Abstract

We experimentally map the transverse profile of diffraction-limited beams using photon-number-resolving detectors. We observe strong compression of diffracted beam profiles for high detected photon number. This effect leads to higher contrast than a conventional irradiance profile between two Airy disk-beams separated by the Rayleigh criterion.

© 2010 Optical Society of America

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  1. S. Lloyd, "Enhanced sensitivity of photodetection via quantum illumination," Science 321, 1463 (2008).
    [CrossRef] [PubMed]
  2. T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
    [CrossRef] [PubMed]
  3. J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
    [CrossRef] [PubMed]
  4. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
    [CrossRef] [PubMed]
  5. M. D’Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
    [CrossRef] [PubMed]
  6. J. P. Dowling, "Quantum optical metrology - the lowdown on high-NOON States," Contemp. Phys. 49, 125 (2008).
    [CrossRef]
  7. M. A. Rubin and S. Kaushik, "Loss-induced limits to phase measurement precision with maximally entangled states," Phys. Rev. A 75, 053805 (2007),
    [CrossRef]
  8. C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  9. R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
    [CrossRef]
  10. S. J. Bentley and R. W. Boyd, "Nonlinear optical lithography with ultra-high sub-Rayleigh resolution," Opt. Express 12, 5735 (2004).
    [CrossRef] [PubMed]
  11. C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
    [CrossRef]
  12. G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
    [CrossRef] [PubMed]
  13. P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
    [CrossRef] [PubMed]
  14. 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]
  15. Lord Rayleigh, "Investigations in optics, with special reference to the spectroscope," Philos. Mag. 8, 261 (1879).
  16. V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, "Sub-Rayleigh-diffraction-bound quantum imaging," Phys. Rev. A 79, 013827 (2009).
    [CrossRef]
  17. A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (2003).
    [CrossRef]
  18. C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2005).
  19. C. Sparrow, Astro Phys. 44, 76 (1916).
    [CrossRef]

2009 (2)

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

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

2008 (3)

J. P. Dowling, "Quantum optical metrology - the lowdown on high-NOON States," Contemp. Phys. 49, 125 (2008).
[CrossRef]

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

S. Lloyd, "Enhanced sensitivity of photodetection via quantum illumination," Science 321, 1463 (2008).
[CrossRef] [PubMed]

2007 (2)

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

M. A. Rubin and S. Kaushik, "Loss-induced limits to phase measurement precision with maximally entangled states," Phys. Rev. A 75, 053805 (2007),
[CrossRef]

2006 (2)

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
[CrossRef] [PubMed]

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (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]

2001 (1)

M. D’Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

2000 (1)

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

1996 (1)

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

1981 (1)

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

1916 (1)

C. Sparrow, Astro Phys. 44, 76 (1916).
[CrossRef]

1879 (1)

Lord Rayleigh, "Investigations in optics, with special reference to the spectroscope," Philos. Mag. 8, 261 (1879).

Abrams, D. S.

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Bachor, H.-A.

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]

Bentley, S. J.

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Boto, N.

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Bouwmeester, D.

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
[CrossRef] [PubMed]

Bowen, W. P.

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.

Braunstein, S. L.

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Cable, H.

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

Caves, C. M.

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

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Chen, J.

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

De Martini, F.

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

Dowling, J. P.

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

J. P. Dowling, "Quantum optical metrology - the lowdown on high-NOON States," Contemp. Phys. 49, 125 (2008).
[CrossRef]

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Eisenberg, H. S.

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
[CrossRef] [PubMed]

Fabre, C.

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]

Fan, J.

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

Fonseca, E. J. S.

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
[CrossRef] [PubMed]

Giovannetti, V.

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

Glasser, R. T.

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

Grosse, N.

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]

Heinzen, D. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Hemmer, P. R.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Itano, W. M.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Kaushik, S.

M. A. Rubin and S. Kaushik, "Loss-induced limits to phase measurement precision with maximally entangled states," Phys. Rev. A 75, 053805 (2007),
[CrossRef]

Khoury, G.

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
[CrossRef] [PubMed]

Kok, P.

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Lam, P. K.

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]

Lloyd, S.

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

S. Lloyd, "Enhanced sensitivity of photodetection via quantum illumination," Science 321, 1463 (2008).
[CrossRef] [PubMed]

Maccone, L.

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

Martinis, J. M.

A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (2003).
[CrossRef]

Migdall, A.

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

Miller, A. J.

A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (2003).
[CrossRef]

Muthukrishnan, A.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Nagata, T.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

Nam, S.

A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (2003).
[CrossRef]

O’Brien, J. L.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

Okamoto, R.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

Pearlman, A. J.

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

Rubin, M. A.

M. A. Rubin and S. Kaushik, "Loss-induced limits to phase measurement precision with maximally entangled states," Phys. Rev. A 75, 053805 (2007),
[CrossRef]

Sasaki, K.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

Sciarrino, F.

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

Scully, M. O.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Sergienko, A. V.

A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (2003).
[CrossRef]

Shapiro, J.

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

Shih, Y.

M. D’Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Sparrow, C.

C. Sparrow, Astro Phys. 44, 76 (1916).
[CrossRef]

Takeuchi, S.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

Treps, N.

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]

Vitelli, C.

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

Wildfeuer, C. F.

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

Williams, C. P.

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Wineland, D. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Zubairy, M. S.

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. J. Miller, S. Nam, J. M. Martinis, and A. V. Sergienko "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," Appl. Phys. Lett. 83, 791 (2003).
[CrossRef]

Astro Phys. (1)

C. Sparrow, Astro Phys. 44, 76 (1916).
[CrossRef]

Contemp. Phys. (1)

J. P. Dowling, "Quantum optical metrology - the lowdown on high-NOON States," Contemp. Phys. 49, 125 (2008).
[CrossRef]

Opt. Express (1)

Philos. Mag. (1)

Lord Rayleigh, "Investigations in optics, with special reference to the spectroscope," Philos. Mag. 8, 261 (1879).

Phys. Rev. A (5)

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

M. A. Rubin and S. Kaushik, "Loss-induced limits to phase measurement precision with maximally entangled states," Phys. Rev. A 75, 053805 (2007),
[CrossRef]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

R. T. Glasser, H. Cable, J. P. Dowling, F. De Martini, F. Sciarrino, and C. Vitelli, "Entanglement-seeded, dual, optical parametric amplification: Applications to quantum imaging and metrology," Phys. Rev. A 78, 012339 (2008).
[CrossRef]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, "Resolution and sensitivity of a Fabry-Perot interferometer with a photon-number-resolving detector," Phys. Rev. A 80, 043822 (2009).
[CrossRef]

Phys. Rev. D (1)

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

Phys. Rev. Lett (1)

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, "Nonlinear Interferometry via Fock-State Projection," Phys. Rev. Lett 96, 203601 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, "Quantum Lithography with Classical Light," Phys. Rev. Lett. 96, 163603 (2006).
[CrossRef] [PubMed]

N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum interferometric optical lithography: Exploiting entanglement to beat the diffraction limit," Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

M. D’Angelo, M. V. Chekhova, and Y. Shih, "Two-photon diffraction and quantum lithography," Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Science (3)

S. Lloyd, "Enhanced sensitivity of photodetection via quantum illumination," Science 321, 1463 (2008).
[CrossRef] [PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, "Beating the standard quantum limit with four entangled photons," Science 316, 726 (2007).
[CrossRef] [PubMed]

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 (1)

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Reconstructed classical spatial distribution with fit. (b) Full width at half maximum of the central fringe vs. photon number. Expected widths using reconstructed classical and conventional single-photon detectors shown for reference. (c) Spatial distribution of the diffraction pattern for up to nine photons with fits. All uncertainties shown are statistical 1 σ values.

Fig. 2.
Fig. 2.

(a) Spatial profile at approximately the Rayleigh criterion for the reconstructed classical signal and photon-number detection at selected photon numbers larger than the mean photon number. (b) Experimental setup. PBS: polarizing beam splitter. (c) Contrast vs. beam separation (in units of the Rayleigh criterion) for selected photon numbers larger than the mean photon number. Contrasts derived from the reconstructed classical profile and single-photon counter profile are shown for reference.

Fig. 3.
Fig. 3.

Calculated spatial distribution of (from left to right) a classically detected Gaussian profile coherent beam with a mean photon number of 10, a 10-photon detection of the same coherent state, a 10-photon detection of thermal light and same mean photon number, and a 10-photon detection of N=10 Fock state.

Equations (1)

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p ( k ) = e μ j = k μ j k ! ( j k ) ! T 2 k ( 1 T 2 ) j k = e μ T 2 ( μ T 2 ) k k ! ,

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