
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[CrossRef]

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P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” the 14th Coherent Laser Radar Conference, Snowmass, CO, July 2007. http://space.hsv.usra.edu/CLRC/presentations/Kumar.ppt

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M. Annamalai, M. Vasilyev, N. Stelmakh, and P. Kumar, “Compact representation of spatial modes of phase-sensitive image amplifier,” the Conference on Lasers and Electro-Optics, Baltimore, MD, May 1–6, 2011, paper JThB77.

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Figures (3)

Fig. 1
Fig. 1

(a) Illustration of the phase matching, as well as the quantum image generation and up-conversion in the far field (transverse momentum space) when both the SPDC pump and the up-conversion pump are propagating in the same direction. (b) A schematic of the corresponding experimental setup. Inserts 2 and 3 in (a) show the quantum image function |F( q s , q i0 ) | 2 for the cases of SPDC pumping by LG00 and LG02 modes, respectively, and insert 1 is the image obtained by scanning a single photon-counting detector across the output plane in the far field. All three inserts are equally applicable to the configuration shown in Fig. 2. SPDC–spontaneous parametric down-conversion, FC–frequency up-conversion.

Fig. 2
Fig. 2

(a) Illustration of the phase matching, as well as the quantum image generation and up-conversion in the far field (transverse momentum space) when the up-conversion pump is propagating along the k i0 2 q i0 direction. (b) A schematic of the corresponding experimental setup. For SPDC pumping by LG02, the quantum image function |F( q s , q i0 ) | 2 is proportional to the product of the red and checkered-purple rings in (a), which is sketched as two green dots. The single- and coincidence-count images for SPDC pumping by LG00 and LG02 modes are still represented by inserts 1–3 in Fig. 1. SPDC–spontaneous parametric down-conversion, FC–frequency up-conversion.

Fig. 3
Fig. 3

The fidelity of the up-converted quantum image as a function of the ratio between the lengths of the up-conversion and SPDC crystals. Black dash-dotted traces correspond to the configuration of Fig. 1, whereas colored solid and dashed traces correspond to the configuration of Fig. 2. The cases of orbital momenta l = 0, l = 2, and l = 4 correspond to the SPDC pumping by LG00, LG02, and LG04 modes, respectively. We do not show the black traces with M = 3, because they are almost indistinguishable from the black traces with M = 4.

Equations (33)

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{ E 1 ( ρ ,z) z = i 2 k 1 ρ 2 E 1 ( ρ ,z)+ 2i ω 1 d eff n 1 c E 2 * ( ρ ,z) E 3 ( ρ ,z) e iΔ k FC z , E 3 ( ρ ,z) z = i 2 k 3 ρ 2 E 3 ( ρ ,z)+ 2i ω 3 d eff n 3 c E 2 ( ρ ,z) E 1 ( ρ ,z) e iΔ k FC z ,
{ a 1 ( ρ ,z) z = i 2 k 1 ρ 2 a 1 ( ρ ,z)+i κ * ( ρ ,z) a 3 ( ρ ,z) e iΔ k FC z , a 3 ( ρ ,z) z = i 2 k 3 ρ 2 a 3 ( ρ ,z)+iκ( ρ ,z) a 1 ( ρ ,z) e iΔ k FC z ,
κ( ρ ,z)= 4 ω 1 ω 3 d eff 2 n 1 n 3 c 2 E 2 ( ρ ,z).
a ˜ 1,3 ( q ,z)= a 1,3 ( ρ ,z) e i q ρ d ρ , a 1,3 ( ρ ,z)= a ˜ 1,3 ( q ,z) e i q ρ d q (2π) 2 .
a ˜ 1,3 ( q ,z)= a ˜ 1,3 ( q ,0)exp( i q 2 2 k 1,3 z ),
a ˜ 1 ( q ,z)= e i q 2 2 k 1 z [t(q) a ˜ 1 ( q ,0)+r(q) a ˜ 3 ( q ,0)], a ˜ 3 ( q ,z)= e i q 2 2 k 3 z [ r * (q) a ˜ 1 ( q ,0)+ t * (q) a ˜ 3 ( q ,0)],
t(q)=( cosγz iΔ k eff 2γ sinγz )×exp( i Δ k eff 2 z ), r(q)=i κ * γ sinγz×exp( i Δ k eff 2 z ),
Δ k eff =Δ k FC + q 2 2 ( 1 k 1 1 k 3 ),
γ= |κ | 2 +Δ k eff 2 /4 .
R=|r | 2 = |κ | 2 γ 2 sin 2 γz
T=|t | 2 =1 |κ | 2 γ 2 sin 2 γz =1R.
{ a 1 ( ρ ,z) z =i κ * ( ρ ) a 3 ( ρ ,z) e iΔ k FC z , a 3 ( ρ ,z) z =iκ( ρ ) a 1 ( ρ ,z) e iΔ k FC z .
t( ρ ,z)=( cosγz iΔ k FC 2γ sinγz )×exp( i Δ k FC 2 z ), r( ρ ,z)=i κ * γ sinγz×exp( i Δ k FC 2 z ),
γ( ρ )= |κ | 2 ( ρ )Δ k FC 2 /4 ,|κ | 2 ( ρ )= 2 ω 1 ω 3 d eff 2 I 2 ( ρ ) ε 0 n 1 n 3 n 2 c 3 ,
a 1 ( ρ ,z)=t( ρ ,z) a 1 ( ρ ,0)+r( ρ ,z) a 3 ( ρ ,0), a 3 ( ρ ,z)= r * ( ρ ,z) a 1 ( ρ ,0)+ t * ( ρ ,z) a 3 ( ρ ,0),
|ψ=|0+ d q s d q i F( q s , q i ) |1 q s |1 q i ,
F( q s , q i ) d r E p ( r ) e iΔ k r = dz e iΔ k z z dxdy E p (x,y) e i(Δ k x x+Δ k y y) = l SPDC e iΔ k z l SPDC /2 sinc( Δ k z l SPDC 2 ) E ˜ p ( q s + q i ),
Δ k = k p k s k i = z ^ Δ k z q s q i z ^ ( k p k s k i + q s 2 2 k s + q i 2 2 k i ) q s q i z ^ q s 2 + q i 2 2 q 0 2 2 k s q s q i ,
|Ψ q s,i = t * ( q s,i ) | 10 q s,i r * ( q s,i ) | 01 q s,i ,
|ψ FC =|0+ d q s d q i F( q s , q i ) t * ( q s ) t * ( q i ) | 10 q s | 10 q i + d q s d q i F( q s , q i ) r * ( q s ) r * ( q i ) | 01 q s | 01 q i d q s d q i F( q s , q i ) r * ( q s ) t * ( q i ) | 01 q s | 10 q i d q s d q i F( q s , q i ) t * ( q s ) r * ( q i ) | 10 q s | 01 q i .
|ψ Heralded, FC = d q s F( q s , q i0 ) [ t * ( q s ) | 10 q s r * ( q s ) | 01 q s ].
η= | Heralded ψ|ψ Heralded,FC | 2 Heralded ψ|ψ Heralded Heralded,FC ψ|ψ Heralded,FC = | d q s |F( q s , q i0 ) | 2 r * ( q s ) | 2 [ d q s |F( q s , q i0 ) | 2 ] 2 ,
Δ k FC = q 0 2 2 ( 1 k 1 1 k 3 )<0, Δ k eff = q s 2 q 0 2 2 ( 1 k 1 1 k 3 ),
Δ q c FC = π 3 q 0 l FC k 1 k 3 k 3 k 1 .
Δ q c SPDC = 2π k s q 0 l SPDC =Δ q c FC 2 3 l FC n s l SPDC n 1 ( 1 k 1 k 3 ) =Δ q c FC 2 ω 2 l FC n s 3 ω 3 l SPDC n 1 .
l SPDC l FC > 2 ω 2 n s 3 ω 3 n 1 ,
Δ k FC =0, Δ k eff = q 2 2 ( 1 k 1 1 k 3 ).
( Δ q c FC ) = 2 3 π l FC k 1 k 3 ( k 3 k 1 ) =Δ q c FC 2 q 0 Δ q c FC >>Δ q c FC ,
N= q 0 Δ q c SPDC = q 0 2 l SPDC 2π k s .
M= 2π z R l SPDC .
Δ q c LP-SPDC = 4π k s l SPDC ,
M= a 0p Δ q c LP-SPDC , N=2 ( q 0 Δ q c LP-SPDC ) 2 ,
a 0p q 0 =M N 2 .

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