Abstract

We propose a N-photon imaging scheme with the resolution reaching the fundamental Heisenberg limit. The key imaging element is a phase-controlled screen which introduces synchronous-position N-photon interference, giving rise to enhanced resolution that exceeds the well-known Rayleigh resolution limit by a factor of N. In the standard wide-field illumination situation, our imaging scheme requires an entangled source to illuminate the object. Besides, we show that classical light is also applicable to realize this Heisenberg-resolution imaging if a scanning-focused-beam illumination is used. Our N-photon imaging scheme is practically realizable by using current well-developed technology.

© 2017 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
    [Crossref]
  2. V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
    [Crossref]
  3. T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
    [Crossref] [PubMed]
  4. J. Oh, Y. Cho, G. Scarcelli, and Y. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
    [Crossref] [PubMed]
  5. O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85(3), 033812 (2012).
    [Crossref]
  6. O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
    [Crossref] [PubMed]
  7. D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
    [Crossref]
  8. F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
    [Crossref]
  9. 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(17), 171104 (2015).
    [Crossref]
  10. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
    [Crossref] [PubMed]
  11. M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
    [Crossref]
  12. E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868 (1999).
    [Crossref]
  13. 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(21), 213601 (2002).
    [Crossref] [PubMed]
  14. M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
    [Crossref] [PubMed]
  15. P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
    [Crossref] [PubMed]
  16. I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328(5980), 879–881 (2010).
    [Crossref] [PubMed]
  17. K. Wang and D. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004).
    [Crossref]
  18. J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
    [Crossref] [PubMed]
  19. G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618 (2004).
    [Crossref]
  20. Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
    [Crossref]
  21. P. Hong and G. Zhang, “Subwavelength interference with an effective entangled source,” Phys. Rev. A 88(4), 043838 (2013);“Super-resolved optical lithography with phase controlled source,” ibid. 91(5), 053830 (2015).
    [Crossref]
  22. A. Pe’Er, B. Dayan, M. Vucelja, Y. Silberberg, and A. Friesem, “Quantum lithography by coherent control of classical light pulses,” Opt. Express 12(26), 6600–6605 (2004).
    [Crossref]
  23. P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
    [Crossref] [PubMed]
  24. W. Ge, P. Hemmer, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. A 87(2), 023818 (2013).
    [Crossref]
  25. P. Hong, “Two-photon imaging assisted by a dynamic random medium,” arXiv preprint arXiv:1701.08348 (2017).
  26. P. Hong and G. Zhang, “Synchronous position two-photon interference of random-phase grating,” J. Opt. Soc. Am. A 32(7), 1256–1261 (2015).
    [Crossref]
  27. Y. Shih, “Entangled photons,” IEEE J. Sel. Topics Quantum Electron. 9(6), 1455–1467 (2003).
    [Crossref]
  28. M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
    [Crossref] [PubMed]
  29. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
    [Crossref]
  30. L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
    [Crossref]
  31. M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
    [Crossref]
  32. Y. Bai, H. Liu, and S. Han, “Transmission area and correlated imaging,” Opt. Express 15(10), 6062–6068 (2007).
    [Crossref] [PubMed]

2017 (1)

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

2016 (1)

2015 (3)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
[Crossref]

P. Hong and G. Zhang, “Synchronous position two-photon interference of random-phase grating,” J. Opt. Soc. Am. A 32(7), 1256–1261 (2015).
[Crossref]

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(17), 171104 (2015).
[Crossref]

2014 (1)

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

2013 (4)

J. Oh, Y. Cho, G. Scarcelli, and Y. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
[Crossref] [PubMed]

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

P. Hong and G. Zhang, “Subwavelength interference with an effective entangled source,” Phys. Rev. A 88(4), 043838 (2013);“Super-resolved optical lithography with phase controlled source,” ibid. 91(5), 053830 (2015).
[Crossref]

W. Ge, P. Hemmer, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. A 87(2), 023818 (2013).
[Crossref]

2012 (2)

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85(3), 033812 (2012).
[Crossref]

2010 (2)

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328(5980), 879–881 (2010).
[Crossref] [PubMed]

2009 (2)

V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

2007 (1)

2006 (1)

P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
[Crossref] [PubMed]

2005 (2)

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
[Crossref]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

2004 (5)

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618 (2004).
[Crossref]

A. Pe’Er, B. Dayan, M. Vucelja, Y. Silberberg, and A. Friesem, “Quantum lithography by coherent control of classical light pulses,” Opt. Express 12(26), 6600–6605 (2004).
[Crossref]

K. Wang and D. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004).
[Crossref]

M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[Crossref] [PubMed]

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

2003 (1)

Y. Shih, “Entangled photons,” IEEE J. Sel. Topics Quantum Electron. 9(6), 1455–1467 (2003).
[Crossref]

2002 (1)

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(21), 213601 (2002).
[Crossref] [PubMed]

2001 (1)

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

1999 (1)

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868 (1999).
[Crossref]

1995 (1)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
[Crossref] [PubMed]

Afek, I.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328(5980), 879–881 (2010).
[Crossref] [PubMed]

Agnew, M.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Ambar, O.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328(5980), 879–881 (2010).
[Crossref] [PubMed]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
[Crossref]

Aspelmeyer, M.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
[Crossref]

Bai, Y.

Berchera, I.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Björk, G.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Boyd, R. W.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Brida, G.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Buller, G. S.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Camacho-Morales, R.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Cao, D.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

K. Wang and D. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004).
[Crossref]

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

Chen, H.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Chen, X.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
[Crossref]

Cho, Y.

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
[Crossref] [PubMed]

Colyer, R.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

Dayan, B.

Degiovanni, I.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Dertinger, T.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Deutsch, Z.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

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(21), 213601 (2002).
[Crossref] [PubMed]

Edgar, M. P.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Enderlein, J.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
[Crossref]

Fonseca, E.

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868 (1999).
[Crossref]

Forneris, J.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Friesem, A.

Gasparoni, S.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

Ge, W.

W. Ge, P. Hemmer, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. A 87(2), 023818 (2013).
[Crossref]

Genovese, M.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Guerrieri, F.

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Han, S.

Hemmer, P.

W. Ge, P. Hemmer, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. A 87(2), 023818 (2013).
[Crossref]

P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
[Crossref] [PubMed]

Hong, P.

P. Hong and G. Zhang, “Synchronous position two-photon interference of random-phase grating,” J. Opt. Soc. Am. A 32(7), 1256–1261 (2015).
[Crossref]

P. Hong and G. Zhang, “Subwavelength interference with an effective entangled source,” Phys. Rev. A 88(4), 043838 (2013);“Super-resolved optical lithography with phase controlled source,” ibid. 91(5), 053830 (2015).
[Crossref]

P. Hong, “Two-photon imaging assisted by a dynamic random medium,” arXiv preprint arXiv:1701.08348 (2017).

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
[Crossref]

Huang, F.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

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(21), 213601 (2002).
[Crossref] [PubMed]

Itzhakov, S.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

Iyer, G.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Izdebski, F.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
[Crossref] [PubMed]

Katamadze, K.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Kim, Y.

Kivshar, Y. S.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref]

Komar, A.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Kravchenko, I.

Kruk, S.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref]

Leach, J.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Levitt, J. M.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

Li, H.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

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(17), 171104 (2015).
[Crossref]

Li, T.

Liu, H.

Lloyd, S.

V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Lundeen, J.

M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[Crossref] [PubMed]

Maccone, L.

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Miroshnichenko, A. E.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Mitchell, M.

M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[Crossref] [PubMed]

Monken, C.

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868 (1999).
[Crossref]

Monticone, D.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Moreva, E.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Muthukrishnan, A.

P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
[Crossref] [PubMed]

Neshev, D. N.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016).
[Crossref]

Oh, J.

Olivero, P.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Oron, D.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85(3), 033812 (2012).
[Crossref]

Padgett, M. J.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Pádua, S.

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868 (1999).
[Crossref]

Pan, J.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

Pe’Er, A.

Rahmani, M.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Scarcelli, G.

J. Oh, Y. Cho, G. Scarcelli, and Y. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
[Crossref] [PubMed]

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618 (2004).
[Crossref]

Schwartz, O.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85(3), 033812 (2012).
[Crossref]

Scully, M.

P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
[Crossref] [PubMed]

Shapiro, J.

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Shih, Y.

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618 (2004).
[Crossref]

Y. Shih, “Entangled photons,” IEEE J. Sel. Topics Quantum Electron. 9(6), 1455–1467 (2003).
[Crossref]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 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(21), 213601 (2002).
[Crossref] [PubMed]

Silberberg, Y.

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328(5980), 879–881 (2010).
[Crossref] [PubMed]

A. Pe’Er, B. Dayan, M. Vucelja, Y. Silberberg, and A. Friesem, “Quantum lithography by coherent control of classical light pulses,” Opt. Express 12(26), 6600–6605 (2004).
[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(17), 171104 (2015).
[Crossref]

Steinberg, A.

M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[Crossref] [PubMed]

Sun, X.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

Tang, H.

Tasca, D. S.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Tenne, R.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

Tisa, S.

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Traina, P.

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

Ursin, R.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

Valencia, A.

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618 (2004).
[Crossref]

Vucelja, M.

Walther, P.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

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(17), 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(17), 171104 (2015).
[Crossref]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

K. Wang and D. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004).
[Crossref]

Wang, L.

Warburton, R. E.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Weiss, S.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Wong, F.

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Wu, L.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
[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(17), 171104 (2015).
[Crossref]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

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(17), 171104 (2015).
[Crossref]

Xu, L.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Yamamoto, Y.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
[Crossref] [PubMed]

Zappa, F.

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

Zárate, Y.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

Zeilinger, A.

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

Zhai, Y.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
[Crossref]

Zhang, D.

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
[Crossref]

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(17), 171104 (2015).
[Crossref]

Zhang, G.

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[Crossref]

P. Hong and G. Zhang, “Synchronous position two-photon interference of random-phase grating,” J. Opt. Soc. Am. A 32(7), 1256–1261 (2015).
[Crossref]

P. Hong and G. Zhang, “Subwavelength interference with an effective entangled source,” Phys. Rev. A 88(4), 043838 (2013);“Super-resolved optical lithography with phase controlled source,” ibid. 91(5), 053830 (2015).
[Crossref]

Zubairy, M.

W. Ge, P. Hemmer, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. A 87(2), 023818 (2013).
[Crossref]

P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
[Crossref] [PubMed]

Adv. Funct. Mater. (1)

M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zárate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible Thermal Tuning of All-Dielectric Metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017).
[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(17), 171104 (2015).
[Crossref]

Europhys. Lett. (1)

G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618 (2004).
[Crossref]

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

Y. Shih, “Entangled photons,” IEEE J. Sel. Topics Quantum Electron. 9(6), 1455–1467 (2003).
[Crossref]

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

Nano Lett. (1)

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13(12), 5832–5836 (2013).
[Crossref] [PubMed]

Nat. Commun. (1)

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Nature (2)

M. Mitchell, J. Lundeen, and A. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[Crossref] [PubMed]

P. Walther, J. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429(6988), 158–161 (2004).
[Crossref] [PubMed]

Nature Nanotech. (1)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotech. 10, 937–943 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (6)

W. Ge, P. Hemmer, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. A 87(2), 023818 (2013).
[Crossref]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85(3), 033812 (2012).
[Crossref]

V. Giovannetti, S. Lloyd, L. Maccone, and J. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79(1), 013827 (2009).
[Crossref]

Y. Zhai, X. Chen, D. Zhang, and L. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005).
[Crossref]

P. Hong and G. Zhang, “Subwavelength interference with an effective entangled source,” Phys. Rev. A 88(4), 043838 (2013);“Super-resolved optical lithography with phase controlled source,” ibid. 91(5), 053830 (2015).
[Crossref]

K. Wang and D. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004).
[Crossref]

Phys. Rev. Lett. (8)

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005).
[Crossref] [PubMed]

D. Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Berchera, P. Olivero, I. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe diffraction limit in confocal microscopy via nonclassical photon statistics,” Phys. Rev. Lett. 113(14), 143602 (2014).
[Crossref]

F. Guerrieri, L. Maccone, F. Wong, J. Shapiro, S. Tisa, and F. Zappa, “Sub-Rayleigh imaging via N-photon detection,” Phys. Rev. Lett. 105(16), 163602 (2010).
[Crossref]

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74(24), 4835 (1995).
[Crossref] [PubMed]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87(1), 013602 (2001).
[Crossref]

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868 (1999).
[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(21), 213601 (2002).
[Crossref] [PubMed]

P. Hemmer, A. Muthukrishnan, M. Scully, and M. Zubairy, “Quantum lithography with classical light,” Phys. Rev. Lett. 96(16), 163603 (2006).
[Crossref] [PubMed]

Proc. Nat. Acad. Sci. U.S.A. (1)

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI),” Proc. Nat. Acad. Sci. U.S.A. 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Science (1)

I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328(5980), 879–881 (2010).
[Crossref] [PubMed]

Other (2)

P. Hong, “Two-photon imaging assisted by a dynamic random medium,” arXiv preprint arXiv:1701.08348 (2017).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 (a): Heisenberg-resolution imaging system through a PCS, in which N-photon imaging (N = 2 in the figure) is obtained by measuring the synchronous-position correlation function. (b): Indistinguishable two-photon paths for a pair of photons to trigger a coincidence at a specific detecting/imaging point, which are introduced when the pair of photons transmit through the same position of the PCS. In (b), two neighboring colored squares on the PCS represents two correlated phase modes e1 (x f ) and e2 (x f ) at the same spatial point x f , respectively.
Fig. 2
Fig. 2 Image for two object points of distance S=8 μm, 6μm, and 4μm, respectively. (a1)–(a3): Conventional single-photon imaging. (b1)–(b3): Lens-assisted two-photon imaging with the resolution improved to the standard quantum limit. (c1)–(c3): two-photon imaging through PCS with the resolution reaching the Heisenberg limit. All figures are normalized by their maximum values, respectively.
Fig. 3
Fig. 3 Heisenberg-resolution incoherent two-photon imaging for two object points of distance S=8 μm (a1), 6μm (a2), and 4μm (a3), respectively. All figures are normalized by their maximum values, respectively.

Equations (11)

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I ( x ) somb 2 ( 2 π NA λ | x 0 + x m | ) ,
E ( + ) ( x ) E 0 ( + ) ( x 0 ) A ( x 0 ) H ( x 0 ; x f ; x ) 2 ( x f ) d x 0 d x f ,
2 * ( x f 1 ) 2 * ( x f 2 ) 2 ( x f 3 ) 2 ( x f 4 ) δ ( x f 1 x f 3 ) δ ( x f 2 x f 4 ) + δ ( x f 1 x f 4 ) δ ( x f 2 x f 3 ) + δ ( x f 1 x f 2 ) δ ( x f 3 x f 4 ) .
G ( 2 ) ( x ) E ( ) ( x 01 ) E ( ) ( x 02 ) E ( + ) ( x 03 ) E ( + ) ( x 04 ) e i k x 01 2 + x 02 2 2 l 1 e i k x 03 2 + x 04 2 2 l 1 × A * ( x 01 ) A * ( x 02 ) A ( x 03 ) A ( x 04 ) [ P b g ( { x 0 } ) + P img ( { x 0 } , { x } ) ] d x 01 d x 04 ,
P bg ( { x 0 } ) = somb ( k D 2 l 1 | x 01 x 03 | ) somb ( k D 2 l 1 | x 02 x 04 | ) + somb ( k d 2 l 1 | x 01 x 04 | ) somb ( k D 2 l 1 | x 02 x 03 | ) ,
P img ( { x 0 } , { x } ) = somb ( k D 2 l 1 | x 01 + x 02 + 2 x m | ) somb ( k D 2 l 1 | x 03 + x 04 + 2 x m | ) .
E ( ) ( x 01 ) E ( ) ( x 02 ) E ( + ) ( x 03 ) E ( + ) ( x 04 ) δ ( x 01 x 02 ) δ ( x 03 x 04 ) .
Δ G qua ( 2 ) ( x ) | A 2 ( x 0 ) e i k x 0 2 l 1 somb ( 2 π NA λ / 2 | x 0 + x m | ) d x 0 | 2 ,
E ( ) ( x 01 ) E ( ) ( x 02 ) E ( + ) ( x 03 ) E ( + ) ( x 04 ) σ x 01 , x 02 , x 03 , x 04 ,
Δ G cla ( 2 ) ( x ) | A ( x 0 ) | 4 somb 2 ( 2 π NA λ / 2 | x 0 + x m | ) d x 0 ,
Δ G cla N ( x ) | A ( x 0 ) | 2 N somb 2 ( 2 π NA λ / N | x 0 + x m | ) d x 0 ,

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