Abstract

As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Experimental generation of amplitude squeezed vector beams

Vanessa Chille, Stefan Berg-Johansen, Marion Semmler, Peter Banzer, Andrea Aiello, Gerd Leuchs, and Christoph Marquardt
Opt. Express 24(11) 12385-12394 (2016)

Generation of two-mode squeezed and entangled light in a single temporal and spatial mode

W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik
Opt. Express 17(16) 14444-14457 (2009)

Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor

Neil Corzo, Alberto M. Marino, Kevin M. Jones, and Paul D. Lett
Opt. Express 19(22) 21358-21369 (2011)

References

  • View by:
  • |
  • |
  • |

  1. R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).
  2. G. Leuchs, “Squeezing the quantum fluctuations of light,” Contemp. Phys. 29, 299 (1988).
    [Crossref]
  3. L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127 (1996).
    [Crossref]
  4. V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B: Quantum Semiclass. Opt. 4, R1 (2002).
    [Crossref]
  5. R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529 (1963).
    [Crossref]
  6. D. Stoler, “Equivalence classes of minimum uncertainty Packets,” Phys. Rev. D 1, 3217 (1970).
    [Crossref]
  7. E. Y. C. Lu, “New coherent states of the electromagnetic field,” Lett. Nuovo Cimento Series 2 2, 1241 (1971).
    [Crossref]
  8. R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
    [Crossref] [PubMed]
  9. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693 (1981).
    [Crossref]
  10. H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
    [Crossref] [PubMed]
  11. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513 (2005).
    [Crossref]
  12. M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
    [Crossref]
  13. D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63, 022309 (2001).
    [Crossref]
  14. C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).
  15. M. D. Levenson, W. H. Richardson, and S. H. Perlmutter, “Stochastic noise in TEM00 laser beam position,” Opt. Lett. 14, 779 (1989).
    [Crossref] [PubMed]
  16. G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
    [Crossref]
  17. A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
    [Crossref]
  18. J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
    [Crossref]
  19. N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
    [Crossref] [PubMed]
  20. M. Kolobov, Quantum Imaging (Springer, 2007).
    [Crossref]
  21. G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. 4, 227 (2010).
    [Crossref]
  22. M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
    [Crossref]
  23. P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
    [Crossref]
  24. L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
    [Crossref] [PubMed]
  25. H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
    [Crossref]
  26. S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
    [Crossref]
  27. S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
    [Crossref]
  28. B. Coutinho dos Santos, K. Dechoum, and A. Z. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
    [Crossref]
  29. K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
    [Crossref] [PubMed]
  30. C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre–Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
    [Crossref]
  31. B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
    [Crossref]
  32. U. M. Titulaer and R. J. Glauber, “Density operators for coherent fields,” Phys. Rev. 145, 1041 (1966).
    [Crossref]
  33. I. H. Deutsch, “A basis-independent approach to quantum optics,” Am. J. Phys. 59, 834 (1991).
    [Crossref]
  34. N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
    [Crossref]
  35. B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
    [Crossref]
  36. S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
    [Crossref]
  37. P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374 (1994).
    [Crossref]
  38. T. Opatrný, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 053813 (2002).
    [Crossref]
  39. E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
    [Crossref]
  40. L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
    [Crossref]
  41. J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
    [Crossref]
  42. N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express 19, 21358 (2011).
    [Crossref] [PubMed]
  43. N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
    [Crossref]
  44. V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
    [Crossref] [PubMed]
  45. C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
    [Crossref]
  46. J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
    [Crossref]
  47. M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
    [Crossref]
  48. M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States,” Phys. Rev. Lett. 102, 163602 (2009).
    [Crossref] [PubMed]
  49. C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
    [Crossref] [PubMed]
  50. S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
    [Crossref]
  51. L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291 (1999).
    [Crossref]
  52. S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670 (1994).
    [Crossref]
  53. D. L. Andrews and M. Babiker, (eds.), The Angular Momentum of Light (Cambridge University Press, 2013).
  54. D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15 (2005).
    [Crossref]
  55. E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546 (2013).
    [Crossref] [PubMed]

2014 (1)

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

2013 (2)

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546 (2013).
[Crossref] [PubMed]

2012 (3)

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

2011 (2)

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

N. Corzo, A. M. Marino, K. M. Jones, and P. D. Lett, “Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor,” Opt. Express 19, 21358 (2011).
[Crossref] [PubMed]

2010 (5)

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
[Crossref]

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. 4, 227 (2010).
[Crossref]

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
[Crossref]

2009 (5)

B. Coutinho dos Santos, K. Dechoum, and A. Z. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre–Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

2008 (1)

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

2007 (1)

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

2006 (3)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
[Crossref] [PubMed]

2005 (3)

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15 (2005).
[Crossref]

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

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

2004 (1)

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

2003 (2)

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

2002 (2)

V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B: Quantum Semiclass. Opt. 4, R1 (2002).
[Crossref]

T. Opatrný, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 053813 (2002).
[Crossref]

2001 (1)

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

2000 (1)

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[Crossref]

1999 (3)

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291 (1999).
[Crossref]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

1998 (2)

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

1996 (1)

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127 (1996).
[Crossref]

1994 (2)

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374 (1994).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670 (1994).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

1991 (1)

I. H. Deutsch, “A basis-independent approach to quantum optics,” Am. J. Phys. 59, 834 (1991).
[Crossref]

1989 (1)

1988 (1)

G. Leuchs, “Squeezing the quantum fluctuations of light,” Contemp. Phys. 29, 299 (1988).
[Crossref]

1985 (1)

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

1981 (1)

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

1971 (1)

E. Y. C. Lu, “New coherent states of the electromagnetic field,” Lett. Nuovo Cimento Series 2 2, 1241 (1971).
[Crossref]

1970 (1)

D. Stoler, “Equivalence classes of minimum uncertainty Packets,” Phys. Rev. D 1, 3217 (1970).
[Crossref]

1966 (1)

U. M. Titulaer and R. J. Glauber, “Density operators for coherent fields,” Phys. Rev. 145, 1041 (1966).
[Crossref]

1963 (1)

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529 (1963).
[Crossref]

Aiello, A.

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Allen, L.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291 (1999).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Andersen, U. L.

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).

Armstrong, S.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

Babiker, M.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291 (1999).
[Crossref]

Bachor, H.-A.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Banzer, P.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Barnett, S. M.

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670 (1994).
[Crossref]

Barsuglia, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Bent, N.

Berg-Johansen, S.

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

Bolduc, E.

Bowen, W. P.

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Boyd, R. W.

Bramati, A.

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

Brambilla, E.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

Braunstein, S. L.

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

Brida, G.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. 4, 227 (2010).
[Crossref]

Buy, C.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

Cai, C.

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Caspani, L.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

Caves, C. M.

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

Chalopin, B.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
[Crossref]

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

Chang, T. J.

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

Chelkowski, S.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
[Crossref]

Corzo, N.

Courty, J.

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

Coutinho dos Santos, B.

B. Coutinho dos Santos, K. Dechoum, and A. Z. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

Danzmann, K.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

Davidovich, L.

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127 (1996).
[Crossref]

de la Souchère, A.

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

de Valcárcel, G. J.

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre–Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

Dechoum, K.

B. Coutinho dos Santos, K. Dechoum, and A. Z. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

Delaubert, V.

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
[Crossref] [PubMed]

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

Deutsch, I. H.

I. H. Deutsch, “A basis-independent approach to quantum optics,” Am. J. Phys. 59, 834 (1991).
[Crossref]

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15 (2005).
[Crossref]

Dodonov, V. V.

V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B: Quantum Semiclass. Opt. 4, R1 (2002).
[Crossref]

Dooley, K. L.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

Ebeling, K. J.

Elser, D.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Euser, T.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Fabre, C.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
[Crossref]

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Ficker, J.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

Filip, R.

C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).

Förtsch, M.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Freise, A.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
[Crossref]

Fulda, P.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
[Crossref]

Gabriel, C.

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Gabrysch, M.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

Gao, J.

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Gatti, A.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

Genovese, M.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. 4, 227 (2010).
[Crossref]

Giacobino, E.

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

Giacomelli, G.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

Glauber, R.

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529 (1963).
[Crossref]

Glauber, R. J.

U. M. Titulaer and R. J. Glauber, “Density operators for coherent fields,” Phys. Rev. 145, 1041 (1966).
[Crossref]

Gottesman, D.

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

Granata, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

Grangier, Ph.

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

Gröblacher, S.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Grosse, N.

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Grote, H.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

Gulden, K. H.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

Guo, J.

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Guo, S.

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Hage, B.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

Harb, C. C.

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
[Crossref] [PubMed]

Hermier, J.-P.

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

Hillery, M.

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[Crossref]

Hollberg, L.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

Hsu, M. T. L.

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

Huck, A.

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

Jacobsen, C. S.

C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).

Janousek, J.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

Jedrkiewicz, O.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

Jennewein, T.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Joly, N.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Jones, K. M.

Karimi, E.

Khoury, A. Z.

B. Coutinho dos Santos, K. Dechoum, and A. Z. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

Kokeyama, K.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
[Crossref]

Kolobov, M.

M. Kolobov, Quantum Imaging (Springer, 2007).
[Crossref]

Kolobov, M. I.

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374 (1994).
[Crossref]

König, F.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

Korolkova, N.

T. Opatrný, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 053813 (2002).
[Crossref]

Kumar, P.

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374 (1994).
[Crossref]

Lam, P. K.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Lassen, M.

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

Lett, P. D.

Leuchs, G.

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

T. Opatrný, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 053813 (2002).
[Crossref]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

G. Leuchs, “Squeezing the quantum fluctuations of light,” Contemp. Phys. 29, 299 (1988).
[Crossref]

Levenson, M. D.

Liu, K.

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Lodahl, P.

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

Lopez, L.

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).

Lu, E. Y. C.

E. Y. C. Lu, “New coherent states of the electromagnetic field,” Lett. Nuovo Cimento Series 2 2, 1241 (1971).
[Crossref]

Lugiato, L.

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

Madsen, L. S.

C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).

Maître, A.

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

Marin, F.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

Marino, A. M.

Marquardt, C.

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15 (2005).
[Crossref]

Mertz, J.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

Michalzik, R.

Morizur, J.-F.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

Moser, M.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

Navarrete-Benlloch, C.

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre–Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

Okamoto, M.

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[Crossref]

Opatrný, T.

T. Opatrný, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 053813 (2002).
[Crossref]

Ott, J. R.

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

Padgett, M.

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291 (1999).
[Crossref]

Perlmutter, S. H.

Poizat, J.-Ph.

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, “Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser,” Opt. Lett. 24, 893 (1999).
[Crossref]

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

Preskill, J.

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

Raymer, M. G.

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

Richardson, W. H.

Roldán, E.

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre–Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

Ruo Berchera, I.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. 4, 227 (2010).
[Crossref]

Russell, P. S.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Santamato, E.

Sasada, H.

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[Crossref]

Scazza, F.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
[Crossref]

Schmitt, S.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

Schnabel, R.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

Schnitzer, P.

Sizmann, A.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

Slusher, R.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

Slutsky, J.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

Smith, B. J.

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

Smolka, S.

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

Spreeuw, R.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Stoler, D.

D. Stoler, “Equivalence classes of minimum uncertainty Packets,” Phys. Rev. D 1, 3217 (1970).
[Crossref]

Titulaer, U. M.

U. M. Titulaer and R. J. Glauber, “Density operators for coherent fields,” Phys. Rev. 145, 1041 (1966).
[Crossref]

Treps, N.

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
[Crossref]

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, “Quantum measurements of spatial conjugate variables: displacement and tilt of a Gaussian beam,” Opt. Lett. 31, 1537 (2006).
[Crossref] [PubMed]

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Usenko, V. C.

C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).

Vahlbruch, H.

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

Valley, J.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

van Loock, P.

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

Vaziri, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Wagner, K.

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

Ward, R.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

Weihs, G.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Woerdman, J.

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Wolff, M.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

Yurke, B.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

Zeilinger, A.

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

Zhong, W.

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

Am. J. Phys. (1)

I. H. Deutsch, “A basis-independent approach to quantum optics,” Am. J. Phys. 59, 834 (1991).
[Crossref]

Contemp. Phys. (2)

G. Leuchs, “Squeezing the quantum fluctuations of light,” Contemp. Phys. 29, 299 (1988).
[Crossref]

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46, 15 (2005).
[Crossref]

Eur. Phys. J. D (2)

C. Gabriel, A. Aiello, S. Berg-Johansen, C. Marquardt, and G. Leuchs, “Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes,” Eur. Phys. J. D 66, 172 (2012).
[Crossref]

J.-F. Morizur, S. Armstrong, N. Treps, J. Janousek, and H.-A. Bachor, “Spatial reshaping of a squeezed state of light,” Eur. Phys. J. D 61, 237 (2010).
[Crossref]

J. Eur. Opt. Soc.-Rapid (1)

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H.-A. Bachor, “Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an Optical Parametric Amplifier,” J. Eur. Opt. Soc.-Rapid 1, 06003 (2006).
[Crossref]

J. Opt. B: Quantum Semiclass. Opt. (2)

N. Treps, N. Grosse, W. P. Bowen, M. T. L. Hsu, A. Maître, C. Fabre, H.-A. Bachor, and P. K. Lam, “Nano-displacement measurements using spatially multimode squeezed light,” J. Opt. B: Quantum Semiclass. Opt. 6, 664 (2004).
[Crossref]

V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B: Quantum Semiclass. Opt. 4, R1 (2002).
[Crossref]

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

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B. 16, 2140 (1999).
[Crossref]

Lett. Nuovo Cimento Series 2 (1)

E. Y. C. Lu, “New coherent states of the electromagnetic field,” Lett. Nuovo Cimento Series 2 2, 1241 (1971).
[Crossref]

Nature Commun. (1)

S. Armstrong, J.-F. Morizur, J. Janousek, B. Hage, N. Treps, P. K. Lam, and H.-A. Bachor, “Programmable multimode quantum networks,” Nature Commun. 3, 1026 (2012).
[Crossref]

Nature Photon. (2)

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon. 4, 227 (2010).
[Crossref]

J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, “Optical entanglement of co-propagating modes,” Nature Photon. 3, 399 (2009).
[Crossref]

New J. Phys. (2)

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys. 9, 414 (2007).
[Crossref]

Opt. Commun. (3)

P. Kumar and M. I. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374 (1994).
[Crossref]

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136 (1998).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670 (1994).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (2)

U. M. Titulaer and R. J. Glauber, “Density operators for coherent fields,” Phys. Rev. 145, 1041 (1966).
[Crossref]

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529 (1963).
[Crossref]

Phys. Rev. A (11)

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[Crossref]

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

T. Opatrný, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 053813 (2002).
[Crossref]

E. Brambilla, L. Caspani, O. Jedrkiewicz, L. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
[Crossref]

L. Lopez, B. Chalopin, A. de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: Squeezed vacuum and Einstein–Podolsky–Rosen-beams generation,” Phys. Rev. A 80, 043816 (2009).
[Crossref]

S. Smolka, J. R. Ott, A. Huck, U. L. Andersen, and P. Lodahl, “Continuous-wave spatial quantum correlations of light induced by multiple scattering,” Phys. Rev. A 86, 033814 (2012).
[Crossref]

N. Treps, V. Delaubert, A. Maître, J. Courty, and C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

C. Navarrete-Benlloch, G. J. de Valcárcel, and E. Roldán, “Generating highly squeezed hybrid Laguerre–Gauss modes in large-Fresnel-number degenerate optical parametric oscillators,” Phys. Rev. A 79, 043820 (2009).
[Crossref]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
[Crossref]

L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[Crossref]

Phys. Rev. D (3)

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, “Experimental demonstration of higher-order Laguerre–Gauss mode interferometry,” Phys. Rev. D 82, 012002 (2010).
[Crossref]

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

D. Stoler, “Equivalence classes of minimum uncertainty Packets,” Phys. Rev. D 1, 3217 (1970).
[Crossref]

Phys. Rev. Lett. (8)

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[Crossref] [PubMed]

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, “First long-term application of squeezed states of light in a gravitational-wave observatory,” Phys. Rev. Lett. 110, 181101 (2013).
[Crossref] [PubMed]

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre–Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

B. Coutinho dos Santos, K. Dechoum, and A. Z. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

C. Gabriel, A. Aiello, W. Zhong, T. Euser, N. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. S. Russell, and G. Leuchs, “Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes,” Phys. Rev. Lett. 106, 060502 (2011).
[Crossref] [PubMed]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-Number Squeezed Solitons from an Asymmetric Fiber-Optic Sagnac Interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[Crossref]

Prog. Opt. (1)

L. Allen, M. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291 (1999).
[Crossref]

Rev. Mod. Phys. (2)

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

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68, 127 (1996).
[Crossref]

Science (1)

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940 (2003).
[Crossref] [PubMed]

Other (4)

M. Kolobov, Quantum Imaging (Springer, 2007).
[Crossref]

R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).

C. S. Jacobsen, L. S. Madsen, V. C. Usenko, R. Filip, and U. L. Andersen, “Elimination of information leakage in quantum information channels,” arXiv:1408.4566 (2014).

D. L. Andrews and M. Babiker, (eds.), The Angular Momentum of Light (Cambridge University Press, 2013).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Experimental setup. A femtosecond laser emits pulses of 220fs duration centered at λ0 = 1558nm. For squeezed light generation, the pulses are split up on a 90:10 beam splitter and launched into a Kerr fiber (χ(3) nonlinearity) of length 3.8 m in a counter-propagating configuration. The exiting pulses typically exhibit −3.0dB of amplitude squeezing prior to the SLM. A pair of folding mirrors (FMa, FMb) allow the squeezer to be bypassed to obtain a coherent shot noise reference for squeezing measurements. The beam impinges on a reflective SLM. An iris aperture selects the 1. diffraction order (see text for details). Another folding mirror (FMc) is used to direct the beam either at a InGaAs camera for mode inspection or at a detector, whose 9 MHz sideband fluctuations and DC amplitude are respectively recorded by an electronic spectrum analyser and a volt meter.

Fig. 2
Fig. 2

Example phase patterns. Basic phase patterns for generating (a) a Laguerre-Gauss beam and (b) a Bessel-Gauss beam. In addition, a blazed grating, kinoform lens and aperture are added to each pattern (not shown, see text for details).

Fig. 3
Fig. 3

Squeezed spatial modes. The average measured amplitude squeezing for each family of modes is shown below the panels. Each panel represents a 4.8×4.8 mm2 region in the camera plane. Relative intensity between panels is arbitrary.

Fig. 4
Fig. 4

Mode quality. Measured cross-sectional intensity distributions (dots) with fitted theoretical curves (lines) for (a) Laguerre-Gauss beams and (b) Bessel-Gauss beams.

Fig. 5
Fig. 5

Amplitude squeezing. Noise trace showing typical amplitude squeezing at 9 MHz in the LG 1 1 beam. Shaded areas correspond to one standard deviation.

Tables (2)

Tables Icon

Table 1 Experimental conversion efficiency and measured squeezing in LG p l beams.

Tables Icon

Table 2 Experimental conversion efficiency and measured squeezing in BG beams.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

E ^ ( r , t ) = i k ω k 2 ( u k ( r , k ) a ^ k u k * ( r , t ) a ^ k ) ,

Metrics