Abstract

The Abbe–Rayleigh diffraction limit constrains spatial resolution for classical imaging methods. Quantum imaging exploits correlations between photons to reproduce structures with higher resolution. Quantum-correlated N-photon states were shown to potentially surpass the classical limit by a factor of 1/N, corresponding to the Heisenberg limit, using a method known as optical centroid measurement (OCM). In this work, the theory of OCM is reformulated for its application in imaging. Using entangled photon pairs and a recently developed integrated time-resolving detector array, OCM is implemented in a proof-of-principle experiment that demonstrates the expected enhancement. Those results show the relevance of entanglement for imaging at the Heisenberg limit.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
    [Crossref]
  2. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
    [Crossref]
  3. D. Simon, G. Jaeger, and A. Sergienko, Quantum Metrology, Imaging, and Communication, Quantum Science and Technology (Springer International, 2016).
  4. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
    [Crossref]
  5. Z. Y. Ou, “Fundamental quantum limit in precision phase measurement,” Phys. Rev. A 55, 2598–2609 (1997).
    [Crossref]
  6. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
    [Crossref]
  7. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
    [Crossref]
  8. 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]
  9. M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
    [Crossref]
  10. G. Björk, L. L. Sánchez-Soto, and J. Söderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
    [Crossref]
  11. E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
    [Crossref]
  12. A. Pe’er, B. Dayan, M. Vucelja, Y. Silberg, A. A. Friesem, Y. Silberberg, A. A. Friesem, Y. Silberg, and A. A. Friesem, “Quantum lithography by coherent control of classical light pulses,” Opt. Express 12, 6600–6605 (2004).
    [Crossref]
  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]
  14. J. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (W. H. Freeman, 2005).
  15. M. Tsang, R. Nair, and X.-M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
    [Crossref]
  16. C. Lupo and S. Pirandola, “Ultimate precision bound of quantum and subwavelength imaging,” Phys. Rev. Lett. 117, 190802 (2016).
    [Crossref]
  17. M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Rehacek, “Achieving the ultimate optical resolution,” Optica 3, 1144–1147 (2016).
    [Crossref]
  18. Z. S. Tang, K. Durak, and A. Ling, “Fault-tolerant and finite-error localization for point emitters within the diffraction limit,” Opt. Express 24, 22004–22012 (2016).
    [Crossref]
  19. W.-K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s curse by imaging using phase information,” Phys. Rev. Lett. 118, 070801 (2017).
    [Crossref]
  20. F. Yang, A. Tashchilina, E. S. Moiseev, C. Simon, and A. I. Lvovsky, “Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode,” Optica 3, 1148–1152 (2016).
    [Crossref]
  21. M. Genovese, “Real applications of quantum imaging,” J. Opt. 18, 073002 (2016).
    [Crossref]
  22. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).
    [Crossref]
  23. Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016–1030 (2007).
    [Crossref]
  24. J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38, 682–684 (2013).
    [Crossref]
  25. I. F. Santos, J. G. Aguirre-Gómez, and S. Pádua, “Comparing quantum imaging with classical second-order incoherent imaging,” Phys. Rev. A 77, 043832 (2008).
    [Crossref]
  26. F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
    [Crossref]
  27. D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
    [Crossref]
  28. L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).
  29. M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102, 253601 (2009).
    [Crossref]
  30. H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
    [Crossref]
  31. L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
    [Crossref]
  32. A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19, 1174–1184 (2002).
    [Crossref]
  33. M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, “Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array,” Opt. Express 24, 28829–28841 (2016).
    [Crossref]
  34. M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36, 190–192 (2011).
    [Crossref]

2017 (1)

W.-K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s curse by imaging using phase information,” Phys. Rev. Lett. 118, 070801 (2017).
[Crossref]

2016 (7)

2015 (1)

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

2014 (1)

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

2013 (1)

2011 (3)

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36, 190–192 (2011).
[Crossref]

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

2010 (1)

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

2009 (2)

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102, 253601 (2009).
[Crossref]

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

2008 (1)

I. F. Santos, J. G. Aguirre-Gómez, and S. Pádua, “Comparing quantum imaging with classical second-order incoherent imaging,” Phys. Rev. A 77, 043832 (2008).
[Crossref]

2007 (3)

Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016–1030 (2007).
[Crossref]

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]

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

2006 (2)

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref]

2004 (1)

2002 (2)

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[Crossref]

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19, 1174–1184 (2002).
[Crossref]

2001 (2)

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

G. Björk, L. L. Sánchez-Soto, and J. Söderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref]

1999 (1)

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[Crossref]

1997 (1)

Z. Y. Ou, “Fundamental quantum limit in precision phase measurement,” Phys. Rev. A 55, 2598–2609 (1997).
[Crossref]

1995 (1)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref]

Abouraddy, A.

Aguirre-Gómez, J. G.

I. F. Santos, J. G. Aguirre-Gómez, and S. Pádua, “Comparing quantum imaging with classical second-order incoherent imaging,” Phys. Rev. A 77, 043832 (2008).
[Crossref]

Bateman, J. D.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Bessire, B.

M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, “Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array,” Opt. Express 24, 28829–28841 (2016).
[Crossref]

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Björk, G.

G. Björk, L. L. Sánchez-Soto, and J. Söderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref]

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref]

Boyd, R. W.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

Chan, K. W. C.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

Chang, H. J.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[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]

Cho, Y.-W.

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref]

Corona, M.

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]

Dayan, B.

Didomenico, L. D.

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

Dowling, J. P.

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

Durak, K.

Edamatsu, K.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[Crossref]

Feizpour, A.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Ferretti, H.

W.-K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s curse by imaging using phase information,” Phys. Rev. Lett. 118, 070801 (2017).
[Crossref]

Friesem, A. A.

Garay-Palmett, K.

Garcia, M. M.

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Gasparini, L.

M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, “Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array,” Opt. Express 24, 28829–28841 (2016).
[Crossref]

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Genovese, M.

M. Genovese, “Real applications of quantum imaging,” J. Opt. 18, 073002 (2016).
[Crossref]

Giovannetti, V.

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

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

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref]

Goodman, J.

J. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (W. H. Freeman, 2005).

Guerrieri, F.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

Hayat, A.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

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]

Hradil, Z.

Itoh, T.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[Crossref]

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref]

Jaeger, G.

D. Simon, G. Jaeger, and A. Sergienko, Quantum Metrology, Imaging, and Communication, Quantum Science and Technology (Springer International, 2016).

Kapale, K. T.

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

Kim, Y.-H.

Kok, P.

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

Lee, H.

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

Li, H.-G.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

Ling, A.

Lloyd, S.

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

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

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref]

Lu, X.-M.

M. Tsang, R. Nair, and X.-M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
[Crossref]

Lupo, C.

C. Lupo and S. Pirandola, “Ultimate precision bound of quantum and subwavelength imaging,” Phys. Rev. Lett. 117, 190802 (2016).
[Crossref]

Lvovsky, A. I.

Maccone, L.

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

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

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

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref]

Mahler, D. H.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Moiseev, E. S.

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]

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]

Nair, R.

M. Tsang, R. Nair, and X.-M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
[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, 726–729 (2007).
[Crossref]

Oh, J.-E.

Okamoto, R.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

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]

Ou, Z. Y.

Z. Y. Ou, “Fundamental quantum limit in precision phase measurement,” Phys. Rev. A 55, 2598–2609 (1997).
[Crossref]

Pádua, S.

I. F. Santos, J. G. Aguirre-Gómez, and S. Pádua, “Comparing quantum imaging with classical second-order incoherent imaging,” Phys. Rev. A 77, 043832 (2008).
[Crossref]

Parmesan, L.

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Paúr, M.

Pe’er, A.

Perenzoni, M.

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Pirandola, S.

C. Lupo and S. Pirandola, “Ultimate precision bound of quantum and subwavelength imaging,” Phys. Rev. Lett. 117, 190802 (2016).
[Crossref]

Rehacek, J.

Rozema, L. A.

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Saleh, B. E. A.

Sánchez-Soto, L. L.

M. Paúr, B. Stoklasa, Z. Hradil, L. L. Sánchez-Soto, and J. Rehacek, “Achieving the ultimate optical resolution,” Optica 3, 1144–1147 (2016).
[Crossref]

G. Björk, L. L. Sánchez-Soto, and J. Söderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref]

Santos, I. F.

I. F. Santos, J. G. Aguirre-Gómez, and S. Pádua, “Comparing quantum imaging with classical second-order incoherent imaging,” Phys. Rev. A 77, 043832 (2008).
[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, 726–729 (2007).
[Crossref]

Scarcelli, G.

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]

Sergienko, A.

D. Simon, G. Jaeger, and A. Sergienko, Quantum Metrology, Imaging, and Communication, Quantum Science and Technology (Springer International, 2016).

Sergienko, A. V.

Shapiro, J. H.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

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

Shih, Y.

Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016–1030 (2007).
[Crossref]

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

Shimizu, R.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[Crossref]

Shin, H.

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

Silberberg, Y.

Silberg, Y.

Simon, C.

Simon, D.

D. Simon, G. Jaeger, and A. Sergienko, Quantum Metrology, Imaging, and Communication, Quantum Science and Technology (Springer International, 2016).

Söderholm, J.

G. Björk, L. L. Sánchez-Soto, and J. Söderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref]

Song, X.-B.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

Stefanov, A.

M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, “Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array,” Opt. Express 24, 28829–28841 (2016).
[Crossref]

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Steinberg, A. M.

W.-K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s curse by imaging using phase information,” Phys. Rev. Lett. 118, 070801 (2017).
[Crossref]

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

Stoklasa, B.

Stoppa, D.

M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, “Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array,” Opt. Express 24, 28829–28841 (2016).
[Crossref]

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

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]

Tang, Z. S.

Tashchilina, A.

Teich, M. C.

Tham, W.-K.

W.-K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s curse by imaging using phase information,” Phys. Rev. Lett. 118, 070801 (2017).
[Crossref]

Tisa, S.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

Tsang, M.

M. Tsang, R. Nair, and X.-M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
[Crossref]

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102, 253601 (2009).
[Crossref]

U’Ren, A. B.

Unternährer, M.

M. Unternährer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, “Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array,” Opt. Express 24, 28829–28841 (2016).
[Crossref]

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Vrijen, R. B.

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[Crossref]

Vucelja, M.

Wang, H.-B.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

Wang, K.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

Wong, F. N. C.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

Xiong, J.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

Xu, D.-Q.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

Xu, H.

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Yablonovitch, E.

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[Crossref]

Yamamoto, Y.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref]

Yang, F.

Zappa, F.

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

Zarghami, M.

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Zhang, D.-J.

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

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]

Appl. Phys. Lett. (1)

D.-Q. Xu, X.-B. Song, H.-G. Li, D.-J. Zhang, H.-B. Wang, J. Xiong, and K. Wang, “Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source,” Appl. Phys. Lett. 106, 171104 (2015).
[Crossref]

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

Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016–1030 (2007).
[Crossref]

J. Opt. (1)

M. Genovese, “Real applications of quantum imaging,” J. Opt. 18, 073002 (2016).
[Crossref]

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

Nat. Photonics (1)

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

Opt. Eng. (1)

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optica (2)

Phys. Rev. A (3)

I. F. Santos, J. G. Aguirre-Gómez, and S. Pádua, “Comparing quantum imaging with classical second-order incoherent imaging,” Phys. Rev. A 77, 043832 (2008).
[Crossref]

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

Z. Y. Ou, “Fundamental quantum limit in precision phase measurement,” Phys. Rev. A 55, 2598–2609 (1997).
[Crossref]

Phys. Rev. Lett. (12)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref]

P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96, 163603 (2006).
[Crossref]

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

G. Björk, L. L. Sánchez-Soto, and J. Söderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref]

C. Lupo and S. Pirandola, “Ultimate precision bound of quantum and subwavelength imaging,” Phys. Rev. Lett. 117, 190802 (2016).
[Crossref]

M. Tsang, “Quantum imaging beyond the diffraction limit by optical centroid measurements,” Phys. Rev. Lett. 102, 253601 (2009).
[Crossref]

H. Shin, K. W. C. Chan, H. J. Chang, and R. W. Boyd, “Quantum spatial superresolution by optical centroid measurements,” Phys. Rev. Lett. 107, 083603 (2011).
[Crossref]

L. A. Rozema, J. D. Bateman, D. H. Mahler, R. Okamoto, A. Feizpour, A. Hayat, and A. M. Steinberg, “Scalable spatial superresolution using entangled photons,” Phys. Rev. Lett. 112, 223602 (2014).
[Crossref]

F. Guerrieri, L. Maccone, F. N. C. Wong, J. H. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105, 163602 (2010).
[Crossref]

W.-K. Tham, H. Ferretti, and A. M. Steinberg, “Beating Rayleigh’s curse by imaging using phase information,” Phys. Rev. Lett. 118, 070801 (2017).
[Crossref]

Phys. Rev. X (1)

M. Tsang, R. Nair, and X.-M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
[Crossref]

Proc. SPIE (1)

K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, “Quantum interferometric sensors,” Proc. SPIE 6603, 660316 (2007).
[Crossref]

Science (1)

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]

Other (3)

D. Simon, G. Jaeger, and A. Sergienko, Quantum Metrology, Imaging, and Communication, Quantum Science and Technology (Springer International, 2016).

J. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (W. H. Freeman, 2005).

L. Gasparini, M. Zarghami, H. Xu, L. Parmesan, M. M. Garcia, M. Unternährer, B. Bessire, A. Stefanov, D. Stoppa, and M. Perenzoni, “A 32 × 32-pixels time-resolved single-photon image sensor with 44.64-μm pitch and 19.48% fill-factor with on-chip row/frame skipping features reaching 800  kHz observation rate for quantum physics applications,” in International Solid-State Circuits Conference (ISSCC) (IEEE, 2018).

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Optical setup consisting of OCM state preparation and single-lens imaging (right). A 405 nm laser source illuminates an object in the plane Σ o . 4 f imaging from Σ o to the output plane Σ o is performed by lenses L 1 and L 2 . The nonlinear crystal (NLC) in the central far-field plane produces photon pairs in SPDC. A band-pass filter (BP) transmits at 810 nm. Resolution-limited imaging is performed by the low-NA lens L 3 from output plane Σ o to image plane Σ i , where the 2D detector array D measures correlations.
Fig. 2.
Fig. 2. Imaging of an object using a single lens with different illumination light sources: Biphoton OCM at 810 nm (a), spatially coherent laser at 810 nm (b) and 405 nm (c), spatially incoherent light at 810 nm (d). The same low NA is used to demonstrate the wavelength dependence of the resolution. The region of 1.4 × 1.4    mm 2 is acquired by a 32 × 32 pixels sensor. Biphoton OCM yields images at half-pixels and achieves a comparable image resolution at 810 nm to that of a coherent light at 405 nm.
Fig. 3.
Fig. 3. Triple-slit object of 70 μm linewidth is used for resolution comparison. Cross sections in low-NA imaging using biphoton OCM at 810 nm (crosses), spatially coherent illumination at 810 nm (squares) and 405 nm (circles), and incoherent light at 810 nm (diamonds) are shown. OCM shows an advantage that is practically identical to the double resolution given with 405 nm.
Fig. 4.
Fig. 4. Projection of the PSF of low-NA single-lens imaging at different light sources. Measurements with coherent light at 810 nm (squares) and 405 nm (circles) are shown with their theoretical curves. The biphoton OCM PSF at 810 nm (dots) closely agrees with 405 nm and confirms its doubled resolution. Statistical 2 σ errors are shown. The OCM PSF surpasses a theoretical SQL-scaling PSF of the centroid of two classically correlated photons at 810 nm (dashed line).

Equations (9)

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I ( ρ ) = | d 2 ρ    A ( ρ ) h ( ρ m ρ ) | 2 = | ( A * h ) ( ρ m ) | 2 ,
| Ψ = d 2 ρ 1 d 2 ρ N    A ( ρ 1 + + ρ N N ) | ρ 1 , , ρ N
X := 1 N k = 1 N ρ k , ξ k := ρ k X , k { 1 , , N } .
G ( N ) ( ρ 1 , , ρ N ) = | d 2 ρ 1 d 2 ρ N A ( X ) h ( ρ 1 m ρ 1 ) h ( ρ N m ρ N ) | .
G ( N ) ( X , ξ 1 , , ξ N 1 ) = | ( A * H ) ( X m ) | 2 ,
H ( X ) = N 2 ( h * * h ) × N ( N X )
H ( X ) = C    jinc ( 2 π R N s o λ | X | ) ,
| Ψ = d 2 q A ˜ ( N q ) | q , , q ,
| Ψ = d 2 ρ 1 d 2 ρ 2 A ( ρ 1 + ρ 2 2 ) sinc ( Δ k L 2 ) | ρ 1 , ρ 2 ,

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