Abstract

By using a Michelson interferometer arrangement, we have measured the phase shift (the Pancharatnam phase) experienced by a light beam whose state of polarization is made to follow, by successive unitary transformations, a closed circuit on the Poincaré sphere. We confirm that the phase shift equals half of the solid angle subtended by the closed circuit at the center of the sphere. This phase is closely related to the topological Berry phase.

© 1988 Optical Society of America

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References

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  1. M. V. Berry, J. Mod. Opt. 34, 1401 (1987); S. Rameseshan, R. Nityananda, Curr. Sci. 55, 1225 (1986).
    [Crossref]
  2. S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956) [reprinted in Collected Works of S. Pancharatnam (Oxford U. Press, Oxford, 1975)].
  3. M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [Crossref]
  4. Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
    [Crossref] [PubMed]
  5. R. Y. Chiao, Y. S. Wu, Phys. Rev. Lett. 57, 933 (1986).
    [Crossref] [PubMed]
  6. A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
    [Crossref] [PubMed]
  7. T. Bitter, D. Dubbers, Phys. Rev. Lett. 59, 251 (1987).
    [Crossref] [PubMed]
  8. R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
    [Crossref] [PubMed]
  9. R. Bhandari, J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
    [Crossref] [PubMed]
  10. After this manuscript was completed we learned of two other recent, somewhat similar experiments: R. Simon, E. C. G. Sudarshan, H. J. Kimble, Phys. Rev. Lett. (to be published); R. Y. Chiao et al., personal communication (Dept. of Physics, University of California, Berkeley, Calif. 94720).
  11. See for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.
  12. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959).
    [Crossref]

1988 (2)

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

R. Bhandari, J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[Crossref] [PubMed]

1987 (3)

T. Bitter, D. Dubbers, Phys. Rev. Lett. 59, 251 (1987).
[Crossref] [PubMed]

M. V. Berry, J. Mod. Opt. 34, 1401 (1987); S. Rameseshan, R. Nityananda, Curr. Sci. 55, 1225 (1986).
[Crossref]

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

1986 (2)

R. Y. Chiao, Y. S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

1984 (1)

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

1959 (1)

Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959).
[Crossref]

1956 (1)

S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956) [reprinted in Collected Works of S. Pancharatnam (Oxford U. Press, Oxford, 1975)].

Aharonov, Y.

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959).
[Crossref]

Anandan, J.

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

Antaramian, A.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, J. Mod. Opt. 34, 1401 (1987); S. Rameseshan, R. Nityananda, Curr. Sci. 55, 1225 (1986).
[Crossref]

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Bhandari, R.

R. Bhandari, J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[Crossref] [PubMed]

Bitter, T.

T. Bitter, D. Dubbers, Phys. Rev. Lett. 59, 251 (1987).
[Crossref] [PubMed]

Bohm, D.

Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959).
[Crossref]

Born, M.

See for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

Chiao, R. Y.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

R. Y. Chiao, Y. S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

Dubbers, D.

T. Bitter, D. Dubbers, Phys. Rev. Lett. 59, 251 (1987).
[Crossref] [PubMed]

Ganga, K. M.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Jiao, H.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Kimble, H. J.

After this manuscript was completed we learned of two other recent, somewhat similar experiments: R. Simon, E. C. G. Sudarshan, H. J. Kimble, Phys. Rev. Lett. (to be published); R. Y. Chiao et al., personal communication (Dept. of Physics, University of California, Berkeley, Calif. 94720).

Nathel, H.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Pancharatnam, S.

S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956) [reprinted in Collected Works of S. Pancharatnam (Oxford U. Press, Oxford, 1975)].

Samuel, J.

R. Bhandari, J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[Crossref] [PubMed]

Simon, R.

After this manuscript was completed we learned of two other recent, somewhat similar experiments: R. Simon, E. C. G. Sudarshan, H. J. Kimble, Phys. Rev. Lett. (to be published); R. Y. Chiao et al., personal communication (Dept. of Physics, University of California, Berkeley, Calif. 94720).

Sudarshan, E. C. G.

After this manuscript was completed we learned of two other recent, somewhat similar experiments: R. Simon, E. C. G. Sudarshan, H. J. Kimble, Phys. Rev. Lett. (to be published); R. Y. Chiao et al., personal communication (Dept. of Physics, University of California, Berkeley, Calif. 94720).

Tomita, A.

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

Wilkinson, S. R.

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

Wolf, E.

See for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

Wu, Y. S.

R. Y. Chiao, Y. S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

J. Mod. Opt. (1)

M. V. Berry, J. Mod. Opt. 34, 1401 (1987); S. Rameseshan, R. Nityananda, Curr. Sci. 55, 1225 (1986).
[Crossref]

Phys. Rev. (1)

Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959).
[Crossref]

Phys. Rev. Lett. (6)

Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

R. Y. Chiao, Y. S. Wu, Phys. Rev. Lett. 57, 933 (1986).
[Crossref] [PubMed]

A. Tomita, R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[Crossref] [PubMed]

T. Bitter, D. Dubbers, Phys. Rev. Lett. 59, 251 (1987).
[Crossref] [PubMed]

R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, H. Nathel, Phys. Rev. Lett. 60, 1214 (1988).
[Crossref] [PubMed]

R. Bhandari, J. Samuel, Phys. Rev. Lett. 60, 1211 (1988).
[Crossref] [PubMed]

Proc. Indian Acad. Sci. Sect. A (1)

S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44, 247 (1956) [reprinted in Collected Works of S. Pancharatnam (Oxford U. Press, Oxford, 1975)].

Proc. R. Soc. London Ser. A (1)

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[Crossref]

Other (2)

After this manuscript was completed we learned of two other recent, somewhat similar experiments: R. Simon, E. C. G. Sudarshan, H. J. Kimble, Phys. Rev. Lett. (to be published); R. Y. Chiao et al., personal communication (Dept. of Physics, University of California, Berkeley, Calif. 94720).

See for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

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Figures (4)

Fig. 1
Fig. 1

Outline of the experimental setup.

Fig. 2
Fig. 2

Outline of the closed path followed by the polarization state of the light on the Poincaré sphere.

Fig. 3
Fig. 3

Measured values of the light intensity I in arbitrary units for various rotation angles β of the quarter-wave plate QP2. The solid curve is described by Eq. (2).

Fig. 4
Fig. 4

Measured values of the phase shift ϕ as a function of the rotation angle β of the quarter-wave plate QP2. The straight line corresponds to ϕ = 2β.

Equations (3)

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J = 1 2 [ 1 + cos θ sin θ e i ϕ sin θ e - i ϕ 1 - cos θ ] .
I ( β ) = 0.62 [ 1 + 0.97 cos ( 2 β + 27.3 ° ) ] ,
cos ( ϕ ) = ( I - 0.62 ) / ( 0.62 × 0.97 ) .

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