Abstract

We demonstrate a novel second-order spatial interference effect between two indistinguishable pairs of disjoint optical paths from a single chaotic source. Beside providing a deeper understanding of the physics of multi-photon interference and coherence, the effect enables retrieving information on both the spatial structure and the relative position of two distant double-pinhole masks, in the absence of first order coherence. We also demonstrate the exploitation of the phenomenon for simulating quantum logic gates, including a controlled-NOT gate operation.

© 2017 Optical Society of America

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Corrections

16 June 2017: Typographical corrections were made to the author listing.


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References

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    [Crossref]
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  8. H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A 73, 023820 (2006).
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  9. J. Liu, Y. Zhou, W. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 21(16), 19209–19218 (2013).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  33. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
    [Crossref] [PubMed]
  34. J. P. Dowling, “Quantum optical metrology - the lowdown on high-N00N states,” Contemp. Phys. 49(2), 125–143 (2008).
    [Crossref]
  35. T. Legero, T. Wilk, M. Hennrich, G. Rempe, and A. Kuhn, “Quantum Beat of Two Single Photons,” Phys. Rev. Lett. 93, 070503 (2004).
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  36. M. D’Angelo, A. Garuccio, and V. Tamma, “Toward real maximally path-entangled N -photon-state sources,” Phys. Rev. A 77, 063826 (2008).
    [Crossref]
  37. N. Cerf, C. Adami, and P. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477 (1998).
    [Crossref]
  38. R. J. C. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
    [Crossref]
  39. K. F. Lee and J. E. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
    [Crossref] [PubMed]
  40. K. H. Kagalwala, G. di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photonics 7(1), 72–78 (2013).
    [Crossref]
  41. T. Peng and Y. H. Shih, “Bell correlation of thermal fields in photon-number fluctuations,” EPL 112(6), 60006 (2015).
    [Crossref]
  42. I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and L. A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2–3), 422–431 (2009).
    [Crossref]
  43. M. E. Pearce, T. Mehringer, J. von Zanthier, and P. Kok, “Precision estimation of source dimensions from higher-order intensity correlations,” Phys. Rev. A 92, 043831 (2015).
    [Crossref]
  44. G. Scarcelli, A. Valencia, and Y. H. Shih, “Two-photon interference with thermal light,” EPL 68(5), 618–624 (2004).
    [Crossref]
  45. S. Oppel, T. Büttner, P. Kok, and J. von Zanthier, “Superresolving multiphoton interferences with independent light sources,” Phys. Rev. Lett. 109, 233603 (2012).
    [Crossref]
  46. T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
    [Crossref]
  47. 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]
  48. K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
    [Crossref]
  49. M. D’Angelo, A. Mazzilli, F. V. Pepe, A. Garuccio, and V. Tamma, “Characterization of two distant double-slit by chaotic light second-order interference,” arxiv: 1609.03416 (2016).
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  53. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical description of statistical light beams,” Phys. Rev. Lett. 10, 277 (1963).
    [Crossref]
  54. A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
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    [Crossref]
  56. V. Tamma, “Analogue algorithm for parallel factorization of an exponential number of large integers: I theoretical description,” Quantum Inform. Process. 15(12), 5259–5280 (2015).
    [Crossref]
  57. V. Tamma, H. Zhang, X. He, A. Garuccio, W. P. Schleich, and Y. H. Shih, “Factoring numbers with a single interferogram,” Phys. Rev. A 83, 020304 (2011).
    [Crossref]
  58. V. Tamma, H. Zhang, X. He, A. Garuccio, and Y. H. Shih, “New factorization algorithm based on a continuous representation of truncated gauss sums,” J. Mod. Opt. 56(18), 2125–2132 (2009).
    [Crossref]
  59. V. Tamma, C. O. Alley, W. P. Schleich, and Y. H. Shih, “Prime number decomposition, the hyperbolic function and multi-path Michelson interferometers,” Found. Phys. 42(1), 111–121 (2012).
    [Crossref]
  60. S. Wölk, W. Merkel, W. P. Schleich, I. S. Averbukh, and B. Girard, “Factorization of numbers with Gauss sums: I. Mathematical background,” New J. Phys. 13, 103007 (2011).
    [Crossref]
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    [Crossref]

2016 (7)

V. Tamma and J. Seiler, “Multipath correlation interference and controlled-not gate simulation with a thermal source,” New J. Phys. 18, 032002 (2016).
[Crossref]

M. Genovese, “Real applications of quantum imaging,” J. Opt. 18(7), 073002 (2016).
[Crossref]

J. Sprigg, T. Peng, and Y. H. Shih, “Super-resolution imaging using the spatial-frequency filtered intensity fluctuation correlation,” Sci. Rep. 6, 38077 (2016).
[Crossref] [PubMed]

P. Kok, “Photonic quantum information processing,” Contemp. Phys. 57(4), 526–544 (2016).
[Crossref]

V. Tamma and S. Laibacher, “Boson sampling with non-identical single photons,” J. Mod. Opt. 63(1), 41–45 (2016).
[Crossref]

V. Tamma and S. Laibacher, “Multi-boson correlation sampling,” Quantum Inf. Process. 15(3), 1241–1262 (2016).
[Crossref]

T. Peng, V. Tamma, and Y. H. Shih, “Experimental controlled-not gate simulation with thermal light,” Sci. Rep. 6, 30152 (2016).
[Crossref] [PubMed]

2015 (6)

M. E. Pearce, T. Mehringer, J. von Zanthier, and P. Kok, “Precision estimation of source dimensions from higher-order intensity correlations,” Phys. Rev. A 92, 043831 (2015).
[Crossref]

V. Tamma, “Analogue algorithm for parallel factorization of an exponential number of large integers: II optical implementation,” Quantum Inform. Process. 15(12), 5243–5257 (2015).
[Crossref]

V. Tamma, “Analogue algorithm for parallel factorization of an exponential number of large integers: I theoretical description,” Quantum Inform. Process. 15(12), 5259–5280 (2015).
[Crossref]

T. Peng and Y. H. Shih, “Bell correlation of thermal fields in photon-number fluctuations,” EPL 112(6), 60006 (2015).
[Crossref]

S. Laibacher and V. Tamma, “From the physics to the computational complexity of multiboson correlation interference,” Phys. Rev. Lett. 115, 243605 (2015).
[Crossref] [PubMed]

V. Tamma and S. Laibacher, “Multiboson correlation interferometry with arbitrary single-photon pure states,” Phys. Rev. Lett. 114, 243601 (2015).
[Crossref] [PubMed]

2014 (3)

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature 512, 409–412 (2014).
[Crossref] [PubMed]

V. Tamma and S. Laibacher, “Multiboson correlation interferometry with multimode thermal sources,” Phys. Rev. A 90, 063836 (2014).
[Crossref]

V. Tamma, “Sampling of bosonic qubits,” Intern. J. Quantum Inf. 12, 1560017 (2014).
[Crossref]

2013 (3)

H. Chen, T. Peng, and Y. H. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A 88, 023808 (2013).
[Crossref]

J. Liu, Y. Zhou, W. Wang, R. F. Liu, K. He, F. L. Li, and Z. Xu, “Spatial second-order interference of pseudothermal light in a Hong-Ou-Mandel interferometer,” Opt. Express 21(16), 19209–19218 (2013).
[Crossref] [PubMed]

K. H. Kagalwala, G. di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photonics 7(1), 72–78 (2013).
[Crossref]

2012 (5)

A. Crespi, M. Lobino, J. C. F. Matthews, A. Politi, C. R. Neal, R. Ramponi, R. Osellame, and J. L. O’Brien, “Measuring protein concentration with entangled photons,” Appl. Phys. Lett. 100(23), 233704 (2012).
[Crossref]

V. Tamma, C. O. Alley, W. P. Schleich, and Y. H. Shih, “Prime number decomposition, the hyperbolic function and multi-path Michelson interferometers,” Found. Phys. 42(1), 111–121 (2012).
[Crossref]

S. Oppel, T. Büttner, P. Kok, and J. von Zanthier, “Superresolving multiphoton interferences with independent light sources,” Phys. Rev. Lett. 109, 233603 (2012).
[Crossref]

K. H. Luo, B. Q. Huang, W. M. Zheng, and L. A. Wu, “Nonlocal imaging by conditional averaging of random reference measurements,” Chin. Phys. Lett. 29(7), 074216 (2012).
[Crossref]

J. Wen, “Forming positive-negative images using conditioned partial measurements from reference arm in ghost imaging,” J. Opt. Soc. Am. A 29(9), 1906–1911 (2012).
[Crossref]

2011 (3)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5(4), 222–229 (2011).
[Crossref]

V. Tamma, H. Zhang, X. He, A. Garuccio, W. P. Schleich, and Y. H. Shih, “Factoring numbers with a single interferogram,” Phys. Rev. A 83, 020304 (2011).
[Crossref]

S. Wölk, W. Merkel, W. P. Schleich, I. S. Averbukh, and B. Girard, “Factorization of numbers with Gauss sums: I. Mathematical background,” New J. Phys. 13, 103007 (2011).
[Crossref]

2009 (2)

V. Tamma, H. Zhang, X. He, A. Garuccio, and Y. H. Shih, “New factorization algorithm based on a continuous representation of truncated gauss sums,” J. Mod. Opt. 56(18), 2125–2132 (2009).
[Crossref]

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and L. A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2–3), 422–431 (2009).
[Crossref]

2008 (2)

J. P. Dowling, “Quantum optical metrology - the lowdown on high-N00N states,” Contemp. Phys. 49(2), 125–143 (2008).
[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]

2006 (2)

G. Scarcelli, V. Berardi, and Y. H. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations,” Phys. Rev. Lett. 96, 063602 (2006).
[Crossref] [PubMed]

H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A 73, 023820 (2006).
[Crossref]

2005 (3)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

M. D’Angelo and Y. H. Shih, “Quantum Imaging,” Laser Phys. Lett. 2(12), 567–596 (2005).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref] [PubMed]

2004 (4)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[Crossref]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, and A. Kuhn, “Quantum Beat of Two Single Photons,” Phys. Rev. Lett. 93, 070503 (2004).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
[Crossref] [PubMed]

G. Scarcelli, A. Valencia, and Y. H. Shih, “Two-photon interference with thermal light,” EPL 68(5), 618–624 (2004).
[Crossref]

2003 (2)

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, “Experimental controlled-NOT logic gate for single photons in the coincidence basis,” Phys. Rev. A 68, 032316 (2003).
[Crossref]

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]

2002 (2)

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301 (2002).
[Crossref]

K. F. Lee and J. E. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
[Crossref] [PubMed]

2001 (2)

R. J. C. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
[Crossref]

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

1998 (1)

N. Cerf, C. Adami, and P. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477 (1998).
[Crossref]

1996 (1)

M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 6 (1996).
[Crossref]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).
[Crossref] [PubMed]

1988 (1)

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921 (1988).
[Crossref] [PubMed]

1987 (1)

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

1963 (2)

R. J. Glauber, “Photon correlations,” Phys. Rev. Lett. 10, 84 (1963).
[Crossref]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical description of statistical light beams,” Phys. Rev. Lett. 10, 277 (1963).
[Crossref]

1956 (2)

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[Crossref]

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Abouraddy, A. F.

K. H. Kagalwala, G. di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photonics 7(1), 72–78 (2013).
[Crossref]

Adami, C.

N. Cerf, C. Adami, and P. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477 (1998).
[Crossref]

Agafonov, I. N.

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and L. A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2–3), 422–431 (2009).
[Crossref]

Alley, C. O.

V. Tamma, C. O. Alley, W. P. Schleich, and Y. H. Shih, “Prime number decomposition, the hyperbolic function and multi-path Michelson interferometers,” Found. Phys. 42(1), 111–121 (2012).
[Crossref]

Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. 61, 2921 (1988).
[Crossref] [PubMed]

C. O. Alley and Y. H. Shih, Proceedings of the Second International Symposium on Foundations of Quantum Mechanics in the Light of New Technology (Tokyo, 1986), pp 47–52;

Averbukh, I. S.

S. Wölk, W. Merkel, W. P. Schleich, I. S. Averbukh, and B. Girard, “Factorization of numbers with Gauss sums: I. Mathematical background,” New J. Phys. 13, 103007 (2011).
[Crossref]

Bache, M.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[Crossref]

Berardi, V.

G. Scarcelli, V. Berardi, and Y. H. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations,” Phys. Rev. Lett. 96, 063602 (2006).
[Crossref] [PubMed]

Borish, V.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature 512, 409–412 (2014).
[Crossref] [PubMed]

Brambilla, E.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
[Crossref]

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]

Büttner, T.

S. Oppel, T. Büttner, P. Kok, and J. von Zanthier, “Superresolving multiphoton interferences with independent light sources,” Phys. Rev. Lett. 109, 233603 (2012).
[Crossref]

Cerf, N.

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E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical description of statistical light beams,” Phys. Rev. Lett. 10, 277 (1963).
[Crossref]

Tamma, V.

V. Tamma and J. Seiler, “Multipath correlation interference and controlled-not gate simulation with a thermal source,” New J. Phys. 18, 032002 (2016).
[Crossref]

V. Tamma and S. Laibacher, “Multi-boson correlation sampling,” Quantum Inf. Process. 15(3), 1241–1262 (2016).
[Crossref]

V. Tamma and S. Laibacher, “Boson sampling with non-identical single photons,” J. Mod. Opt. 63(1), 41–45 (2016).
[Crossref]

T. Peng, V. Tamma, and Y. H. Shih, “Experimental controlled-not gate simulation with thermal light,” Sci. Rep. 6, 30152 (2016).
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S. Laibacher and V. Tamma, “From the physics to the computational complexity of multiboson correlation interference,” Phys. Rev. Lett. 115, 243605 (2015).
[Crossref] [PubMed]

V. Tamma and S. Laibacher, “Multiboson correlation interferometry with arbitrary single-photon pure states,” Phys. Rev. Lett. 114, 243601 (2015).
[Crossref] [PubMed]

V. Tamma, “Analogue algorithm for parallel factorization of an exponential number of large integers: II optical implementation,” Quantum Inform. Process. 15(12), 5243–5257 (2015).
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[Crossref]

V. Tamma and S. Laibacher, “Multiboson correlation interferometry with multimode thermal sources,” Phys. Rev. A 90, 063836 (2014).
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V. Tamma, “Sampling of bosonic qubits,” Intern. J. Quantum Inf. 12, 1560017 (2014).
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V. Tamma, C. O. Alley, W. P. Schleich, and Y. H. Shih, “Prime number decomposition, the hyperbolic function and multi-path Michelson interferometers,” Found. Phys. 42(1), 111–121 (2012).
[Crossref]

V. Tamma, H. Zhang, X. He, A. Garuccio, W. P. Schleich, and Y. H. Shih, “Factoring numbers with a single interferogram,” Phys. Rev. A 83, 020304 (2011).
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V. Tamma, H. Zhang, X. He, A. Garuccio, and Y. H. Shih, “New factorization algorithm based on a continuous representation of truncated gauss sums,” J. Mod. Opt. 56(18), 2125–2132 (2009).
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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, A. Mazzilli, F. V. Pepe, A. Garuccio, and V. Tamma, “Characterization of two distant double-slit by chaotic light second-order interference,” arxiv: 1609.03416 (2016).

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R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
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M. E. Pearce, T. Mehringer, J. von Zanthier, and P. Kok, “Precision estimation of source dimensions from higher-order intensity correlations,” Phys. Rev. A 92, 043831 (2015).
[Crossref]

S. Oppel, T. Büttner, P. Kok, and J. von Zanthier, “Superresolving multiphoton interferences with independent light sources,” Phys. Rev. Lett. 109, 233603 (2012).
[Crossref]

Wang, W.

Wen, J.

White, A. G.

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).
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Wilk, T.

T. Legero, T. Wilk, M. Hennrich, G. Rempe, and A. Kuhn, “Quantum Beat of Two Single Photons,” Phys. Rev. Lett. 93, 070503 (2004).
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L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
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Zhang, H.

V. Tamma, H. Zhang, X. He, A. Garuccio, W. P. Schleich, and Y. H. Shih, “Factoring numbers with a single interferogram,” Phys. Rev. A 83, 020304 (2011).
[Crossref]

V. Tamma, H. Zhang, X. He, A. Garuccio, and Y. H. Shih, “New factorization algorithm based on a continuous representation of truncated gauss sums,” J. Mod. Opt. 56(18), 2125–2132 (2009).
[Crossref]

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K. H. Luo, B. Q. Huang, W. M. Zheng, and L. A. Wu, “Nonlocal imaging by conditional averaging of random reference measurements,” Chin. Phys. Lett. 29(7), 074216 (2012).
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Appl. Phys. Lett. (1)

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EPL (2)

T. Peng and Y. H. Shih, “Bell correlation of thermal fields in photon-number fluctuations,” EPL 112(6), 60006 (2015).
[Crossref]

G. Scarcelli, A. Valencia, and Y. H. Shih, “Two-photon interference with thermal light,” EPL 68(5), 618–624 (2004).
[Crossref]

Found. Phys. (1)

V. Tamma, C. O. Alley, W. P. Schleich, and Y. H. Shih, “Prime number decomposition, the hyperbolic function and multi-path Michelson interferometers,” Found. Phys. 42(1), 111–121 (2012).
[Crossref]

Intern. J. Quantum Inf. (1)

V. Tamma, “Sampling of bosonic qubits,” Intern. J. Quantum Inf. 12, 1560017 (2014).
[Crossref]

J. Mod. Opt. (3)

V. Tamma and S. Laibacher, “Boson sampling with non-identical single photons,” J. Mod. Opt. 63(1), 41–45 (2016).
[Crossref]

V. Tamma, H. Zhang, X. He, A. Garuccio, and Y. H. Shih, “New factorization algorithm based on a continuous representation of truncated gauss sums,” J. Mod. Opt. 56(18), 2125–2132 (2009).
[Crossref]

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, and L. A. Wu, “High-visibility intensity interference and ghost imaging with pseudo-thermal light,” J. Mod. Opt. 56(2–3), 422–431 (2009).
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Nature (4)

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature 512, 409–412 (2014).
[Crossref] [PubMed]

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[Crossref]

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

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]

Nature Photonics (1)

K. H. Kagalwala, G. di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photonics 7(1), 72–78 (2013).
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New J. Phys. (2)

S. Wölk, W. Merkel, W. P. Schleich, I. S. Averbukh, and B. Girard, “Factorization of numbers with Gauss sums: I. Mathematical background,” New J. Phys. 13, 103007 (2011).
[Crossref]

V. Tamma and J. Seiler, “Multipath correlation interference and controlled-not gate simulation with a thermal source,” New J. Phys. 18, 032002 (2016).
[Crossref]

Opt. Express (1)

Phys. Rev. A (13)

V. Tamma and S. Laibacher, “Multiboson correlation interferometry with multimode thermal sources,” Phys. Rev. A 90, 063836 (2014).
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H. Kim, O. Kwon, W. Kim, and T. Kim, “Spatial two-photon interference in a Hong-Ou-Mandel interferometer,” Phys. Rev. A 73, 023820 (2006).
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V. Tamma, H. Zhang, X. He, A. Garuccio, W. P. Schleich, and Y. H. Shih, “Factoring numbers with a single interferogram,” Phys. Rev. A 83, 020304 (2011).
[Crossref]

H. Chen, T. Peng, and Y. H. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A 88, 023808 (2013).
[Crossref]

M. E. Pearce, T. Mehringer, J. von Zanthier, and P. Kok, “Precision estimation of source dimensions from higher-order intensity correlations,” Phys. Rev. A 92, 043831 (2015).
[Crossref]

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

Phys. Rev. Lett. (13)

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical description of statistical light beams,” Phys. Rev. Lett. 10, 277 (1963).
[Crossref]

S. Oppel, T. Büttner, P. Kok, and J. von Zanthier, “Superresolving multiphoton interferences with independent light sources,” Phys. Rev. Lett. 109, 233603 (2012).
[Crossref]

K. F. Lee and J. E. Thomas, “Experimental simulation of two-particle quantum entanglement using classical fields,” Phys. Rev. Lett. 88, 097902 (2002).
[Crossref] [PubMed]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
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G. Scarcelli, V. Berardi, and Y. H. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations,” Phys. Rev. Lett. 96, 063602 (2006).
[Crossref] [PubMed]

T. Legero, T. Wilk, M. Hennrich, G. Rempe, and A. Kuhn, “Quantum Beat of Two Single Photons,” Phys. Rev. Lett. 93, 070503 (2004).
[Crossref] [PubMed]

S. Laibacher and V. Tamma, “From the physics to the computational complexity of multiboson correlation interference,” Phys. Rev. Lett. 115, 243605 (2015).
[Crossref] [PubMed]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

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

V. Tamma and S. Laibacher, “Multiboson correlation interferometry with arbitrary single-photon pure states,” Phys. Rev. Lett. 114, 243601 (2015).
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Quantum Inf. Process. (1)

V. Tamma and S. Laibacher, “Multi-boson correlation sampling,” Quantum Inf. Process. 15(3), 1241–1262 (2016).
[Crossref]

Quantum Inform. Process. (2)

V. Tamma, “Analogue algorithm for parallel factorization of an exponential number of large integers: II optical implementation,” Quantum Inform. Process. 15(12), 5243–5257 (2015).
[Crossref]

V. Tamma, “Analogue algorithm for parallel factorization of an exponential number of large integers: I theoretical description,” Quantum Inform. Process. 15(12), 5259–5280 (2015).
[Crossref]

Sci. Rep. (2)

T. Peng, V. Tamma, and Y. H. Shih, “Experimental controlled-not gate simulation with thermal light,” Sci. Rep. 6, 30152 (2016).
[Crossref] [PubMed]

J. Sprigg, T. Peng, and Y. H. Shih, “Super-resolution imaging using the spatial-frequency filtered intensity fluctuation correlation,” Sci. Rep. 6, 38077 (2016).
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Science (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
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Other (7)

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

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C. O. Alley and Y. H. Shih, Proceedings of the Second International Symposium on Foundations of Quantum Mechanics in the Light of New Technology (Tokyo, 1986), pp 47–52;

R. J. Glauber, Quantum Theory of Optical Coherence: Selected Papers and Lectures (John Wiley and Sons, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
[Crossref]

M. D’Angelo, A. Mazzilli, F. V. Pepe, A. Garuccio, and V. Tamma, “Characterization of two distant double-slit by chaotic light second-order interference,” arxiv: 1609.03416 (2016).

Y. H. Shih, An Introduction to Quantum Optics (CRC Press Taylor and Francis Group, 2011).

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Figures (3)

Fig. 1
Fig. 1 Optical interferometer for sensing two remote double-pinhole masks through the observation of spatial second-order interference between indistinguishable pairs of disjoint optical paths. Light emitted by a single 1 dimensional chaotic source, after being split by a balanced non-polarizing beam splitter, propagates through two double-pinhole masks placed at the same distance z from the source and reaches two point-like detectors, DC and DT, placed at distance f from the masks. A correlation measurement between the fluctuations of the number of photons at the detectors DC and DT is performed.
Fig. 2
Fig. 2 Simulation of the measurement of the stretching/shrinking dCdT of one mask with respect to the other in the setup of Fig. 1 with z = 500mm and f = 100mm. The source is assumed to have a constant profile, with size a = 2mm, and wavelength λ = 632nm, so that the coherence length is lcoh = λz/a = 0.158mm. When the two pinholes in each mask are placed symmetrically with respect to the optical axis (sC = sT = 0), the observable effect of small variations in dCdT is enhanced when the transverse position xC = xT of the two detectors is increased, as demonstrated by the dashed (yellow) curve as compared to the dash-dot (blue) one. A further enhancement is obtained by displacing equally both masks with respect to the optical axis in the opposite direction of the detectors, as demonstrated by the continuous (green) curve.
Fig. 3
Fig. 3 Interferometer for the simulation of controlled-Uϕ gates, with Uϕ defined in Eq. (16). In the first part of the interferometer, the initial polarization state of the light is prepared. The second part, from the ports C and T to the ports C and T, respectively, performs a polarization-dependent transformation. Correlation measurements in the fluctuations of the number of photons are performed at the interferometer output. R ϕ C and R ϕ T are two half-wave plates that rotate the polarization of the angles ϕC and ϕT, respectively; F is a half-wave plate implementing a flip from the horizontal (H) polarization to the vertical (V) polarization and vice versa; H, V, θC and θT represent the polarization directions of the corresponding polarizers.

Tables (2)

Tables Icon

Table 1 Summary of the conditions for monitoring the transverse spatial structure and position of two remote double-pinhole masks by performing the correlation measurement of Eq. (14) in the setup in Fig. 1. In each of the five experimental scenarios one variable parameter is monitored, and the other parameters are fixed in order to “magnify” the effect of small variations of the monitored parameter; the corresponding “magnification” factors are reported in the third column of the table.

Tables Icon

Table 2 Summary of the experimental conditions for characterizing two remote pinhole masks by measuring in the setup in Fig. 1 the period of the second order interference pattern given by Eq. (14).

Equations (47)

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

G ( 2 ) ( x p , x q ) n ( x p ) n ( x q ) = n ( x p ) n ( x q ) + Δ n ( x p ) Δ n ( x q ) ,
ρ ^ H = [ k d 2 α k , H ] P ( { α k , H } ) k | α k , H S α k , H | ,
P ( { α k , H } ) = k 1 π n k exp ( | α k , H | 2 n k ) ,
G ( 2 ) ( x p , x q ) = G ( 1 ) ( x p ) G ( 1 ) ( x q ) + | G ( 1 ) ( x p , x q ) | 2 ,
| x 1 C x 1 T | l c o h | x 2 C x 2 T | l c o h ;
| x 1 C x 2 T | l c o h | x 1 T x 2 C | l c o h .
Δ n ( x p ) Δ n ( x q ) 0 ( p , q ) = ( 1 C , 1 T ) , ( 2 C , 2 T ) .
Δ n ( x C ) Δ n ( x T ) | G ( 1 ) ( x C , x T ) | 2 .
G ( 1 ) ( x C , x T ) = T r [ ρ ^ H E ^ C ( ) ( x C ) E ^ T ( + ) ( x T ) ]
E ^ d ( + ) ( x d ) = K d κ g { κ ; S , x d } a ^ S ( κ ) ,
Δ n ( x C ) Δ n ( x T ) | G 1 C ( 1 ) , 1 T ( x C , x T ) + G 2 C ( 1 ) , 2 T ( x C , x T ) | 2 ,
G p , q ( 1 ) ( x C , x T ) B P * ( x C ) B q ( x T ) F T { | A ( x S ) | 2 } [ ( x p x q ) / ( λ z ) ] ,
G 1 C , 1 T ( 1 ) ( x C , x T ) B 1 C * ( x C ) B 1 T ( x T ) , G 2 C , 2 T ( 1 ) ( x C , x T ) B 2 C * ( x C ) B 2 T ( x T ) G 1 C , 2 T ( 1 ) ( x C , x T ) = G 2 C , 1 T ( 1 ) ( x C , x T ) = 0
Δ n ( x C ) Δ n ( x T ) | 1 + e i ϕ ( s C , d C , s T , d T , x C , x T ) | 2 ,
ϕ ( s C , d C , s T , d T , x C , x T ) = 2 π λ ( s T d T s C d C h x T d T x C d C f ) ,
U ϕ : = ( 0 e i ϕ e i ϕ 0 ) .
| ϕ C C : = cos ϕ C | H C + sin ϕ C | V C ,
| ϕ T T : = cos ϕ T | H T + sin ϕ T | V T ,
| ψ = cos ϕ C | H C | ϕ T T + e i ϕ sin ϕ C | V C | ϕ T ( F ) T ,
| ϕ T ( F ) T : = sin ϕ T | H T + cos ϕ T | V T .
P U ϕ : = | θ C , θ T | ψ | 2 = | cos ϕ C cos θ C cos ( ϕ T θ T ) + e i ϕ sin ϕ C sin θ C sin ( ϕ T + θ   T ) | 2 .
P CNOT : = | θ C , θ T | ψ | 2 = | cos ϕ C cos θ C cos ( ϕ T θ T ) + sin ϕ C sin θ C sin ( ϕ T + θ T ) | 2 .
Δ n ( x C , θ C ) Δ n ( x T , θ T ) | G 1 C , 1 T ( 1 ) ( x C , θ C , x T , θ T ) + G 2 C , 2 T ( 1 ) ( x C , θ C , x T , θ T ) | 2 P U ϕ ,
| ϕ ( s C , d C , s T , d T , x C , x T ) | 1 ,
Δ n ( x C , θ C ) Δ n ( x T , θ T ) P C N O T ,
g { κ ; S , x d } = 1 2 e i φ ( d ) d x S d x M A ( x S ) M ( x M ) e i κ x S { i ω 2 π c e i ω z / c z G ( | x S x M | ) [ ω / ( c z ) ] } × { i ω 2 π c e i ω f / c f G ( | x M x d | ) [ ω / ( c f ) ] } ,
M ( x M ) : = x p δ ( x M x P )
G ( | α | ) [ β ] : = e i β 2 | α | 2
G ( | α + α | ) [ β ] = G ( | α | ) [ β ] G ( | α | ) [ β ] e i β α α
g { κ ; S , x d } = p = 1 d , 2 d B j ( x d ) d x S A ( x S ) G ( | x S | ) [ ω / ( c z ) ] e i [ κ ω x p / ( z c ) ] x S ,
B p ( x d ) : = 1 2 ( ω 2 π c ) 2 e i [ φ ( d ) + ω ( z + f ) / c ] 2 f G ( | x d | ) [ ω / ( c f ) ] G ( | x p | ) [ ω / ( c h ) ] e i ω x d x p / ( f c ) .
g { κ ; S , x d } = p = 1 d , 2 d g p { κ ; S , x d } ,
g p { κ ; S , x d } : = B p ( x d ) d x S A ( x S ) G ( | x S | ) [ ω / ( c z ) ] e i [ κ ω x p / ( z c ) ] x S ,
G ( 1 ) ( x C , x T ) = p = 1 C , 2 C q = 1 T , 2 T | K | 2 T r [ ρ ^ H d κ d κ x p * { κ ; S , x C } g q { κ ; S , x T } a ^ S ( κ ) a ^ S ( κ ) ] .
G ( 1 ) ( x C , x T ) = p = 1 C , 2 C q = 1 T , 2 T G p , q ( 1 ) ( x C , x T ) .
G p , q ( 1 ) ( x C , x T ) : = | K | 2 T r [ ρ ^ H d κ d κ g p * { κ ; S , x C } g q { κ ; S , x T } a ^ S ( κ ) a ^ S ( κ ) ] ,
T r [ ρ ^ a ( κ ) a ( κ ) ] = n κ δ ( κ κ ) ,
G p , q ( 1 ) ( x C , x T ) = K B p * ( x C ) B q ( x T ) F T { | A ( x S ) | 2 } [ ω ( x p x q ) / ( 2 π c z ) ] ,
G ( 1 ) ( x C , x T ) = G 1 C , 1 T ( 1 ) ( x C , x T ) + G 2 C , 2 T ( 1 ) ( x C , x T )
Δ n ( x C ) Δ n ( x T ) = | K F T { | A ( x S ) | 2 } ( 0 ) [ B 1 C * ( x C ) B 1 T ( x T ) + B 2 C * ( x C ) B 2 T ( x T ) ] | 2 .
Δ n ( x C ) Δ n ( x T ) = K | e i ω / ( 2 c h ) ( x 1 C 2 x 1 T 2 ) e i ω / ( c f ) ( x C x 1 C x T x 1 T ) + e i ω / ( 2 c h ) ( x 2 C 2 x 2 T 2 ) e i ω / ( c f ) ( x C x 2 C x T x 2 T ) | 2 ,
Δ n ( x C , θ C ) Δ n ( x T , θ T ) = | G ( 1 ) ( x C , θ C ; x T , θ T ) | 2
G ( 1 ) ( x C , θ C ; x T , θ T ) = T r [ ρ ^ H ^ C , S ( ) ( x C ) ^ T , S ( + ) ( x T ) ] = K d κ L C * ( κ ) L T ( κ ) ,
^ d , S ( + ) ( x d ) : = K d κ e i ω t L d ( κ ) a ^ S ( H ) ( κ ) ,
L C ( κ ) : = 1 2 [ g 1 C { κ ; S , x C } cos θ C cos ϕ C + g 2 C { κ ; S , x C } sin θ C sin ϕ C ] ,
L T ( κ ) : = 1 2 [ g 1 T { κ ; S , x T } cos ( θ T ϕ T ) + g 2 T { κ ; S , x T } sin ( θ T + ϕ T ) ]
G ( 1 ) ( x C , θ C ; x T , θ T ) = i 2 K d κ [ cos θ C cos ϕ C cos ( θ T ϕ T ) g 1 C * { κ ; S , x C } g 1 T { κ ; S , x T } + sin θ C sin ϕ C sin ( θ T + ϕ T ) g 2 C * { κ ; S , x C } g 2 T { κ ; S , x T } cos θ C cos ϕ C sin ( θ T + ϕ T ) g 1 C * { κ ; S , x C } g 2 T { κ ; S , x T } sin θ C sin ϕ C cos ( θ T + ϕ T ) g 2 C * { κ ; S , x C } g 1 T { κ ; S , x T } ] .

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