Abstract

Spatially formed two-photon interference fringes with fringe periods smaller than the diffraction limit are demonstrated. In the experiment, a fringe formed by two-photon NOON states with wavelength λ=702.2 nm is observed using a specially developed near-field scanning optical microscope probe and two-photon detection setup. The observed fringe period of 328.2 nm is well below the diffraction limit (351 nm = λ/2). Another experiment with a path-length difference larger than the coherent length of photons confirms that the observed fringe is due to two-photon interference.

©2007 Optical Society of America

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References

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  1. L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Phil. Mag. 8, 261274 (1879).
  2. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
    [Crossref] [PubMed]
  3. P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
    [Crossref]
  4. G. Bjork and L. L. Sánchez-Soto, “Entangled-state Lithography: Tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
    [Crossref] [PubMed]
  5. E. J. S. Fonseca, C. H. Monken, and S. Páuda, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
    [Crossref]
  6. M. D–Angelo, M. V. Chekhova, and Y. Shih , “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
    [Crossref]
  7. T. B. Pittman, Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Experimental tests of Bell’s inequalities based on space-time and spin variables,” Phys. Rev. A 51, 3495 – 3498 (1995).
    [Crossref] [PubMed]
  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] [PubMed]
  9. 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] [PubMed]
  10. Y. H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
    [Crossref]
  11. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
    [Crossref] [PubMed]
  12. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy of a nanometric scale,” Science 251, 1468–1470 (1991).
    [Crossref] [PubMed]
  13. Y. H. Zhai, X.-H. Chen, D. Zhang, and L.-A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72, 043805 (2005).
    [Crossref]
  14. J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005).
    [Crossref] [PubMed]
  15. C. K. Hong, Z. Y. Ou, and L. Mandel , “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044~2046 (1987).
    [Crossref] [PubMed]
  16. 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]
  17. K. Edamatsu, G. Oohata, R. Shimizu, and T. Itoh, “Generation of ultraviolet entangled photons in a semiconductor,” Nature 431, 167–170 (2004).
    [Crossref] [PubMed]
  18. R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
    [Crossref] [PubMed]
  19. K.-S. Lee, D.-Y. Yang, S. H. Park, and R. H. Kim, “Recent developments in the use of two-photon polymerization in precise 2D and 3D microfabrications,” Polym. Adv. Technol. 17, 72–82 (2006).
    [Crossref]
  20. P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158–161 (2004).
    [Crossref] [PubMed]

2007 (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] [PubMed]

2006 (2)

R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
[Crossref] [PubMed]

K.-S. Lee, D.-Y. Yang, S. H. Park, and R. H. Kim, “Recent developments in the use of two-photon polymerization in precise 2D and 3D microfabrications,” Polym. Adv. Technol. 17, 72–82 (2006).
[Crossref]

2005 (2)

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

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

2004 (2)

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

K. Edamatsu, G. Oohata, R. Shimizu, and T. Itoh, “Generation of ultraviolet entangled photons in a semiconductor,” Nature 431, 167–170 (2004).
[Crossref] [PubMed]

2003 (1)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref] [PubMed]

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

2001 (4)

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

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
[Crossref]

G. Bjork and L. L. Sánchez-Soto, “Entangled-state Lithography: Tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref] [PubMed]

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 (2)

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

Y. H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

1999 (1)

E. J. S. Fonseca, C. H. Monken, and S. Páuda, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[Crossref]

1995 (1)

T. B. Pittman, Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Experimental tests of Bell’s inequalities based on space-time and spin variables,” Phys. Rev. A 51, 3495 – 3498 (1995).
[Crossref] [PubMed]

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy of a nanometric scale,” Science 251, 1468–1470 (1991).
[Crossref] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel , “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044~2046 (1987).
[Crossref] [PubMed]

1879 (1)

L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Phil. Mag. 8, 261274 (1879).

Abrams, D. S.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
[Crossref]

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

Aspelmeyer, M.

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

Atkinson, P.

R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy of a nanometric scale,” Science 251, 1468–1470 (1991).
[Crossref] [PubMed]

Bjork, G.

G. Bjork and L. L. Sánchez-Soto, “Entangled-state Lithography: Tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[Crossref] [PubMed]

Boto, A. N.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
[Crossref]

Boto, N.

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

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref] [PubMed]

Braunstein, S. L.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
[Crossref]

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

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]

Cao, D. Z.

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

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]

Chen, X.-H.

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

Cooper, K.

R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
[Crossref] [PubMed]

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]

Dowling, J. P.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
[Crossref]

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

Edamatsu, K.

K. Edamatsu, G. Oohata, R. Shimizu, and T. Itoh, “Generation of ultraviolet entangled photons in a semiconductor,” Nature 431, 167–170 (2004).
[Crossref] [PubMed]

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] [PubMed]

Fonseca, E. J. S.

E. J. S. Fonseca, C. H. Monken, and S. Páuda, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[Crossref]

Gasparoni, S.

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

Gerry, C. C.

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]

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy of a nanometric scale,” Science 251, 1468–1470 (1991).
[Crossref] [PubMed]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel , “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044~2046 (1987).
[Crossref] [PubMed]

Huang, F.

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

Itoh, T.

K. Edamatsu, G. Oohata, R. Shimizu, and T. Itoh, “Generation of ultraviolet entangled photons in a semiconductor,” Nature 431, 167–170 (2004).
[Crossref] [PubMed]

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] [PubMed]

Kim, R. H.

K.-S. Lee, D.-Y. Yang, S. H. Park, and R. H. Kim, “Recent developments in the use of two-photon polymerization in precise 2D and 3D microfabrications,” Polym. Adv. Technol. 17, 72–82 (2006).
[Crossref]

Kim, Y. H.

Y. H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

Kok, P.

P. Kok, A. N. Boto, D. S. Abrams, C. P. Williams, S. L. Braunstein, and J. P. Dowling, “Quantum-interferometric optical lithography: towards arbitrary two-dimensional patterns,” Phys Rev. A 63, 063407 (2001).
[Crossref]

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

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy of a nanometric scale,” Science 251, 1468–1470 (1991).
[Crossref] [PubMed]

Kulik, S. P.

Y. H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

Lee, K.-S.

K.-S. Lee, D.-Y. Yang, S. H. Park, and R. H. Kim, “Recent developments in the use of two-photon polymerization in precise 2D and 3D microfabrications,” Polym. Adv. Technol. 17, 72–82 (2006).
[Crossref]

Li, H. G.

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

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel , “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044~2046 (1987).
[Crossref] [PubMed]

Monken, C. H.

E. J. S. Fonseca, C. H. Monken, and S. Páuda, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[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] [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]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[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]

Oohata, G.

K. Edamatsu, G. Oohata, R. Shimizu, and T. Itoh, “Generation of ultraviolet entangled photons in a semiconductor,” Nature 431, 167–170 (2004).
[Crossref] [PubMed]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel , “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044~2046 (1987).
[Crossref] [PubMed]

Pan, J.-W.

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

Park, S. H.

K.-S. Lee, D.-Y. Yang, S. H. Park, and R. H. Kim, “Recent developments in the use of two-photon polymerization in precise 2D and 3D microfabrications,” Polym. Adv. Technol. 17, 72–82 (2006).
[Crossref]

Páuda, S.

E. J. S. Fonseca, C. H. Monken, and S. Páuda, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[Crossref]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Experimental tests of Bell’s inequalities based on space-time and spin variables,” Phys. Rev. A 51, 3495 – 3498 (1995).
[Crossref] [PubMed]

Pryde, G. J.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref] [PubMed]

Ralph, T. C.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[Crossref] [PubMed]

Rayleigh, L.

L. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Phil. Mag. 8, 261274 (1879).

Ritchie, D. A.

R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
[Crossref] [PubMed]

Rubin, M. H.

T. B. Pittman, Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Experimental tests of Bell’s inequalities based on space-time and spin variables,” Phys. Rev. A 51, 3495 – 3498 (1995).
[Crossref] [PubMed]

Sánchez-Soto, L. L.

G. Bjork and L. L. Sánchez-Soto, “Entangled-state Lithography: Tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[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]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Experimental tests of Bell’s inequalities based on space-time and spin variables,” Phys. Rev. A 51, 3495 – 3498 (1995).
[Crossref] [PubMed]

Shields, A. J.

R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
[Crossref] [PubMed]

Shih, Y.

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

Y. H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A 62, 011802 (2000).
[Crossref]

Shih, Y. H.

T. B. Pittman, Y. H. Shih, A. V. Sergienko, and M. H. Rubin, “Experimental tests of Bell’s inequalities based on space-time and spin variables,” Phys. Rev. A 51, 3495 – 3498 (1995).
[Crossref] [PubMed]

Shimizu, R.

K. Edamatsu, G. Oohata, R. Shimizu, and T. Itoh, “Generation of ultraviolet entangled photons in a semiconductor,” Nature 431, 167–170 (2004).
[Crossref] [PubMed]

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] [PubMed]

Stevenson, R. M.

R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006).
[Crossref] [PubMed]

Sun, X. J.

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

Trautman, J. K.

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Figures (4)
Fig. 1.
Fig. 1. Interference of two coherent plane waves. When two coherent plane waves with wavelength λ intersect at an angle of 2θ, an interference fringe with period p (= λ/2sinθ) is obtained. An interference fringe modified by a limited beam diameter is shown for comparison with experimental results.

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Fig. 2.
Fig. 2. Schematic of experimental setup. Photon pairs entangled in polarization, (|VV〉 a +|HH〉 a )/√2, are generated from two beta barium borate (BBO) crystals and pass through an interference filter (IF) and a single mode fiber (SMF). Then, the entangled photons are spatially separated into paths b and c depending on their polarization in a calcite crystal (Cal). The polarization in path b is rotated by 90 degrees by a half wave plate (WP), giving a two-photon NOON state ((|2〉 d |0〉 e +|0〉 d |2〉 e )/√2). An aspheric lens (L) is used to focus the photons to a small spot and to form an interference fringe in the focal plane (FP). An NSOM probe with an elliptical opening (inset) is scanned with a piezo-actuator along the focal plane The single-mode fiber output of the probe is divided by a 50:50 fiber coupler and detected by single-photon counting modules (SPCM).

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Fig. 3.
Fig. 3. (a) Interference fringe of single photons. The lateral axis indicates the position of the NSOM probe. The vertical axes indicate single counting rates. A polarizer is placed before the single mode fiber to select only horizontally polarized photons. The polarization is then rotated 45 degrees. Since the effective detection efficiency (<1×10-3) including the collection efficiency of the probe is so small, the generated fringe is the that for a single-photon state in two modes, (|1〉 d |0〉 e +|0〉 d |1〉 e )/√2, when only the output of one of the two detectors is recorded. The black line is a sinusoidal curve weighted by a Gaussian function (see text) fitted to the experimental data. (b) Interference fringe of entangled photons beating the diffraction limit. The vertical axes indicate coincidence count rates (red dots, left axis). The black line is a fit to the experimental data. The fringe period of 328.2 nm is smaller than the diffraction limit of 3 51.1 nm. Single count rates of one of the two detectors measured at the same time are shown for reference (blue dots, right axis). For (a) and (b), the NSOM probe was scanned with 25-nm steps. The accumulation time for one data point was 5 seconds. The error bars show ± c o u n t s assuming Poisson statistics.

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Fig. 4.
Fig. 4. Interference fringes of (a) single photons and (b) entangled photons for a path difference much larger than the coherent length of each photon (~75 μm) (red dots, left axis). The path difference of about 500 μm was achieved by inserting a glass plate in one of the optical paths. The fringe period of 327.5 nm in (b) beats the diffraction limit of 351.1 nm. Single count rates of one of the two detectors measured at the same time are shown for reference (blue dots, right axis). The NSOM probe was scanned with a 25-nm step. The accumulation time for one data point was 10 seconds. The error bars show ± c o u n t s assuming Poisson statistics.

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Equations (1)

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I N = { 1 + cos ⁡ ( 2 πNr p ) } 2

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