Abstract

Ghost imaging with thermal fermions is calculated via two-particle interference based on the superposition principle for different alternatives in Feynman’s path integral theory. It is found that ghost imaging with fully polarized thermal fermions can be simulated by ghost imaging with fully polarized thermal bosons and classical particles. Photons in pseudothermal light are employed to experimentally study fermionic ghost imaging. Ghost imaging with thermal bosons and fermions is discussed based on the point-to-point (spot) correlation between the object and image planes. The employed method offers an efficient guidance for future ghost imaging with real thermal fermions, which may also be generalized to study other second-order interference phenomena with fermions.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]

2016 (8)

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with ‘positive-negative’ light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nature Commun. 7, 12010 (2016).
[Crossref]

D. Shin, F. H. Xu, D. Venkatraman, R. Lussana, F. Villa, F. Zappa, V. K Goyal, F. N. C. Wong, and J. H. Shapiro, “Photon-efficient imaging with a single-photon camera,” Nature Commun. 7, 12046 (2016).
[Crossref]

H. Yu, R. H. Lu, S. S. Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-transform ghost imaging with hard X-rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

P. Ryczkowski, M. Barbier, Ari T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10, 167–170 (2016).
[Crossref]

H. C. Liu, “High-order correlation of chaotic bosons and fermions,” Phys. Rev. A 94, 023827 (2016).
[Crossref]

J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
[Crossref]

2015 (1)

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref] [PubMed]

2014 (4)

J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, “Quantum imaging with undetected photons,” Nature 512, 409–415 (2014).
[Crossref] [PubMed]

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, M. F. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 24268–24275 (2014).
[Crossref] [PubMed]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

2013 (4)

W. Chen and X. D. Chen, “Object authentication in computational ghost imaging with the realizations less than 5% of Nyquist limit,” Opt. Lett. 38, 546–548 (2013).
[Crossref] [PubMed]

J. B. Liu, Y. Zhou, W. T. 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, 19209–19218 (2013).
[Crossref] [PubMed]

F. Töppel and A. Aiello, “Identical classical particles: Half fermions and half bosons,” Phys. Rev. A 88, 012130 (2013).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

2012 (3)

2010 (1)

J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynman’s path-integral theory,” Phys. Rev. A 82, 013822 (2010).
[Crossref]

2009 (3)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131119 (2009).
[Crossref]

S. Gan, D. Z. Cao, and K. G. Wang, “Dark quantum imaging with fermions,” Phys. Rev. A 80, 043809 (2009).
[Crossref]

L. G. Wang, S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Hanbury Brown-Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79, 033835 (2009).
[Crossref]

2008 (1)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
[Crossref]

2007 (1)

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[Crossref] [PubMed]

2006 (2)

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

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

2005 (2)

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]

Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[Crossref]

2004 (2)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[Crossref] [PubMed]

J. Chen and S. S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
[Crossref]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

2001 (1)

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[Crossref] [PubMed]

1999 (2)

M. Henny, S. Oberholzer, C. Strunk, T. Heinze, K. Ensslin, M. Holland, and C. Schonenberger, “The fermionic Hanbury Brown and Twiss experiment,” Science 284, 296–298 (1999).
[Crossref] [PubMed]

W. D. Oliver, J. Kim, R. C. Liu, and Y. Yamamoto, “Hanbury Brown and Twiss type experiment with electrons,” Science 284, 299–301 (1999).
[Crossref] [PubMed]

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, 3429–3432(R) (1995).
[Crossref]

1991 (1)

X. Y. Zou, L. J. Wang, and L. Mandel, “Induced coherence and indistinguishability in optical interference,” Phys. Rev. Lett. 67, 318–321 (1991).
[Crossref] [PubMed]

1988 (1)

D. N. Klyshko, “Effect of focusing on photon correlation in parametric light scattering,” Zh. Eksp. Teor. Fiz. 94, 82–90 (1988).

1964 (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

1963 (3)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[Crossref]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical lgith beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[Crossref]

1961 (1)

U. Fano, “Quantum theory of interference effect in the mixing of light from phase-independent sources,” Am. J. Phys. 29, 539–545 (1961).
[Crossref]

1958 (1)

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light II. An experimental test of the theory for partially coherent light,” Proc. R. Soc. London Ser. A 243, 291–319 (1958).
[Crossref]

1957 (1)

R. H. Brown and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. Basic theory: The correlation between photons in coherent beams of radiation,” Proc. R. Soc. London Ser. A 242, 300–324 (1957).
[Crossref]

1956 (2)

R. Hanbury Brown and R. Q. Twiss, “Corrrelation between photons in two coherent beams of light,” Nature 177, 27–28 (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.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[Crossref] [PubMed]

Aiello, A.

F. Töppel and A. Aiello, “Identical classical particles: Half fermions and half bosons,” Phys. Rev. A 88, 012130 (2013).
[Crossref]

Aspect, A.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[Crossref] [PubMed]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[Crossref] [PubMed]

Baldwin, K. G. H.

R. I. Khakimov, B. M. Henson, D. K. Shin, S. S. Hodgman, R. G. Dall, K. G. H. Baldwin, and A. G. Truscott, “Ghost Imaging with Atoms,” arXiv:1607.02240v1 (2016).

Barbier, M.

P. Ryczkowski, M. Barbier, Ari T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10, 167–170 (2016).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Berardi, V.

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

Boiron, D.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[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, 409–415 (2014).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, (7th ed.) (Cambridge University Press, Cambridge, 1999).
[Crossref]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Bowman, R.

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1, 285–289 (2014).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Boyd, R. W.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process, doi: (2012).
[Crossref]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
[Crossref] [PubMed]

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D. Shin, F. H. Xu, D. Venkatraman, R. Lussana, F. Villa, F. Zappa, V. K Goyal, F. N. C. Wong, and J. H. Shapiro, “Photon-efficient imaging with a single-photon camera,” Nature Commun. 7, 12046 (2016).
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R. I. Khakimov, B. M. Henson, D. K. Shin, S. S. Hodgman, R. G. Dall, K. G. H. Baldwin, and A. G. Truscott, “Ghost Imaging with Atoms,” arXiv:1607.02240v1 (2016).

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O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131119 (2009).
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W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
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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, 3429–3432(R) (1995).
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M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nature Commun. 7, 12010 (2016).
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W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with ‘positive-negative’ light modulation,” Opt. Commun. 371, 105–111 (2016).
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H. Yu, R. H. Lu, S. S. Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-transform ghost imaging with hard X-rays,” Phys. Rev. Lett. 117, 113901 (2016).
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H. Yu, R. H. Lu, S. S. Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-transform ghost imaging with hard X-rays,” Phys. Rev. Lett. 117, 113901 (2016).
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Xu, F. H.

D. Shin, F. H. Xu, D. Venkatraman, R. Lussana, F. Villa, F. Zappa, V. K Goyal, F. N. C. Wong, and J. H. Shapiro, “Photon-efficient imaging with a single-photon camera,” Nature Commun. 7, 12046 (2016).
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C. Q. Zhao, W. L. Gong, M. L. Chen, E. R. Li, H. Wang, W. D. Xu, and S. S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
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J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
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J. B. Liu, Y. Zhou, W. T. 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, 19209–19218 (2013).
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W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with ‘positive-negative’ light modulation,” Opt. Commun. 371, 105–111 (2016).
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X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, M. F. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 24268–24275 (2014).
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H. Yu, R. H. Lu, S. S. Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-transform ghost imaging with hard X-rays,” Phys. Rev. Lett. 117, 113901 (2016).
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W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with ‘positive-negative’ light modulation,” Opt. Commun. 371, 105–111 (2016).
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X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, M. F. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 24268–24275 (2014).
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D. Shin, F. H. Xu, D. Venkatraman, R. Lussana, F. Villa, F. Zappa, V. K Goyal, F. N. C. Wong, and J. H. Shapiro, “Photon-efficient imaging with a single-photon camera,” Nature Commun. 7, 12046 (2016).
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Zhai, G. J.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with ‘positive-negative’ light modulation,” Opt. Commun. 371, 105–111 (2016).
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X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, M. F. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 24268–24275 (2014).
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J. B. Liu and G. Q. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynman’s path-integral theory,” Phys. Rev. A 82, 013822 (2010).
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C. Q. Zhao, W. L. Gong, M. L. Chen, E. R. Li, H. Wang, W. D. Xu, and S. S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
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W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with ‘positive-negative’ light modulation,” Opt. Commun. 371, 105–111 (2016).
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J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
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J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
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J. B. Liu, Y. Zhou, W. T. 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, 19209–19218 (2013).
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H. Yu, R. H. Lu, S. S. Han, H. L. Xie, G. H. Du, T. Q. Xiao, and D. M. Zhu, “Fourier-transform ghost imaging with hard X-rays,” Phys. Rev. Lett. 117, 113901 (2016).
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L. G. Wang, S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Hanbury Brown-Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79, 033835 (2009).
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L. G. Wang, S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Hanbury Brown-Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79, 033835 (2009).
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J. B. Liu, D. Wei, H. Chen, Y. Zhou, H. B. Zheng, H. Gao, F. L. Li, and Z. Xu, “Second-order interference of two independent and tunable single-mode continuous-wave lasers,” Chin. Phys. B 25, 034203 (2016).
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J. B. Liu, Y. Zhou, F. L. Li, and Z. Xu, “The second-order interference between laser and thermal light,” Europhys. Lett. 105, 64007 (2014).
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M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nature Commun. 7, 12010 (2016).
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D. Shin, F. H. Xu, D. Venkatraman, R. Lussana, F. Villa, F. Zappa, V. K Goyal, F. N. C. Wong, and J. H. Shapiro, “Photon-efficient imaging with a single-photon camera,” Nature Commun. 7, 12046 (2016).
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S. Gan, D. Z. Cao, and K. G. Wang, “Dark quantum imaging with fermions,” Phys. Rev. A 80, 043809 (2009).
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H. C. Liu, “High-order correlation of chaotic bosons and fermions,” Phys. Rev. A 94, 023827 (2016).
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F. Töppel and A. Aiello, “Identical classical particles: Half fermions and half bosons,” Phys. Rev. A 88, 012130 (2013).
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J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
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L. G. Wang, S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Hanbury Brown-Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79, 033835 (2009).
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Phys. Rev. E (1)

Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
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W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
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B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
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J. B. Liu, H. Chen, Y. Zhou, H. B. Zheng, F. L. Li, and Z. Xu, “Second-order fermionic interference with independent photons,” arXiv: 1609.08248 [quant-ph] (2016).

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Scheme for ghost imaging with thermal fermions. S: particle source. BS: 50:50 non-polarized beam splitter. Obj: object for imaging. BD: bucket detector. D1: scannable detector. l1: the distance between S and D1. l2: the optical distance between S and object via BS.

Fig. 2
Fig. 2

Experimental setup for ghost imaging with thermal “fermionic photons”. Laser: single-mode continuous-wave laser. L: lens. RG: Rotating ground glass. The meanings of other symbols are similar as the ones in Fig. 1.

Fig. 3
Fig. 3

Calculated two-particle coincidence counts of thermal “fermionic photons” in a HBT interferometer. x and y are two transverse spatial coordinates of the scanning detector, respectively. CC is two-particle coincidence counts.

Fig. 4
Fig. 4

Detail analysis of the second-order coherence function of thermal “fermionic photons” in a HBT interferometer. (a) is the top view of the second-order coherence function in Fig. 3. (b), (c) and (d) are the one-dimension second-order coherence functions along lines 1, 2 and 3 in (a), respectively. y1y2 is the relative distance between D1 and D2 in y-axis. x1x2 is the relative distance between D1 and D2 in x-axis. xy1xy2 is the relative distance between D1 and D2 along line 3. The black squares are the calculated two-particle coincidence counts. The red lines are theoretical fittings of the data by employing Eq. (5).

Fig. 5
Fig. 5

Fermionic ghost imaging. (a) and (c) are objects for imaging. (b) and (d) are reconstructed fermionic ghost images for (a) and (c), respectively. (c) and (d) are the one-dimension functions along the red dash lines in (a) and (b), respectively. The reasons why the calculated ghost images deviating from the original images are due to the resolution of our system is about the same size of the object for imaging and the spatial anticorrelation function is not circular symmetry.

Fig. 6
Fig. 6

Imaging principle. (a) classical imaging with focus lens. (b) point-to-spot correlation of intensity in the object and image planes in (a). xI is the coordinate of image plane and I(xI) is the intensity distribution in the image plane. (c) ghost imaging with thermal particles. The two red lines and two black lines are two different alternatives for two particles emitted by thermal source to trigger a two-particle coincidence count, respectively. (d) point-to-spot correlation of the second-order coherence function for thermal bosons (peak) and fermions (dip). xIxO is transverse position difference between the coordinates in the image and object planes, respectively. g(2)(xIxO) is the normalized second-order coherence function.

Equations (12)

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G F 2 ( r 1 , t 1 ; r 2 , t 2 ) = | A a 1 A b 2 A a 2 A b 1 | 2 ,
G F ( 2 ) ( ρ 1 ) = S Obj | A a 1 A b 2 A a 2 A b 1 | 2 | T ( ρ 2 ) | 2 d ρ 2 ,
g S β = exp [ i ( k S β r S β ω S β t S β ) ] r S β ,
g F ( 2 ) ( ρ 1 ρ 2 ) = 1 somb 2 ( π d λ l | ρ 1 ρ 2 | ) ,
g F ( 2 ) ( x 1 x 2 ) = 1 sinc 2 [ π d λ l ( x 1 x 2 ) ] ,
g F 2 ( ρ 1 ) = S Obj [ 1 somb 2 ( π d λ l | ρ 1 ρ 2 | ) ] | T ( ρ 2 ) | 2 d ρ 2 .
g F ( 2 ) ( ρ 1 ) = c 1 | T ( ρ 1 ) | 2 ,
G B ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | A a 1 A b 2 + A a 2 A b 1 | 2 ,
g B ( 2 ) ( ρ 1 ) = S Obj [ 1 + somb 2 ( π d λ l | ρ 1 ρ 2 | ) ] | T ( ρ 2 ) | 2 d ρ 2 .
G C ( 2 ) ( r 1 , t 1 ; r 2 , t 2 ) = | A a 1 A b 2 | 2 + | A a 2 A b 1 | 2 .
g C ( 2 ) ( ρ 1 ) = S Obj | T ( ρ 2 ) | 2 d ρ 2 ,
g F ( 2 ) ( ρ 1 ) = 2 g C ( 2 ) ( ρ 1 ) g B ( 2 ) ( ρ 1 ) ,

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