Abstract

We have measured the phase structure of a glass wedge with single photons and biphotons in a Mach–Zehnder interferometer using parametric downconverted light from a Hong–Ou–Mandel particle interferometer as the source. By scanning the wedge through the focus of a microscope objective we find a doubling of the period of the interference pattern in the coincidence counts for biphotons compared to the single-photon experiment. We compare our measurement setup with classical ones and discuss some of the problems of superresolution in quantum lithography.

© 2007 Optical Society of America

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References

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  1. Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).
  2. E. Mohler, J. Brendel, R. Lange, and W. Martienssen, Europhys. Lett. 8, 511 (1989).
    [CrossRef]
  3. J. Brendel, Reihe Physik 28, Frankfurt(Main) (1994).
  4. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
    [CrossRef] [PubMed]
  5. E. J. S. Fonseca, C. H. Monken, and S. Pádua, Phys. Rev. Lett. 82, 2868 (1999).
    [CrossRef]
  6. E. J. Galvez, C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, Am. J. Phys. 73, 127 (2005).
    [CrossRef]
  7. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
    [CrossRef] [PubMed]
  8. E. M. Nagasako, S. J. Bentley, R. W. Boid, and G. S. Agarwal, Phys. Rev. A 64, 043802 (2001).
    [CrossRef]
  9. K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
    [CrossRef] [PubMed]
  10. P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
    [CrossRef] [PubMed]
  11. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
    [CrossRef] [PubMed]
  12. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
    [CrossRef] [PubMed]
  13. R. Hanbury Brown, and R. Q. Twiss, Nature 177, 27 (1956).
    [CrossRef]
  14. K. J. Siebert, H. Schmitzer, and W. Dultz, Phys. Lett. A 300, 341 (2002).
    [CrossRef]
  15. D. F. V. James and P. G. Kwiat, Phys. Rev. Lett. 89, 183601 (2002).
    [CrossRef] [PubMed]
  16. M. A. Albota and F. N. C. Wong, Opt. Lett. 29, 1449 (2004).
    [CrossRef] [PubMed]
  17. C. Williams, J. Dowling, and G. della Rossa, "Lithography using quantum entangled particles," U.S. patent 6,630,290 (October 7, 2003).

2005 (1)

E. J. Galvez, C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, Am. J. Phys. 73, 127 (2005).
[CrossRef]

2004 (3)

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

M. A. Albota and F. N. C. Wong, Opt. Lett. 29, 1449 (2004).
[CrossRef] [PubMed]

2002 (3)

K. J. Siebert, H. Schmitzer, and W. Dultz, Phys. Lett. A 300, 341 (2002).
[CrossRef]

D. F. V. James and P. G. Kwiat, Phys. Rev. Lett. 89, 183601 (2002).
[CrossRef] [PubMed]

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

2001 (1)

E. M. Nagasako, S. J. Bentley, R. W. Boid, and G. S. Agarwal, Phys. Rev. A 64, 043802 (2001).
[CrossRef]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

1999 (1)

E. J. S. Fonseca, C. H. Monken, and S. Pádua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

1995 (1)

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

1989 (1)

E. Mohler, J. Brendel, R. Lange, and W. Martienssen, Europhys. Lett. 8, 511 (1989).
[CrossRef]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

1956 (1)

R. Hanbury Brown, and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

1802 (1)

Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).

Am. J. Phys. (1)

E. J. Galvez, C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, Am. J. Phys. 73, 127 (2005).
[CrossRef]

Europhys. Lett. (1)

E. Mohler, J. Brendel, R. Lange, and W. Martienssen, Europhys. Lett. 8, 511 (1989).
[CrossRef]

Nature (3)

R. Hanbury Brown, and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, Nature 429, 158 (2004).
[CrossRef] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Opt. Lett. (1)

Philos. Trans. R. Soc. London (1)

Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).

Phys. Lett. A (1)

K. J. Siebert, H. Schmitzer, and W. Dultz, Phys. Lett. A 300, 341 (2002).
[CrossRef]

Phys. Rev. A (1)

E. M. Nagasako, S. J. Bentley, R. W. Boid, and G. S. Agarwal, Phys. Rev. A 64, 043802 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

K. Edamatsu, R. Shimizu, and T. Itoh, Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

E. J. S. Fonseca, C. H. Monken, and S. Pádua, Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

D. F. V. James and P. G. Kwiat, Phys. Rev. Lett. 89, 183601 (2002).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

Other (2)

C. Williams, J. Dowling, and G. della Rossa, "Lithography using quantum entangled particles," U.S. patent 6,630,290 (October 7, 2003).

J. Brendel, Reihe Physik 28, Frankfurt(Main) (1994).

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Figures (3)

Fig. 1
Fig. 1

Biphoton interferometer with a Hong–Ou–Mandel beam splitter BS 1 in the entrance. The wedge W is shifted in the focus of lens L and changes the phase in the upper interferometer arm. A variable optical path and dispersion compensation is used in the lower arm. PC are polarization controllers in the fiber lines.

Fig. 2
Fig. 2

Single-photon and biphoton interference pattern. The period of the fringes is halved from single photons to biphotons. The line is a least-square fit to the data points. The beat period for single photons is 121 μ m , and for the biphotons it is 56 μ m .

Fig. 3
Fig. 3

Phase dependency of the single-photon counts (below) and of the coincidence counts of the biphoton experiment (above) on the shift Δ of the wedge. The line is a linear fit to the data points.

Equations (4)

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ψ 2 = 1 2 ( 2 0 exp ( i 2 φ ) + 0 2 )
I C exp ( i 2 φ ) 1 2 = 4 sin 2 φ .
ψ 1 = 1 2 ( 1 0 exp ( i φ ) + 0 1 ) ,
I exp ( i φ ) + 1 2 = 4 sin 2 φ 2 .

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