Abstract

We demonstrate experimentally a novel technique for characterizing transverse spatial coherence by using the Wigner distribution function. The method is based on the measurement of interference between a pair of rotated and displaced replicas of the input beam with an area-integrating detector, and it provides an optimal signal-to-noise ratio in regimes when array detectors are not available. We analyze the quantum-optical picture of the presented measurement for single-photon signals and discuss possible applications in quantum information processing.

© 2003 Optical Society of America

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  1. A. Wax, C. H. Yang, V. Backman, M. Kalashnikov, R. R. Dasari, and M. S. Feld, J. Opt. Soc. Am. A 19, 737 (2002).
    [CrossRef]
  2. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
    [CrossRef] [PubMed]
  3. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
    [CrossRef] [PubMed]
  4. A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
    [CrossRef]
  5. E. P. Wigner, Phys. Rev. 40, 749 (1932).
    [CrossRef]
  6. M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
    [CrossRef]
  7. D. Dragoman, in Progress in Optics, Vol. XXXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1997).
  8. K.-H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
    [CrossRef]
  9. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, and M. G. Raymer, Opt. Lett. 20, 1181 (1995).
    [CrossRef] [PubMed]
  10. A. Wax and J. E. Thomas, Opt. Lett. 21, 1427 (1996).
    [CrossRef] [PubMed]
  11. K. F. Lee, F. Reil, S. Bali, A. Wax, and J. E. Thomas, Opt. Lett. 24, 1370 (1999).
    [CrossRef]
  12. I. Białynicki-Birula, in Progress in Optics, Vol. XXXVI, E. Wolf, ed. (Elsevier, Amsterdam, 1996).
  13. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef]
  14. S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996).
    [CrossRef] [PubMed]
  15. K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996).
    [CrossRef] [PubMed]
  16. K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
    [CrossRef]

2002 (3)

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

A. Wax, C. H. Yang, V. Backman, M. Kalashnikov, R. R. Dasari, and M. S. Feld, J. Opt. Soc. Am. A 19, 737 (2002).
[CrossRef]

2000 (2)

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
[CrossRef]

1997 (1)

D. Dragoman, in Progress in Optics, Vol. XXXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1997).

1996 (4)

I. Białynicki-Birula, in Progress in Optics, Vol. XXXVI, E. Wolf, ed. (Elsevier, Amsterdam, 1996).

S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996).
[CrossRef] [PubMed]

K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996).
[CrossRef] [PubMed]

A. Wax and J. E. Thomas, Opt. Lett. 21, 1427 (1996).
[CrossRef] [PubMed]

1995 (1)

1982 (1)

K.-H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

1978 (1)

M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
[CrossRef]

1932 (1)

E. P. Wigner, Phys. Rev. 40, 749 (1932).
[CrossRef]

Backman, V.

Bali, S.

Banaszek, K.

K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
[CrossRef]

K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Bastiaans, M. J.

M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
[CrossRef]

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Beck, M.

Beveratos, A.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Bialynicki-Birula, I.

I. Białynicki-Birula, in Progress in Optics, Vol. XXXVI, E. Wolf, ed. (Elsevier, Amsterdam, 1996).

Brenner, K.-H.

K.-H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Brouri, R.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Clarke, L.

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Dasari, R. R.

Dragoman, D.

D. Dragoman, in Progress in Optics, Vol. XXXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1997).

Feld, M. S.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Gacoin, T.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Grangier, P.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Hu, E.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Imamoglu, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Kalashnikov, M.

Kiraz, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Kurtsiefer, C.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Lee, K. F.

Lohmann, A. W.

K.-H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Mayer, A.

Mayer, S.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

McAlister, D. F.

Michler, P.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Padgett, M. J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

Petroff, P. M.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Poizat, J. P.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Raymer, M. G.

Reil, F.

Schoenfeld, W. V.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Thomas, J. E.

Villing, A.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Vogel, W.

S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996).
[CrossRef] [PubMed]

Wallentowitz, S.

S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996).
[CrossRef] [PubMed]

Wax, A.

Weinfurter, H.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

Wigner, E. P.

E. P. Wigner, Phys. Rev. 40, 749 (1932).
[CrossRef]

Wódkiewicz, K.

K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
[CrossRef]

K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996).
[CrossRef] [PubMed]

Yang, C. H.

Zarda, P.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

Zhang, L. D.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

M. J. Bastiaans, Opt. Commun. 25, 26 (1978).
[CrossRef]

K.-H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef]

Phys. Rev. (1)

E. P. Wigner, Phys. Rev. 40, 749 (1932).
[CrossRef]

Phys. Rev. A (2)

S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996).
[CrossRef] [PubMed]

K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef]

K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996).
[CrossRef] [PubMed]

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Phys. Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

Science (1)

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. D. Zhang, E. Hu, and A. Imamoğlu, Science 290, 2282 (2000).
[CrossRef] [PubMed]

Other (2)

I. Białynicki-Birula, in Progress in Optics, Vol. XXXVI, E. Wolf, ed. (Elsevier, Amsterdam, 1996).

D. Dragoman, in Progress in Optics, Vol. XXXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1997).

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Figures (2)

Fig. 1
Fig. 1

Experimental apparatus for measuring the Wigner function.

Fig. 2
Fig. 2

Surface and contour plots of Wigner distribution functions measured for (a) collimated and (b) slightly divergent single-mode beams and for (c) a laser beam reflected off a glass wedge.

Equations (3)

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

Wx,k=1π2d2ξ exp2ikξE*x-ξEx+ξ.
Wx,k= 1π2d2ξexp-ikξEx-ξ*×expikξEx+ξ.
I1,2=π2 cos φ2Wx,k,

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