Abstract

Spatial interference of quantum mechanical particles exhibits a fundamental feature of quantum mechanics. A two-mode entangled state of N particles known as N00N state can give rise to non-classical interference. We report the first experimental observation of a three-photon N00N state exhibiting Young’s double-slit type spatial quantum interference. Compared to a single-photon state, the three-photon entangled state generates interference fringes that are three times denser. Moreover, its interference visibility of 0.49 ± 0.09 is well above the limit of 0.1 for spatial super-resolution of classical origin.

© 2011 OSA

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2010 (4)

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled NOON state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879 (2010).
[CrossRef] [PubMed]

I. Afek, O. Ambar, and Y. Silberberg, “Classical bound for Mach-Zehnder superresolution,” Phys. Rev. Lett. 104, 123602 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (2)

M. D’Angelo, A. Garuccio, and V. Tamma, “Toward real maximally path-entangled N -photon-state sources,” Phys. Rev. A 77, 063826 (2008).
[CrossRef]

J. P. Dowling, “Quantum optical metrology—the lowdown of high-N00N states,” Contemp. Phys. 49, 125 (2008).
[CrossRef]

2007 (5)

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature 448, 784 (2007).
[CrossRef] [PubMed]

H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99, 163604 (2007).
[CrossRef] [PubMed]

K. T. Kapale and J. P. Dowling, “Bootstrapping approach for generating maximally path-entangled photon states,” Phys. Rev. Lett. 99, 053602 (2007).
[CrossRef] [PubMed]

Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15, 14244 (2007).
[CrossRef] [PubMed]

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

2006 (1)

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[CrossRef]

2004 (4)

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

S. J. Bentley and R. W. Boyd, “Nonlinear optical lithography with ultra-high sub-Rayleigh resolution,” Opt. Express 12, 5735 (2004).
[CrossRef] [PubMed]

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 (2004).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330 (2004).
[CrossRef] [PubMed]

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] [PubMed]

J. Fiurášek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
[CrossRef]

2001 (2)

M. D’Angelo, M. V. Chekhova, and Y. H. 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]

2000 (2)

A. 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 (2000).
[CrossRef] [PubMed]

Y.-H. Kim, R. Yu, S. P. Kulik, and Y. Shih, “Delayed “choice” quantum eraser,” Phys. Rev. Lett. 84, 1 (2000).
[CrossRef] [PubMed]

1999 (2)

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multi photon wave packet,” Phys. Rev. Lett. 82, 2868 (1999)
[CrossRef]

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

1995 (1)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie wave,” Phys. Rev. Lett. 74, 4835 (1995).
[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 (1987).
[CrossRef] [PubMed]

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]

A. 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 (2000).
[CrossRef] [PubMed]

Afek, I.

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879 (2010).
[CrossRef] [PubMed]

I. Afek, O. Ambar, and Y. Silberberg, “Classical bound for Mach-Zehnder superresolution,” Phys. Rev. Lett. 104, 123602 (2010).
[CrossRef] [PubMed]

Ambar, O.

I. Afek, O. Ambar, and Y. Silberberg, “Classical bound for Mach-Zehnder superresolution,” Phys. Rev. Lett. 104, 123602 (2010).
[CrossRef] [PubMed]

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879 (2010).
[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 (2004).
[CrossRef] [PubMed]

Bentley, S. J.

Björk, G.

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

A. 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 (2000).
[CrossRef] [PubMed]

Boyd, R. W.

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]

A. 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 (2000).
[CrossRef] [PubMed]

Cable, H.

H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99, 163604 (2007).
[CrossRef] [PubMed]

Chekhova, M. V.

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

Choi, S.-K.

Chuang, I.

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

Couteau, C.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

D’Angelo, M.

M. D’Angelo, A. Garuccio, and V. Tamma, “Toward real maximally path-entangled N -photon-state sources,” Phys. Rev. A 77, 063826 (2008).
[CrossRef]

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

Dowling, J. P.

J. P. Dowling, “Quantum optical metrology—the lowdown of high-N00N states,” Contemp. Phys. 49, 125 (2008).
[CrossRef]

K. T. Kapale and J. P. Dowling, “Bootstrapping approach for generating maximally path-entangled photon states,” Phys. Rev. Lett. 99, 053602 (2007).
[CrossRef] [PubMed]

H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99, 163604 (2007).
[CrossRef] [PubMed]

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]

A. 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 (2000).
[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, 213601 (2002).
[CrossRef] [PubMed]

Feynman, R. P.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison Wesley, 1965), Vol. III.

Fiurášek, J.

J. Fiurášek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
[CrossRef]

Fonseca, E. J. S.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multi photon wave packet,” Phys. Rev. Lett. 82, 2868 (1999)
[CrossRef]

Fujiwara, H.

Garuccio, A.

M. D’Angelo, A. Garuccio, and V. Tamma, “Toward real maximally path-entangled N -photon-state sources,” Phys. Rev. A 77, 063826 (2008).
[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 (2004).
[CrossRef] [PubMed]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330 (2004).
[CrossRef] [PubMed]

Grangier, P.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature 448, 784 (2007).
[CrossRef] [PubMed]

Guo, G. C.

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[CrossRef]

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 (1987).
[CrossRef] [PubMed]

Huang, Y. F.

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[CrossRef]

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] [PubMed]

Jacobson, J.

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

Jennewein, T.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

Jeong, H.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature 448, 784 (2007).
[CrossRef] [PubMed]

Kapale, K. T.

K. T. Kapale and J. P. Dowling, “Bootstrapping approach for generating maximally path-entangled photon states,” Phys. Rev. Lett. 99, 053602 (2007).
[CrossRef] [PubMed]

Kawabe, Y.

Kim, H.

Kim, Y.-H.

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled NOON state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

Y.-H. Kim, R. Yu, S. P. Kulik, and Y. Shih, “Delayed “choice” quantum eraser,” Phys. Rev. Lett. 84, 1 (2000).
[CrossRef] [PubMed]

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]

A. 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 (2000).
[CrossRef] [PubMed]

Kulik, S. P.

Y.-H. Kim, R. Yu, S. P. Kulik, and Y. Shih, “Delayed “choice” quantum eraser,” Phys. Rev. Lett. 84, 1 (2000).
[CrossRef] [PubMed]

Kwon, O.

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled NOON state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

Laflamme, R.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

Leighton, R. B.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison Wesley, 1965), Vol. III.

Liu, B. H.

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[CrossRef]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330 (2004).
[CrossRef] [PubMed]

Lundeen, J. S.

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

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330 (2004).
[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 (1987).
[CrossRef] [PubMed]

Mitchell, M. W.

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

Monken, C. H.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multi photon wave packet,” Phys. Rev. Lett. 82, 2868 (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 (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 (2007).
[CrossRef] [PubMed]

Okamoto, R.

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

Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15, 14244 (2007).
[CrossRef] [PubMed]

Ou, Z. Y.

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[CrossRef]

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

Ourjoumtsev, A.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature 448, 784 (2007).
[CrossRef] [PubMed]

Pádua, S.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multi photon wave packet,” Phys. Rev. Lett. 82, 2868 (1999)
[CrossRef]

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 (2004).
[CrossRef] [PubMed]

Park, H.-S.

Ra, Y.-S.

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled NOON state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

Sands, M.

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison Wesley, 1965), Vol. III.

Sasaki, K.

Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15, 14244 (2007).
[CrossRef] [PubMed]

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

Shih, Y.

Y.-H. Kim, R. Yu, S. P. Kulik, and Y. Shih, “Delayed “choice” quantum eraser,” Phys. Rev. Lett. 84, 1 (2000).
[CrossRef] [PubMed]

Shih, Y. H.

M. D’Angelo, M. V. Chekhova, and Y. H. 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] [PubMed]

Silberberg, Y.

I. Afek, O. Ambar, and Y. Silberberg, “Classical bound for Mach-Zehnder superresolution,” Phys. Rev. Lett. 104, 123602 (2010).
[CrossRef] [PubMed]

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879 (2010).
[CrossRef] [PubMed]

Sinha, U.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

Steinberg, A. M.

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

Sun, F. W.

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[CrossRef]

Takeuchi, S.

Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15, 14244 (2007).
[CrossRef] [PubMed]

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

Tamma, V.

M. D’Angelo, A. Garuccio, and V. Tamma, “Toward real maximally path-entangled N -photon-state sources,” Phys. Rev. A 77, 063826 (2008).
[CrossRef]

Tualle-Brouri, R.

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature 448, 784 (2007).
[CrossRef] [PubMed]

Ursin, R.

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 (2004).
[CrossRef] [PubMed]

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 (1999).
[CrossRef]

Walther, P.

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 (2004).
[CrossRef] [PubMed]

Weihs, G.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

Williams, C. 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]

A. 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 (2000).
[CrossRef] [PubMed]

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 (1999).
[CrossRef]

Yamamoto, Y.

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

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed., (Oxford University Press, 2006).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed., (Oxford University Press, 2006).

Yu, R.

Y.-H. Kim, R. Yu, S. P. Kulik, and Y. Shih, “Delayed “choice” quantum eraser,” Phys. Rev. Lett. 84, 1 (2000).
[CrossRef] [PubMed]

Zeilinger, A.

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 (2004).
[CrossRef] [PubMed]

Contemp. Phys. (1)

J. P. Dowling, “Quantum optical metrology—the lowdown of high-N00N states,” Contemp. Phys. 49, 125 (2008).
[CrossRef]

Nature (3)

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 (2004).
[CrossRef] [PubMed]

A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ‘Schrödinger cats’ from photon number states,” Nature 448, 784 (2007).
[CrossRef] [PubMed]

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

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 (1999).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (5)

F. W. Sun, B. H. Liu, Y. F. Huang, Z. Y. Ou, and G. C. Guo, “Observation of the four-photon de Broglie wavelength by state-projection measurement,” Phys. Rev. A 74, 033812 (2006).
[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]

O. Kwon, Y.-S. Ra, and Y.-H. Kim, “Observing photonic de Broglie waves without the maximally-path-entangled NOON state,” Phys. Rev. A 81, 063801 (2010).
[CrossRef]

J. Fiurášek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002).
[CrossRef]

M. D’Angelo, A. Garuccio, and V. Tamma, “Toward real maximally path-entangled N -photon-state sources,” Phys. Rev. A 77, 063826 (2008).
[CrossRef]

Phys. Rev. Lett. (10)

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]

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multi photon wave packet,” Phys. Rev. Lett. 82, 2868 (1999)
[CrossRef]

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

H. Cable and J. P. Dowling, “Efficient generation of large number-path entanglement using only linear optics and feed-forward,” Phys. Rev. Lett. 99, 163604 (2007).
[CrossRef] [PubMed]

K. T. Kapale and J. P. Dowling, “Bootstrapping approach for generating maximally path-entangled photon states,” Phys. Rev. Lett. 99, 053602 (2007).
[CrossRef] [PubMed]

A. 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 (2000).
[CrossRef] [PubMed]

Y.-H. Kim, R. Yu, S. P. Kulik, and Y. Shih, “Delayed “choice” quantum eraser,” Phys. Rev. Lett. 84, 1 (2000).
[CrossRef] [PubMed]

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

I. Afek, O. Ambar, and Y. Silberberg, “Classical bound for Mach-Zehnder superresolution,” Phys. Rev. Lett. 104, 123602 (2010).
[CrossRef] [PubMed]

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

Science (4)

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

I. Afek, O. Ambar, and Y. Silberberg, “High-N00N states by mixing quantum and classical light,” Science 328, 879 (2010).
[CrossRef] [PubMed]

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418 (2010).
[CrossRef] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330 (2004).
[CrossRef] [PubMed]

Other (2)

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison Wesley, 1965), Vol. III.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed., (Oxford University Press, 2006).

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