Abstract

A polarized photon with well-defined orbital angular momentum that emerges from a Mach–Zehnder interferometer (MZI) is shown to seemingly circumvent wave–particle duality constraints. For certain phase differences between the MZI arms, this pattern yields both reliable which-path information and high phase sensitivity.

© 2008 Optical Society of America

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References

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  1. W. K. Wootters and W. H. Zurek, Phys. Rev. D 19, 473 (1979).
    [CrossRef]
  2. R. J. Glauber, in New Techniques and Ideas in Quantum Measurement Theory, D.M.Greenberger, ed., Vol. 480 of Annals of the New York Academy of Sciences (Blackwell, 1986), pp. 336-372.
  3. G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1995).
    [CrossRef] [PubMed]
  4. B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
    [CrossRef] [PubMed]
  5. S. Dürr, T. Nonn, and G. Rempe, Nature 395, 33 (1998).
    [CrossRef]
  6. P. D. D. Schwindt, P. G. Kwiat, and B. G. Englert, Phys. Rev. A 60, 4285 (1999).
    [CrossRef]
  7. G. J. Pryde, J. L. O'Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, Phys. Rev. Lett. 92, 190402 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  10. N. Bar-Gill and G. Kurizki, Phys. Rev. Lett. 97, 230402 (2006).
    [CrossRef]
  11. T. Nagata, R. Okamoto, J. L. O'Brien, K. Sasaki, and S. Takeuchi, Science 316, 726 (2007).
    [CrossRef] [PubMed]
  12. K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O'Brien, and A. G. White, Phys. Rev. Lett. 98, 223601 (2007).
    [CrossRef] [PubMed]
  13. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  14. Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
    [CrossRef]
  15. M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 3006 (1998).
    [CrossRef]
  16. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef] [PubMed]
  17. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
    [CrossRef]
  18. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
    [CrossRef] [PubMed]
  19. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

2007

M. Kolár, T. Opatrný, N. Bar-Gill, N. Erez, and G. Kurizki, New J. Phys. 9, 129 (2007).
[CrossRef]

T. Nagata, R. Okamoto, J. L. O'Brien, K. Sasaki, and S. Takeuchi, Science 316, 726 (2007).
[CrossRef] [PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O'Brien, and A. G. White, Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef] [PubMed]

2006

M. Kolár, T. Opatrný, N. Bar-Gill, and G. Kurizki, Int. J. Mod. Phys. B 20, 1390 (2006).
[CrossRef]

N. Bar-Gill and G. Kurizki, Phys. Rev. Lett. 97, 230402 (2006).
[CrossRef]

2004

G. J. Pryde, J. L. O'Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

2003

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[CrossRef]

2002

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

1999

P. D. D. Schwindt, P. G. Kwiat, and B. G. Englert, Phys. Rev. A 60, 4285 (1999).
[CrossRef]

1998

S. Dürr, T. Nonn, and G. Rempe, Nature 395, 33 (1998).
[CrossRef]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 3006 (1998).
[CrossRef]

1996

B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
[CrossRef] [PubMed]

1995

G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1995).
[CrossRef] [PubMed]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

1979

W. K. Wootters and W. H. Zurek, Phys. Rev. D 19, 473 (1979).
[CrossRef]

Czech. J. Phys.

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[CrossRef]

Int. J. Mod. Phys. B

M. Kolár, T. Opatrný, N. Bar-Gill, and G. Kurizki, Int. J. Mod. Phys. B 20, 1390 (2006).
[CrossRef]

Nature

S. Dürr, T. Nonn, and G. Rempe, Nature 395, 33 (1998).
[CrossRef]

New J. Phys.

M. Kolár, T. Opatrný, N. Bar-Gill, N. Erez, and G. Kurizki, New J. Phys. 9, 129 (2007).
[CrossRef]

Opt. Commun.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 3006 (1998).
[CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

P. D. D. Schwindt, P. G. Kwiat, and B. G. Englert, Phys. Rev. A 60, 4285 (1999).
[CrossRef]

G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1995).
[CrossRef] [PubMed]

Phys. Rev. D

W. K. Wootters and W. H. Zurek, Phys. Rev. D 19, 473 (1979).
[CrossRef]

Phys. Rev. Lett.

B. G. Englert, Phys. Rev. Lett. 77, 2154 (1996).
[CrossRef] [PubMed]

G. J. Pryde, J. L. O'Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef] [PubMed]

N. Bar-Gill and G. Kurizki, Phys. Rev. Lett. 97, 230402 (2006).
[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O'Brien, and A. G. White, Phys. Rev. Lett. 98, 223601 (2007).
[CrossRef] [PubMed]

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

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 81, 4828 (1998).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Science

T. Nagata, R. Okamoto, J. L. O'Brien, K. Sasaki, and S. Takeuchi, Science 316, 726 (2007).
[CrossRef] [PubMed]

Other

R. J. Glauber, in New Techniques and Ideas in Quantum Measurement Theory, D.M.Greenberger, ed., Vol. 480 of Annals of the New York Academy of Sciences (Blackwell, 1986), pp. 336-372.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

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Figures (3)

Fig. 1
Fig. 1

Example of the rotational symmetry of the Laguerre–Gaussian beam L G p l : vector plot of the transverse beam profile for p = 0 , l = 2 . The arrows represent the electric field vector at a given time and fixed propagation length for a (a) right-hand polarized photon ( s = 1 , onefold symmetry), (b) left-hand polarized photon ( s = + 1 , threefold symmetry).

Fig. 2
Fig. 2

Schematic of the proposed realization. A particular example of state (6), l x , is injected into the MZI, formed by two 50%–50% (nonpolarizing) beam splitters BS1 and BS2 and two mirrors. After passing the rotated Dove prism and wave plate (WP), the linear polarization is rotated by a different angle in each arm, depending on the interferometric phase. This allows us to infer WW information by measuring the resulting photon polarization in basis ± 45 with detectors ( + ) and ( ) after BS2.

Fig. 3
Fig. 3

Detection probability P + (solid), phase sensitivity S (dotted) and distinguishability D (dashed) as a function of α for c 1 = c 2 = 1 2 , for (a) l = 0 (S and D match each other) and (b) l = 2 [Eqs. (7, 8, 9)].

Equations (10)

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

D 2 + V 2 1 ,
ψ input = 2 1 2 ( k 1 1 + k 2 2 ) ,
( S κ 1 2 κ κ + 1 2 κ ) 2 + D 2 1 S 2 + D 2 > 1 , κ > 1 .
O α D ( α ) UP W P D U = D ( α ) [ a I + b P HW ( α ) ] .
D ( α ) P HW ( α ) [ l R ] = exp [ i 2 ( l 1 ) α ] l L ,
D ( α ) P HW ( α ) [ l L ] = exp [ i 2 ( l + 1 ) α ] l R .
Ψ in = l ψ = l ( c 1 R + c 2 L )
P + = 1 2 + c 1 2 cos [ ( l 1 ) α ] + c 2 2 cos [ ( l + 1 ) α ] 2 .
S = 2 ( l + 1 ) d P + d α = c 1 2 ( l 1 ) ( l + 1 ) sin [ ( l 1 ) α ] + c 2 2 sin [ ( l + 1 ) α ] .
D = 2 c 1 c 2 sin ( α ) , for all l .

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