Abstract

The theory of ghost imaging is examined by taking into account the quantum state of the light source explicitly. It is proved that ghost images can be obtained by any light source that is non-Poissonian. It is also shown that ghost images with unity visibility can be achieved with either quantum or classical correlation.

© 2012 Optical Society of America

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References

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  1. For a comprehensive review, see J. H. Shapiro and R. W. Boyd, Quantum Inf. Process, doi:10.1007/s11128-011-0356-5 (to be published).
    [CrossRef]
  2. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef]
  3. R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef]
  4. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef]
  5. B. I. Erkmen, and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
    [CrossRef]
  6. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
    [CrossRef]
  7. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  8. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 3343 (2009).
    [CrossRef]
  9. C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.
  10. S. Karmakar, Y.-H. Zhai, H. Chen, and Y. Shih, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QFD3.
  11. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
    [CrossRef]

2009

2008

B. I. Erkmen, and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

2005

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

2004

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

2002

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

1995

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

1989

R. F. Werner, Phys. Rev. A 40, 4277 (1989).
[CrossRef]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
[CrossRef]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

Boyd, R. W.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, Opt. Lett. 34, 3343 (2009).
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

For a comprehensive review, see J. H. Shapiro and R. W. Boyd, Quantum Inf. Process, doi:10.1007/s11128-011-0356-5 (to be published).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Chan, K. W. C.

Chen, B.

C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.

Chen, H.

S. Karmakar, Y.-H. Zhai, H. Chen, and Y. Shih, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QFD3.

Chen, Q.

C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Erkmen, B. I.

B. I. Erkmen, and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

Gan, H. Y.

C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.

Gatti, A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
[CrossRef]

Karmakar, S.

S. Karmakar, Y.-H. Zhai, H. Chen, and Y. Shih, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QFD3.

Li, H.

C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.

Lugiato, L. A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
[CrossRef]

O’Sullivan, M. N.

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Shapiro, J. H.

B. I. Erkmen, and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

For a comprehensive review, see J. H. Shapiro and R. W. Boyd, Quantum Inf. Process, doi:10.1007/s11128-011-0356-5 (to be published).
[CrossRef]

Sheng, C.-X.

C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.

Shih, Y.

S. Karmakar, Y.-H. Zhai, H. Chen, and Y. Shih, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QFD3.

Shih, Y. H.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Werner, R. F.

R. F. Werner, Phys. Rev. A 40, 4277 (1989).
[CrossRef]

Zhai, Y.-H.

S. Karmakar, Y.-H. Zhai, H. Chen, and Y. Shih, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QFD3.

Opt. Lett.

Phys. Rev. A

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef]

B. I. Erkmen, and J. H. Shapiro, Phys. Rev. A 77, 043809 (2008).
[CrossRef]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

R. F. Werner, Phys. Rev. A 40, 4277 (1989).
[CrossRef]

Phys. Rev. Lett.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. Lett. 93, 093602 (2004);
[CrossRef]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. 89, 113601 (2002).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Quantum Inf. Process

For a comprehensive review, see J. H. Shapiro and R. W. Boyd, Quantum Inf. Process, doi:10.1007/s11128-011-0356-5 (to be published).
[CrossRef]

Other

C.-X. Sheng, Q. Chen, H. Y. Gan, B. Chen, and H. Li, “Photon counting ghost imaging using non-Poisson light source,” Optik, submitted for publication.

S. Karmakar, Y.-H. Zhai, H. Chen, and Y. Shih, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QFD3.

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Figures (1)

Fig. 1.
Fig. 1.

Generic setup of ghost imaging.

Equations (19)

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G(x)=1Ms=1MNo(s)nr(s)(x),
No(s)=xO(x)[n(s)(x)nr(s)(x)]
G(x)=xO(x)[n(x)nr(x)nr(x)nr(x)]=xO(x){[nnrnrnr]+δϵ(xx)×[nnrnnrnr2+nr2]},
P(n,nr)=P(n)n!(nnr)!nr!pnr(1p)nnr,
G(x)=p(1p)n2[T+Δ2nnn2O(x)],
VG(xin)G(xout)G(xin)+G(xout)=Δ2nn2Tn2+Δ2nn,
G^(x)=1Ms=1MN^o(s)n^r(s)(x),
a^o(x)=pa^(x)+i1pv^(x),
a^r(x)=i1pa^(x)+pv^(x),
G^(x)=p(1p)xO(x)a^(x)a^(x)a^(x)a^(x)=p(1p)xO(x)[n^(x)n^(x)n^(x)δ(xx)],
|ψ=n1,n2,=0Cn1,n2,{[a(x1)]n1n1![a(x2)]n2n2!}|vac,
|ψ(2)=xC(x,x)|2x+xxC(x,x)|1x,1xdxdxC(x,x)|1x,1x,
ρ^=kwk|ψkψk|.
ρ^=kwkiρ^k(xi),
G^(x)=p(1p)xO(x)kwk{n^k(x)n^k(x)+δ(xx)[Δ2n^k(x)n^k(x)]},
ρ^(N,cl)=1N!x[a^(x)]N|vacvac|[a^(x)]N,
|Ψ(N)=1N!x[a(x)]N|vac.
Δ2G^(x)=G^2(x)G^(x)2=116Mx,xO(x)O(x){[n^2(x)n^(x)n^(x)n^(x)n^(x)n^(x)n^(x)+n^(x)n^(x)n^(x)]+δ(xx)δ(xx)[2n^2(x)n^(x)22n^(x)]+δ(xx)[n^2(x)n^(x)+n^(x)n^(x)]2δ(xx)[2n^2(x)n^(x)n^(x)n^(x)n^(x)]}.
Δ2G^(x)=116M[2n^3T2+(2n^3+4n^2)T].

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