Abstract

We show that it is possible to estimate the shape of an object by measuring only the fluctuations of a probing field, allowing us to expose the object to a minimal light intensity. This scheme, based on noise measurements through homodyne detection, is useful in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough such that photon counting is not an option. We generate a few-photon state of multi-spatial-mode vacuum-squeezed twin beams using four-wave mixing and direct one of these twin fields through a binary intensity mask whose shape is to be imaged. Exploiting either the classical fluctuations in a single beam or quantum correlations between the twin beams, we demonstrate that under some conditions quantum correlations can provide an enhancement in sensitivity when estimating the shape of the object.

© 2012 OSA

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  1. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon 5, 222–229 (2011).
    [CrossRef]
  2. M. I. Kolobov, “The spatial behavior of non-classical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
    [CrossRef]
  3. M. I. Kolobov, Quantum Imaging, 1st ed. (Springer, 2006).
  4. 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, 21358–21369 (2011).
    [CrossRef] [PubMed]
  5. V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
    [CrossRef] [PubMed]
  6. M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
    [CrossRef] [PubMed]
  7. N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
    [CrossRef] [PubMed]
  8. V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
    [CrossRef]
  9. N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
    [CrossRef] [PubMed]
  10. J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
    [CrossRef]
  11. E. Brambilla, L. Caspani, O. Jedrkiewicz, L. A. Lugiato, and A. Gatti, “High-sensitivity imaging with multi-mode twin beams,” Phys. Rev. A 77, 053807 (2008).
    [CrossRef]
  12. L. A. Lugiato and A. Gatti, “Spatial structure of a squeezed vacuum,” Phys. Rev. Lett. 70, 3868–3871 (1993).
    [CrossRef] [PubMed]
  13. A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator below threshold,” Phys. Rev. A 52, 1675–1690 (1995).
    [CrossRef] [PubMed]
  14. A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.
  15. G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon 4, 227–230 (2010).
    [CrossRef]
  16. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
    [CrossRef] [PubMed]
  17. Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
    [CrossRef]
  18. C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
    [CrossRef]
  19. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
    [CrossRef]
  20. V. Boyer, A. Marino, R. C. Pooser, and P. D. Lett, “Entangled images four four-wave mixing,” Science 321, 544 –547 (2008).
    [CrossRef] [PubMed]
  21. M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
    [CrossRef]
  22. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  23. C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett. 73, 1605–1608 (1994).
    [CrossRef] [PubMed]
  24. M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
    [CrossRef]

2011 (2)

2010 (2)

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon 4, 227–230 (2010).
[CrossRef]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

2009 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
[CrossRef]

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

2008 (4)

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

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

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

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

2005 (1)

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

2004 (1)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

2003 (2)

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

2002 (1)

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

2001 (1)

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

2000 (1)

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1995 (1)

A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator below threshold,” Phys. Rev. A 52, 1675–1690 (1995).
[CrossRef] [PubMed]

1994 (1)

C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett. 73, 1605–1608 (1994).
[CrossRef] [PubMed]

1993 (2)

L. A. Lugiato and A. Gatti, “Spatial structure of a squeezed vacuum,” Phys. Rev. Lett. 70, 3868–3871 (1993).
[CrossRef] [PubMed]

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
[CrossRef]

Abouraddy, A. F.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

Abram, I.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
[CrossRef]

Andersen, U.

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Arimondo, E.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Bachor, H.-A.

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Bowen, W. P.

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

Boyer, V.

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

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

Brambilla, E.

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Brida, G.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon 4, 227–230 (2010).
[CrossRef]

Buchler, B.

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Caspani, L.

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

Clark, J. B.

A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.

Corzo, N.

Coudreau, T.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

Dubessy, R.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

Ducci, S.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Fabre, C.

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

Gatti, A.

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator below threshold,” Phys. Rev. A 52, 1675–1690 (1995).
[CrossRef] [PubMed]

L. A. Lugiato and A. Gatti, “Spatial structure of a squeezed vacuum,” Phys. Rev. Lett. 70, 3868–3871 (1993).
[CrossRef] [PubMed]

Genovese, M.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon 4, 227–230 (2010).
[CrossRef]

Gigan, S.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon 5, 222–229 (2011).
[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Glorieux, Q.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.

Goda, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

Goode, D. P.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

Grangier, P.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
[CrossRef]

Gray, M. B.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

Gross, N.

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

Grosse, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

Guibal, S.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

Guidoni, L.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

Jedrkiewicz, O.

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

Jones, K. M.

Kim, C.

C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett. 73, 1605–1608 (1994).
[CrossRef] [PubMed]

Kolobov, M. I.

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
[CrossRef] [PubMed]

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

M. I. Kolobov, Quantum Imaging, 1st ed. (Springer, 2006).

Kumar, P.

C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett. 73, 1605–1608 (1994).
[CrossRef] [PubMed]

Lam, P. K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Lett, P. D.

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, 21358–21369 (2011).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

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

A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.

Levenson, J. A.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
[CrossRef]

Likforman, J.-P.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon 5, 222–229 (2011).
[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Lugiato, L.

A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator below threshold,” Phys. Rev. A 52, 1675–1690 (1995).
[CrossRef] [PubMed]

Lugiato, L. A.

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[CrossRef]

L. A. Lugiato and A. Gatti, “Spatial structure of a squeezed vacuum,” Phys. Rev. Lett. 70, 3868–3871 (1993).
[CrossRef] [PubMed]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon 5, 222–229 (2011).
[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Maitre, A.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Marino, A.

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

Marino, A. M.

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, 21358–21369 (2011).
[CrossRef] [PubMed]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.

Martinelli, M.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Mavalvala, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

McClelland, D. E.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

McCormick, C. F.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

McKenzie, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

Mikhailov, E. E.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

Nasr, M. B.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

Nguyen, N.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

Pooser, R. C.

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

Reinhard, B. M.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

Rivera, T.

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
[CrossRef]

Rong, G.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

Ruo Berchera, I.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon 4, 227–230 (2010).
[CrossRef]

Saleh, B. E. A.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

Sergienko, A. V.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

Teich, M. C.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

Treps, N.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Yang, L.

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

J. Opt. B (1)

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S421–S428 (2005).
[CrossRef]

JOSA B (1)

J. A. Levenson, I. Abram, T. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” JOSA B 10, 2233–2238 (1993).
[CrossRef]

Nature Photon (2)

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon 4, 227–230 (2010).
[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature Photon 5, 222–229 (2011).
[CrossRef]

Opt. Commun. (1)

M. B. Nasr, D. P. Goode, N. Nguyen, G. Rong, L. Yang, B. M. Reinhard, B. E. A. Saleh, and M. C. Teich, “Quantum optical coherence tomography of a biological sample,” Opt. Commun. 282, 1154–1159 (2009).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (7)

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-Λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82, 033819 (2010).
[CrossRef]

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Maitre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

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V. Giovannetti, S. Lloyd, and L. Maccone, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
[CrossRef]

Phys. Rev. Lett (1)

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett 88, 203601 (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

M. I. Kolobov and C. Fabre, “Quantum limits on optical resolution,” Phys. Rev. Lett. 85, 3789–3792 (2000).
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A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Science (2)

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

N. Treps, N. Gross, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[CrossRef] [PubMed]

Other (2)

A. M. Marino, J. B. Clark, Q. Glorieux, and P. D. Lett, E-print arXiv:1203.0577v1.

M. I. Kolobov, Quantum Imaging, 1st ed. (Springer, 2006).

Supplementary Material (1)

» Media 1: AVI (447 KB)     

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Figures (5)

Fig. 1
Fig. 1

(a) Four-wave mixing in 85Rb. Probe and conjugate fields are coupled over a range of angles Δϕ and selected for measurement via homodyne detection at ϕ. (b) Double-Λ scheme in 85Rb. (c) Experimental set-up. Probe and conjugate local oscillators are shaped into bow ties and are rotated with respect to the mask. Resultant homodyne signals are subtracted. The black dotted circles joined by the arrow indicate coherence areas, localized regions of correlations between the probe and conjugate. LO denotes the local oscillator and SV the squeezed vacuum light.

Fig. 2
Fig. 2

A spatial light modulator writes a diffraction grating with a region of constant phase in the desired transverse shape of the local oscillator. A coherent state is scattered from the diffraction grating and an f-f optical system and telescope focus the Fourier transform of the pattern into a Rb cell where 4WM occurs, generating two local oscillators at the appropriate frequencies and desired shape in the far field.

Fig. 3
Fig. 3

(a) Mean quadrature noise power N for the conjugate’s excess noise (red squares) and twin beam difference signal (blue triangles) as a function of overlap between the mask and the conjugate LO. Standard deviations of the mean are on the order of the marker size and not illustrated. Third order polynomial fits to the data are included. (b) Comparison of the uncertainty in the estimated LO-mask overlap for the classical and quantum techniques, on a log scale, as a function of the overlap for the single and twin beam measurements.

Fig. 4
Fig. 4

(a) Probe and conjugate LOs are generated in the shape of each letter of the alphabet and used in a balanced homodyne detection. The conjugate field illuminates the mask whose shape is to be estimated. (b) Deviation from initial excess noise for the classical noise imaging technique upon insertion of the mask versus choice of letter for the local oscillator. (c) Deviation from initial squeezing level for the quantum noise imaging technique upon insertion of the mask. The baseline of squeezing between the twin beams for the LO letter Z is −2.2 dB, measured without the mask. With the mask inserted, only the mask shaped as the letter Z maintains any squeezing. The gray regions in (b)–(c) represent the value of Di and its associated uncertainty for the correct LO choice, Z. The letter “I” in the chosen font did not produce a bright enough local oscillator to elevate the quadrature noise power above the electronic noise floor of our detectors.

Fig. 5
Fig. 5

Local oscillators used for the alphabet gun test ( Media 1).

Equations (2)

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Δ O est = Δ N | N O | .
D i = N masked i N baseline i .

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