Abstract

We demonstrated tunable mixed classical light (TMCL) using a mixture of a laser and a pseudothermal light. The TMCL was generated by adjusting the photon number ratio of a laser and a pseudothermal light. The photon number statistics of the TMCL continuously changed from the Poisson distribution to the Bose–Einstein distribution. The g(2)(0) value of the TMCL was measured using the Hanbury Brown–Twiss method, and we could arbitrarily control the g(2)(0) value between 1.0 and 1.7. The experimental g(2)(0) value of the TMCL as a function of the photon number ratio of the two light sources was in close agreement with the calculated result.

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References

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  1. R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford University, 1983).
  2. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [CrossRef] [PubMed]
  3. G. Scarcelli, A. Valencia, and Y. H. Shih, “Experimental study of the momentum correlation of a pseudo-thermal field in the photon-counting regime,” Phys. Rev. A 70, 051802(R)(2004).
    [CrossRef]
  4. D. Zhang, Y.-H. Zhai, L.-A. Wu, and X.-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
    [CrossRef] [PubMed]
  5. M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
    [CrossRef]
  6. W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
    [CrossRef]
  7. R. J. Glauber, “Optical coherence and photon statistics,” in Quantum Optics and Electronics, Les Houches lectures delivered at the Summer School of Theoretical Physics, University of Grenoble, 1964, C.DeWitt, A.Blandin, and C.Cohen-Tannoudji, eds. (Gordon and Breach, 1965), p. 621.
  8. G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138, B1012–B1016 (1965).
    [CrossRef]
  9. F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
    [CrossRef]
  10. F. T. Arecchi, A. Berne, and P. Bulamacchi, “High-order fluctuations in a single-mode laser field,” Phys. Rev. Lett. 16, 32–35(1966).
    [CrossRef]
  11. F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
    [CrossRef]
  12. R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–32 (1956).
    [CrossRef]
  13. P. Koczyk, P. Wiewior, and C. Radzewicz, “Photon counting statistics-undergraduate experiment,” Am. J. Phys. 64, 240–245(1996).
    [CrossRef]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

2006

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

2005

2004

G. Scarcelli, A. Valencia, and Y. H. Shih, “Experimental study of the momentum correlation of a pseudo-thermal field in the photon-counting regime,” Phys. Rev. A 70, 051802(R)(2004).
[CrossRef]

1996

P. Koczyk, P. Wiewior, and C. Radzewicz, “Photon counting statistics-undergraduate experiment,” Am. J. Phys. 64, 240–245(1996).
[CrossRef]

1995

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

1966

F. T. Arecchi, A. Berne, and P. Bulamacchi, “High-order fluctuations in a single-mode laser field,” Phys. Rev. Lett. 16, 32–35(1966).
[CrossRef]

F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
[CrossRef]

1965

G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138, B1012–B1016 (1965).
[CrossRef]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
[CrossRef]

1964

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

1956

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–32 (1956).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, A. Berne, and P. Bulamacchi, “High-order fluctuations in a single-mode laser field,” Phys. Rev. Lett. 16, 32–35(1966).
[CrossRef]

F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
[CrossRef]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
[CrossRef]

Bache, M.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Berne, A.

F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
[CrossRef]

F. T. Arecchi, A. Berne, and P. Bulamacchi, “High-order fluctuations in a single-mode laser field,” Phys. Rev. Lett. 16, 32–35(1966).
[CrossRef]

Brambilla, E.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Brown, R. H.

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–32 (1956).
[CrossRef]

Bulamacchi, P.

F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
[CrossRef]

F. T. Arecchi, A. Berne, and P. Bulamacchi, “High-order fluctuations in a single-mode laser field,” Phys. Rev. Lett. 16, 32–35(1966).
[CrossRef]

Chen, X.-H.

Ferri, F.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Gatti, A.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Glauber, R. J.

R. J. Glauber, “Optical coherence and photon statistics,” in Quantum Optics and Electronics, Les Houches lectures delivered at the Summer School of Theoretical Physics, University of Grenoble, 1964, C.DeWitt, A.Blandin, and C.Cohen-Tannoudji, eds. (Gordon and Breach, 1965), p. 621.

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Koczyk, P.

P. Koczyk, P. Wiewior, and C. Radzewicz, “Photon counting statistics-undergraduate experiment,” Am. J. Phys. 64, 240–245(1996).
[CrossRef]

Lachs, G.

G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138, B1012–B1016 (1965).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford University, 1983).

Lugiato, L. A.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Magatti, D.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

Mandel, L.

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

Martienssen, W.

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

Radzewicz, C.

P. Koczyk, P. Wiewior, and C. Radzewicz, “Photon counting statistics-undergraduate experiment,” Am. J. Phys. 64, 240–245(1996).
[CrossRef]

Scarcelli, G.

G. Scarcelli, A. Valencia, and Y. H. Shih, “Experimental study of the momentum correlation of a pseudo-thermal field in the photon-counting regime,” Phys. Rev. A 70, 051802(R)(2004).
[CrossRef]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

G. Scarcelli, A. Valencia, and Y. H. Shih, “Experimental study of the momentum correlation of a pseudo-thermal field in the photon-counting regime,” Phys. Rev. A 70, 051802(R)(2004).
[CrossRef]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Sona, A.

F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
[CrossRef]

Spiller, E.

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

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Twiss, R. Q.

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–32 (1956).
[CrossRef]

Valencia, A.

G. Scarcelli, A. Valencia, and Y. H. Shih, “Experimental study of the momentum correlation of a pseudo-thermal field in the photon-counting regime,” Phys. Rev. A 70, 051802(R)(2004).
[CrossRef]

Wiewior, P.

P. Koczyk, P. Wiewior, and C. Radzewicz, “Photon counting statistics-undergraduate experiment,” Am. J. Phys. 64, 240–245(1996).
[CrossRef]

Wolf, E.

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

Wu, L.-A.

Zhai, Y.-H.

Zhang, D.

Am. J. Phys.

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

P. Koczyk, P. Wiewior, and C. Radzewicz, “Photon counting statistics-undergraduate experiment,” Am. J. Phys. 64, 240–245(1996).
[CrossRef]

IEEE J. Quantum Electron.

F. T. Arecchi, A. Berne, A. Sona, and P. Bulamacchi, “Photocount distributions and field statistics,” IEEE J. Quantum Electron. QE-2, 341–350 (1966).
[CrossRef]

Nature

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–32 (1956).
[CrossRef]

Opt. Lett.

Phys. Rev.

G. Lachs, “Theoretical aspects of mixtures of thermal and coherent radiation,” Phys. Rev. 138, B1012–B1016 (1965).
[CrossRef]

Phys. Rev. A

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73, 053802 (2006).
[CrossRef]

G. Scarcelli, A. Valencia, and Y. H. Shih, “Experimental study of the momentum correlation of a pseudo-thermal field in the photon-counting regime,” Phys. Rev. A 70, 051802(R)(2004).
[CrossRef]

Phys. Rev. Lett.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15, 912–916 (1965).
[CrossRef]

F. T. Arecchi, A. Berne, and P. Bulamacchi, “High-order fluctuations in a single-mode laser field,” Phys. Rev. Lett. 16, 32–35(1966).
[CrossRef]

Other

R. J. Glauber, “Optical coherence and photon statistics,” in Quantum Optics and Electronics, Les Houches lectures delivered at the Summer School of Theoretical Physics, University of Grenoble, 1964, C.DeWitt, A.Blandin, and C.Cohen-Tannoudji, eds. (Gordon and Breach, 1965), p. 621.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford University, 1983).

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

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for the TMCL manipulated continuously from a coherent light to a pseudothermal light (M, mirror; BS, beam splitter; ND, neutral density filter; L, lens; CL, collimation lens; FBS, fiber beam splitter; SPD, single-photo detector).

Fig. 2
Fig. 2

Photon number statistics for (a) the laser, (b) the pseudothermal light, and (c) the TMCL; (a) Poisson distribution (experiment, black squares; theory, solid curve), (b) Bose– Einstein (experiment, gray circles; theory, dashed curve), and (c) superposition distribution (experiment, open triangles; theory, dotted curve).

Fig. 3
Fig. 3

g ( 2 ) ( τ ) according to time delay τ for the laser (black squares), the pseudothermal light (gray circles), and the mixed light (open triangles).

Fig. 4
Fig. 4

Numerically calculated g ( 2 ) ( 0 ) value according to the thermal ( n th ) and the laser ( n coh ) photon numbers.

Fig. 5
Fig. 5

Experimental and theoretical results of the g ( 2 ) ( 0 ) values of the TMCL as a function of the photon number ratio of the pseudothermal light to the laser (experiment, circles; theory, dashed curve).

Equations (22)

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

P coh ( n ) = n ¯ n n ! e n ¯ ,
P th ( n ) = n ¯ n ( 1 + n ¯ ) n + 1 .
P mix ( n ) = n ¯ th n ( 1 + n ¯ th ) n + 1 e n coh 1 + n th L n ( n coh n th + n th 2 ) ,
g ( 2 ) ( 0 ) = 1 + ( Δ n ) 2 n ¯ n ¯ 2 ,
a k | α k = α k | α k ,
ρ = P ( α ) | α α | d 2 α ,
P ( n ) = n | ρ | n = P ( α ) | α | n | 2 d 2 α .
| α | n | 2 = ( | α | 2 n / n ! ) e | α | 2 .
P ( α ) = P 1 ( α ) P 2 ( α α ) d 2 α .
P coh ( α ) = δ 2 ( α β ) ,
P th ( α ) = 1 π n ¯ th exp [ | α | 2 n ¯ th ] .
P mix ( α ) = 1 π n ¯ th exp [ | α β | 2 n ¯ th ] .
P mix ( n ) = 2 exp [ | β | 2 n ¯ th + 1 ] 0 | α | 2 n exp [ ( | α | 2 + | β | 2 ) / ( n ¯ th + 1 ) χ 0 ] I 0 [ | α | | β | χ 0 n ¯ th + 1 ] | α | d | α | ,
P mix ( n ) = { ( 1 1 + n ¯ th ) [ n ¯ th 1 + n ¯ th ] n exp [ | β | 2 1 + n ¯ th ] } { F 1 1 ( n ; 1 ; | β | 2 n ¯ th 2 + n ¯ th ) } ,
L n α ( x ) = F 1 1 ( n , α + 1 , x ) ( α + 1 ) n n ! .
P mix ( n ) = { n ¯ th n ( 1 + n ¯ th ) n + 1 exp [ | β | 2 1 + n ¯ th ] } L n ( x ) ,
P mix ( n ) = n ¯ th n ( 1 + n ¯ th ) n + 1 e n ¯ coh 1 + n ¯ th L n ( s ) ,
L n ( s ) = e s n ! d n d s n ( s n e s ) = e s n ! ( n ! e s + s n d n d s n e s ) = 1 + e s n ! s n d n d s n e s .
P mix ( n ) = n ¯ th n ( 1 + n ¯ th ) n + 1 e n ¯ coh 1 + n ¯ th ( 1 + e s n ! s n d n d s n e s ) = n ¯ th n ( 1 + n ¯ th ) n + 1 e n ¯ coh 1 + n ¯ th + n ¯ th n ( 1 + n ¯ th ) n + 1 e n ¯ coh 1 + n ¯ th e s n ! s n d n d s n e s ,
P mix ( n ) = n ¯ th n ( 1 + n ¯ th ) n + 1 e n ¯ coh 1 + n ¯ th + e n ¯ coh 1 + n ¯ th 1 n ! n ¯ coh n ( 1 + n ¯ th ) 2 n + 1 .
P coh ( n ) = e n ¯ coh n ¯ coh n n ! .
P th ( n ) = n ¯ th n ( 1 + n ¯ th ) n + 1 .

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