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.

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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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. T. Nagata, R. Okamoto, J. L. O'Brien, K. Sasaki, and S. Takeuchi, Science 316, 726 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [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 (3)

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 (2)

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 (2)

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 (1)

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

2002 (1)

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

1999 (1)

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

1998 (3)

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 (1)

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

1995 (1)

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

1992 (1)

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

1979 (1)

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

Czech. J. Phys. (1)

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

Int. J. Mod. Phys. B (1)

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

Nature (1)

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

New J. Phys. (1)

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

Opt. Commun. (1)

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

Phys. Rev. A (3)

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 (1)

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

Phys. Rev. Lett. (7)

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 (1)

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

Other (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.

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)

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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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