Abstract

Classically, the resolution of optical measurements is limited by the Rayleigh limit and their sensitivity by the shot noise limit. However, non-classical measurements can surpass these limits. Measuring the photon number parity using a photon-number resolving detector, super resolved phase measurements up to 144 better than the Rayleigh limit are presented, with coherent states of up to 4,200 photons on average. An additional measurement that can be implemented with standard single-photon detectors is proposed and demonstrated. With this scheme, super resolution at the shot noise limit is demonstrated with coherent states of up to 200 photons on average.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Super-resolving quantum lidar: entangled coherent-state sources with binary-outcome photon counting measurement suffice to beat the shot-noise limit

Qiang Wang, Lili Hao, Yong Zhang, Lu Xu, Chenghua Yang, Xu Yang, and Yuan Zhao
Opt. Express 24(5) 5045-5056 (2016)

Deterministic phase measurements exhibiting super-sensitivity and super-resolution

Clemens Schäfermeier, Miroslav Ježek, Lars S. Madsen, Tobias Gehring, and Ulrik L. Andersen
Optica 5(1) 60-64 (2018)

Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors

Yang Gao, Petr M. Anisimov, Christoph F. Wildfeuer, Jerome Luine, Hwang Lee, and Jonathan P. Dowling
J. Opt. Soc. Am. B 27(6) A170-A174 (2010)

References

  • View by:
  • |
  • |
  • |

  1. G. Meyer and N. M. Amer, “Novel optical approach to atomic force microscopy,” Appl. Phys. Lett. 53, 1045–1047 (1988).
    [Crossref]
  2. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
    [Crossref]
  3. J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
    [Crossref]
  4. J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
    [Crossref]
  5. C. Kothe, G. Björk, and M. Bourennane, “Arbitrarily high super-resolving phase measurements at telecommunication wavelengths,” Phys. Rev. A 81, 063836 (2010).
    [Crossref]
  6. B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
    [Crossref] [PubMed]
  7. 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]
  8. 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]
  9. K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
    [Crossref] [PubMed]
  10. E. Distante, M. Ježek, and U. L. Andersen, “Super resolution with coherent states at the shot noise limit,” Phys. Rev. Lett. 111, 033603 (2013).
    [Crossref]
  11. Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
    [Crossref]
  12. A. Kuzmich and L. Mandel, “Sub-shot-noise interferometric measurements with two-photon states,” Quant. Semiclass. Opt. 10, 493 (1998).
    [Crossref]
  13. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
    [Crossref] [PubMed]
  14. T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).
    [Crossref] [PubMed]
  15. I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
    [Crossref] [PubMed]
  16. 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 (1996).
    [Crossref] [PubMed]
  17. C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
    [Crossref]
  18. C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).
    [Crossref]
  19. C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
    [Crossref]
  20. A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” J. Mod. Opt. 58, 945–953 (2011).
    [Crossref]
  21. P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
    [Crossref] [PubMed]
  22. W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
    [Crossref]
  23. L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
    [Crossref]
  24. L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
    [Crossref]
  25. L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
    [Crossref]
  26. H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
    [Crossref]
  27. E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
    [Crossref]
  28. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
    [Crossref] [PubMed]
  29. S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72, 3439–3443 (1994).
    [Crossref] [PubMed]
  30. X. M. Feng, G. R. Jin, and W. Yang, “Quantum interferometry with two outcomes in the presence of phase diffusion,” quant-ph arXiv:1404.1229v2.
  31. G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal multi-photon phase sensing with a single interference fringe,” Sci. Rep. 3, 2684 (2013).
    [Crossref] [PubMed]

2013 (3)

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

E. Distante, M. Ježek, and U. L. Andersen, “Super resolution with coherent states at the shot noise limit,” Phys. Rev. Lett. 111, 033603 (2013).
[Crossref]

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal multi-photon phase sensing with a single interference fringe,” Sci. Rep. 3, 2684 (2013).
[Crossref] [PubMed]

2012 (1)

L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
[Crossref]

2011 (2)

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” J. Mod. Opt. 58, 945–953 (2011).
[Crossref]

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

2010 (7)

C. Kothe, G. Björk, and M. Bourennane, “Arbitrarily high super-resolving phase measurements at telecommunication wavelengths,” Phys. Rev. A 81, 063836 (2010).
[Crossref]

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[Crossref]

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[Crossref]

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

2009 (1)

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]

2008 (2)

J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[Crossref]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
[Crossref] [PubMed]

2007 (4)

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[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, 726–729 (2007).
[Crossref] [PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

2006 (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]

2004 (2)

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref] [PubMed]

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

2003 (1)

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

2001 (1)

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).
[Crossref]

2000 (1)

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
[Crossref]

1998 (1)

A. Kuzmich and L. Mandel, “Sub-shot-noise interferometric measurements with two-photon states,” Quant. Semiclass. Opt. 10, 493 (1998).
[Crossref]

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 (1996).
[Crossref] [PubMed]

1994 (1)

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72, 3439–3443 (1994).
[Crossref] [PubMed]

1988 (1)

G. Meyer and N. M. Amer, “Novel optical approach to atomic force microscopy,” Appl. Phys. Lett. 53, 1045–1047 (1988).
[Crossref]

Aasi, J.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Abadie, J.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Abbott, B. P.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Abbott, R.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Abbott, T. D.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Abernathy, M. R.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Adami, C.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

Adams, C.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Adams, T.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Addesso, P.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Adhikari, R. X.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Afek, I.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Affeldt, C.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Agarwal, G. S.

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

Aguiar, O. D.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Ajith, P.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Allen, B.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Amador Ceron, E.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Amariutei, D.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Ambar, O.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Amer, N. M.

G. Meyer and N. M. Amer, “Novel optical approach to atomic force microscopy,” Appl. Phys. Lett. 53, 1045–1047 (1988).
[Crossref]

Andersen, U. L.

E. Distante, M. Ježek, and U. L. Andersen, “Super resolution with coherent states at the shot noise limit,” Phys. Rev. Lett. 111, 033603 (2013).
[Crossref]

Anderson, S. B.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Anderson, W. G.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Anisimov, P. M.

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[Crossref]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Arai, K.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Araya, M. C.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Arceneaux, C.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Ast, S.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Aston, S. M.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Atkinson, D.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Aufmuth, P.

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Bakstein, M.

L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
[Crossref]

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

Bartlett, S. D.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[Crossref] [PubMed]

Berry, D. W.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[Crossref] [PubMed]

Björk, G.

C. Kothe, G. Björk, and M. Bourennane, “Arbitrarily high super-resolving phase measurements at telecommunication wavelengths,” Phys. Rev. A 81, 063836 (2010).
[Crossref]

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 (1996).
[Crossref] [PubMed]

Bourennane, M.

C. Kothe, G. Björk, and M. Bourennane, “Arbitrarily high super-resolving phase measurements at telecommunication wavelengths,” Phys. Rev. A 81, 063836 (2010).
[Crossref]

Bouwmeester, D.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

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]

Braunstein, S. L.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72, 3439–3443 (1994).
[Crossref] [PubMed]

Campos, R. A.

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).
[Crossref]

Caves, C. M.

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72, 3439–3443 (1994).
[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]

Chiruvelli, A.

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” J. Mod. Opt. 58, 945–953 (2011).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Diamanti, E.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

Distante, E.

E. Distante, M. Ježek, and U. L. Andersen, “Super resolution with coherent states at the shot noise limit,” Phys. Rev. Lett. 111, 033603 (2013).
[Crossref]

Dovrat, L.

L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
[Crossref]

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

Dowling, J. P.

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[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]

J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[Crossref]

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

Eisenberg, H. S.

L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
[Crossref]

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

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]

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]

Feng, X. M.

X. M. Feng, G. R. Jin, and W. Yang, “Quantum interferometry with two outcomes in the presence of phase diffusion,” quant-ph arXiv:1404.1229v2.

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]

Gao, Y.

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[Crossref]

Gerry, C. C.

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[Crossref]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).
[Crossref]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
[Crossref]

Gilchrist, A.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

Giovannetti, V.

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

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 (1996).
[Crossref] [PubMed]

Higgins, B. L.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[Crossref] [PubMed]

Hockney, G. M.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

Hodelin, J. F.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Hofmann, H. F.

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal multi-photon phase sensing with a single interference fringe,” Sci. Rep. 3, 2684 (2013).
[Crossref] [PubMed]

Huver, S. D.

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Inoue, K.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

Istrati, D.

L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
[Crossref]

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

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 (1996).
[Crossref] [PubMed]

Ježek, M.

E. Distante, M. Ježek, and U. L. Andersen, “Super resolution with coherent states at the shot noise limit,” Phys. Rev. Lett. 111, 033603 (2013).
[Crossref]

Jin, G. R.

X. M. Feng, G. R. Jin, and W. Yang, “Quantum interferometry with two outcomes in the presence of phase diffusion,” quant-ph arXiv:1404.1229v2.

Khoury, G.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

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.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

Kothe, C.

C. Kothe, G. Björk, and M. Bourennane, “Arbitrarily high super-resolving phase measurements at telecommunication wavelengths,” Phys. Rev. A 81, 063836 (2010).
[Crossref]

Kuzmich, A.

A. Kuzmich and L. Mandel, “Sub-shot-noise interferometric measurements with two-photon states,” Quant. Semiclass. Opt. 10, 493 (1998).
[Crossref]

Lee, H.

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” J. Mod. Opt. 58, 945–953 (2011).
[Crossref]

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

Lita, A. E.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
[Crossref] [PubMed]

Lloyd, S.

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

Luine, J.

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[Crossref]

Lundeen, J. S.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref] [PubMed]

Maccone, L.

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

Mandel, L.

A. Kuzmich and L. Mandel, “Sub-shot-noise interferometric measurements with two-photon states,” Quant. Semiclass. Opt. 10, 493 (1998).
[Crossref]

Meyer, G.

G. Meyer and N. M. Amer, “Novel optical approach to atomic force microscopy,” Appl. Phys. Lett. 53, 1045–1047 (1988).
[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. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
[Crossref] [PubMed]

Mimih, J.

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[Crossref]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[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, 726–729 (2007).
[Crossref] [PubMed]

Nam, S. W.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
[Crossref] [PubMed]

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, 726–729 (2007).
[Crossref] [PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (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, 726–729 (2007).
[Crossref] [PubMed]

Oliver, W. D.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

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]

Pezzé, L.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Plick, W. N.

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Pregnell, K. L.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

Prevedel, R.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

Pryde, G. J.

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal multi-photon phase sensing with a single interference fringe,” Sci. Rep. 3, 2684 (2013).
[Crossref] [PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[Crossref] [PubMed]

Raterman, G. M.

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Resch, K. J.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

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, 726–729 (2007).
[Crossref] [PubMed]

Shaham, A.

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

Silberberg, Y.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Smerzi, A.

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref] [PubMed]

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, 726–729 (2007).
[Crossref] [PubMed]

Waks, E.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

White, A. G.

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

Wildfeuer, C. F.

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[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]

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 (1996).
[Crossref] [PubMed]

Wiseman, H. M.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[Crossref] [PubMed]

Xiang, G. Y.

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal multi-photon phase sensing with a single interference fringe,” Sci. Rep. 3, 2684 (2013).
[Crossref] [PubMed]

Yamamoto, Y.

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

Yang, W.

X. M. Feng, G. R. Jin, and W. Yang, “Quantum interferometry with two outcomes in the presence of phase diffusion,” quant-ph arXiv:1404.1229v2.

Yurtsever, U.

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

Appl. Phys. Lett. (1)

G. Meyer and N. M. Amer, “Novel optical approach to atomic force microscopy,” Appl. Phys. Lett. 53, 1045–1047 (1988).
[Crossref]

Contemp. Phys. (1)

J. P. Dowling, “Quantum optical metrology-the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron. 9, 1502–1511 (2003).
[Crossref]

J. Mod. Opt. (2)

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” J. Mod. Opt. 58, 945–953 (2011).
[Crossref]

H. Lee, U. Yurtsever, P. Kok, G. M. Hockney, C. Adami, S. L. Braunstein, and J. P. Dowling, “Towards photo-statistics from photon-number discriminating detectors,” J. Mod. Opt. 51, 1517–1528 (2004).
[Crossref]

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

Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J. Opt. Soc. Am. B 27, A170–A174 (2010).
[Crossref]

Nat. Photon. (2)

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

J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, C. Affeldt, O. D. Aguiar, P. Ajith, B. Allen, E. Amador Ceron, D. Amariutei, S. B. Anderson, W. G. Anderson, K. Arai, M. C. Araya, C. Arceneaux, S. Ast, S. M. Aston, D. Atkinson, P. Aufmuth, and et al., “Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light,” Nat. Photon. 7, 613–619 (2013).
[Crossref]

Nature (2)

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007).
[Crossref] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429, 161–164 (2004).
[Crossref] [PubMed]

New J. Phys. (1)

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys. 12, 113025 (2010).
[Crossref]

Opt. Express (2)

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
[Crossref] [PubMed]

L. Dovrat, M. Bakstein, D. Istrati, A. Shaham, and H. S. Eisenberg, “Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion,” Opt. Express 20, 2266–2276 (2010).
[Crossref]

Phys. Rev. A (6)

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 (1996).
[Crossref] [PubMed]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
[Crossref]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).
[Crossref]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).
[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]

C. Kothe, G. Björk, and M. Bourennane, “Arbitrarily high super-resolving phase measurements at telecommunication wavelengths,” Phys. Rev. A 81, 063836 (2010).
[Crossref]

Phys. Rev. Lett. (6)

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]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).
[Crossref] [PubMed]

E. Distante, M. Ježek, and U. L. Andersen, “Super resolution with coherent states at the shot noise limit,” Phys. Rev. Lett. 111, 033603 (2013).
[Crossref]

S. L. Braunstein and C. M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72, 3439–3443 (1994).
[Crossref] [PubMed]

L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, “Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry,” Phys. Rev. Lett. 99, 223602 (2007).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: Parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Phys. Scr. (1)

L. Dovrat, M. Bakstein, D. Istrati, and H. S. Eisenberg, “Simulations of photon detection in silicon photomultiplier number-resolving detectors,” Phys. Scr. T147, 014010 (2012).
[Crossref]

Quant. Semiclass. Opt. (1)

A. Kuzmich and L. Mandel, “Sub-shot-noise interferometric measurements with two-photon states,” Quant. Semiclass. Opt. 10, 493 (1998).
[Crossref]

Sci. Rep. (1)

G. Y. Xiang, H. F. Hofmann, and G. J. Pryde, “Optimal multi-photon phase sensing with a single interference fringe,” Sci. Rep. 3, 2684 (2013).
[Crossref] [PubMed]

Science (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, 726–729 (2007).
[Crossref] [PubMed]

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010).
[Crossref] [PubMed]

Other (1)

X. M. Feng, G. R. Jin, and W. Yang, “Quantum interferometry with two outcomes in the presence of phase diffusion,” quant-ph arXiv:1404.1229v2.

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

The experimental setup. The coherent states are produced by a Ti:Sapphire laser and their average photon number is controlled by a calibrated variable neutral density filter (NDF). The Mach-Zehnder interferometer (MZI) is composed from two polarizers (P) at 45° and a phase shifter (PS). One of the output modes from the MZI is filtered spectrally by 3nm band pass filter (BPF) and spatially by a single mode fiber (SMF). This mode is detected by the silicon photomultiplier (SiPM, Hamamatsu Photonics, S10362-11-100U) detector.

Fig. 2
Fig. 2

(a) Parity and (b) P0 dependence on the phase. The presented measurements are for average photon numbers of 4.6 ± 0.2 (purple squares), 25 ± 1 (red circles), 200 ± 8 (blue triangles), 1,190 ± 50 (pink inverted triangles), and 4,150 ± 150 (green rhombuses). The dashed black lines represent the classic interference curves, and are presented for comparison reasons. Errors are not shown, as they are smaller than the symbols.

Fig. 3
Fig. 3

The effects of finite visibility and dark counts on the signal peak heights for parity (blue squares) and P0 (orange triangles). The peak heights decrease when states with more photons are used, according to Eq. (8).

Fig. 4
Fig. 4

Experimental phase uncertainties for 200 photons on average (blue squares), as a function of the phase for (a) parity and (b) P0. The theoretical fits to Eqs. (3) and (5) are presented with solid black lines, and to Eq. (9) by orange dashed lines. Errors are shown when larger than their symbols. They represent the standard deviation in the phase uncertainty estimation process.

Fig. 5
Fig. 5

(a) The resolution and (b) the smallest uncertainty. Parity results are presented by blue squares and P0 results with orange triangles. Solid lines are the theoretical predictions. For the resolution there are no free parameters and the predictions for sensitivity use the visibility values from the fits of Fig. 3. The parity resolution reaches λ 288, 144 times better than the Rayleigh λ/2 limit (dashed line in (a)). The P0 sensitivity follows the SNL (dashed line in (b)) up to 200 photons. Parity has better resolution but larger deviation from the SNL. Errors were calculated as before and shown when larger than their symbol.

Equations (9)

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

π ^ = n = 0 ( 1 ) n P n ,
α | π ^ | α = e 2 | α | 2 = e 2 n ¯ cos 2 ( ϕ 2 ) e n ¯ ( ϕ π ) 2 2 ,
Δ ϕ = Δ π ^ | d π ^ d ϕ | = e 4 n ¯ cos 2 ( ϕ 2 ) 1 n ¯ 2 sin 2 ( ϕ ) 1 n ¯ ( 1 + ( 2 n ¯ + 1 ) ( ϕ π ) 2 8 ) ,
α | Z ^ | α = e | α | 2 = e n ¯ cos 2 ( ϕ 2 ) e n ¯ ( ϕ π ) 2 4 .
Δ ϕ = Δ Z ^ | d Z ^ d ϕ | = e n ¯ cos 2 ( ϕ 2 ) 1 n ¯ 2 4 sin 2 ( ϕ ) 1 n ¯ ( 1 + ( n ¯ 2 + 1 ) ( ϕ π ) 2 8 ) ,
π ^ = k = 0 ( 1 ) k P k d c n k = 0 ( 1 ) n k P n k coh = e 2 n d e 2 | α | 2 ,
P 0 = e n d e | α | 2
h ( n ¯ ) = exp [ β ( n d + n ¯ ( 1 V ) 1 + V ) ] ,
Δ ϕ = 1 + V β n ¯ V h β ( n ¯ ) e 2 β 2 n ¯ V 1 + V cos 2 ( ϕ 2 ) 1 sin 2 ( ϕ ) ,

Metrics