Abstract

It is shown that a holographic setup for real-time interferometry can be used to realize a quantum eraser (QE) experiment. Circular polarized light is used to distinguish between the photons of the reconstructed image of the object and the direct object wave consisting of scattered photons from the illuminated flat object. To erase the “which path information,” a linear polarizer is used. The experimental results show that polarized light, after depolarizing reflection from a dielectric surface, contains an internal polarization structure, which can be described extending the well-known Jones vector formalism.

© 2008 Optical Society of America

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References

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  1. A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “The concept of the photon--revisited,” OPN Trends 3(1), S18-S27 (2003).
  2. W. Martienssen, Einführung in die Physik (Introduction to Physics) (Akademische Verlagsgesellschaft, 1976).
  3. S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).
  4. S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
    [CrossRef]
  5. Slavich Certified Photo Materials, http://www.slavich.com/.
  6. G. Wernicke, Humboldt University, Faculty of Math and Science No. 1, Uter den Linden 6, D-10099 Berlin, Germany (private communication).
  7. N. D. Shewandrow, Die Polarisation des Lichtes, WTB No. 44 (Akademieverlag, 1973).
  8. E. Hecht, Optics (Addison-Wesley, 1989).
  9. J. M. Stone, Radiation and Optics (McGraw-Hill, 1963).
  10. P. Hariharan, Optical Interferometry (Academic, 1985).
  11. G. K. Ackermann and J. Eichler, Holography--A Practical Approach (Wiley-VCH, 2007), p. 206.
  12. R. B. Laughlin, A Different Universe--Reinventing Physics from the Bottom Down (Basic Books Group, 2005).

2003 (2)

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “The concept of the photon--revisited,” OPN Trends 3(1), S18-S27 (2003).

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).

2002 (1)

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Ackermann, G. K.

G. K. Ackermann and J. Eichler, Holography--A Practical Approach (Wiley-VCH, 2007), p. 206.

Eichler, J.

G. K. Ackermann and J. Eichler, Holography--A Practical Approach (Wiley-VCH, 2007), p. 206.

Hariharan, P.

P. Hariharan, Optical Interferometry (Academic, 1985).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1989).

Laughlin, R. B.

R. B. Laughlin, A Different Universe--Reinventing Physics from the Bottom Down (Basic Books Group, 2005).

Martienssen, W.

W. Martienssen, Einführung in die Physik (Introduction to Physics) (Akademische Verlagsgesellschaft, 1976).

Monken, C. H.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Muthukrishnan, A.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “The concept of the photon--revisited,” OPN Trends 3(1), S18-S27 (2003).

Pádua, S.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Scully, M. O.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “The concept of the photon--revisited,” OPN Trends 3(1), S18-S27 (2003).

Shewandrow, N. D.

N. D. Shewandrow, Die Polarisation des Lichtes, WTB No. 44 (Akademieverlag, 1973).

Stone, J. M.

J. M. Stone, Radiation and Optics (McGraw-Hill, 1963).

Terra Cunha, M. O.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Walborn, S. P.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Wernicke, G.

G. Wernicke, Humboldt University, Faculty of Math and Science No. 1, Uter den Linden 6, D-10099 Berlin, Germany (private communication).

Zubairy, M. S.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “The concept of the photon--revisited,” OPN Trends 3(1), S18-S27 (2003).

OPN Trends (1)

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “The concept of the photon--revisited,” OPN Trends 3(1), S18-S27 (2003).

Phys. Rev. A (1)

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Sci. Am. (1)

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Quantum erasure,” Sci. Am. 91, 336-344(2003).

Other (9)

W. Martienssen, Einführung in die Physik (Introduction to Physics) (Akademische Verlagsgesellschaft, 1976).

Slavich Certified Photo Materials, http://www.slavich.com/.

G. Wernicke, Humboldt University, Faculty of Math and Science No. 1, Uter den Linden 6, D-10099 Berlin, Germany (private communication).

N. D. Shewandrow, Die Polarisation des Lichtes, WTB No. 44 (Akademieverlag, 1973).

E. Hecht, Optics (Addison-Wesley, 1989).

J. M. Stone, Radiation and Optics (McGraw-Hill, 1963).

P. Hariharan, Optical Interferometry (Academic, 1985).

G. K. Ackermann and J. Eichler, Holography--A Practical Approach (Wiley-VCH, 2007), p. 206.

R. B. Laughlin, A Different Universe--Reinventing Physics from the Bottom Down (Basic Books Group, 2005).

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Figures (4)

Fig. 1
Fig. 1

Holographic setup for real-time interferometry: Beam splitter (BS); mirror (M); quarter wave plate (QW) to make left or right circular polarization; holographic plate (PP); object (O), upper part dielectric (white), lower part metallic structure (gray); QE in three positions; dashed lines and mirrors, not used second illumination beam of the whole transmission hologram setup; eye, observers position looking through the holographic plate.

Fig. 2
Fig. 2

Real-time interferometry experiment: Upper part, dielectric material (white painted metal); lower part, metallic. The metallic part is extended up to the second horizontal line. Reconstruction wave and object wave are right circular polarized (Experiment 1 of Table 1). Both parts show interference lines due to slight mismatch of object wave and reconstruction wave.

Fig. 3
Fig. 3

Real-time interferometry experiment: Upper part, dielectric; lower part, metallic. Both waves are left circular polarized (Experiment 6 of Table 1). No interference within dielectric part. The faint interference fringes are discussed in the Section 3.

Fig. 4
Fig. 4

Random polarized light: incident light (A); dielectric object and two object points a and b (B); holographic plate (C); scattered light from two adjacent points a and b of the object showing phase differences in a simple way (D). The scattered wave from each point is left and/or right circular polarized. The unknown phase factors ( α n , m ) of all object points cover the range from 0 to 2 π .

Tables (1)

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Table 1 Interference Experiments and Theoretical Wave Functions

Equations (27)

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O L , R M = A ( x ^ e i ϕ o ± i y ^ e i ϕ o ) .
E = [ E x E y ] = [ E o , x e i ϕ x E o , y e i ϕ y ] ,
O L , R M = S o [ 1 ± i ] ,
S o = A e i φ o .
R L , R = S r [ 1 ± i ] ,
S r = R e i φ r .
O L D = 1 2 ( S n 1 [ 1 i ] + S n 2 [ 1 i ] ) ,
O R D = 1 2 ( S n 3 [ 1 i ] + S n 4 [ 1 i ] ) .
S n , m = B n e i φ n , m ,
O Lin M = S o [ 1 0 ] .
R Lin = S R [ 1 0 ] .
O Lin D = 1 2 ( O L D + O R D ) .
J = [ ( O R R * ) R + O ] · [ ( O R R * ) R + O ] * .
J int = ( O R R * ) R O * + c . c .
J int = 2 ( S o S R * ) R O * + c . c .
J int = 2 { [ ( S o S R * ) ] R R } O R M * + c . c . ,
J int = S o S R * S R [ 1 i ] S o * [ 1 i ] + c . c .
J int = 2 A 2 R 2 cos ( ϕ o ϕ o ) .
J int = S o S R * R R O L M * + c . c .
J int = S o S R * R R O Lin M * + c . c . ,
J int = S o S R * S R [ 1 i ] S o * [ 1 0 ] + c . c .
J int = ( S n , 1 S R * ) R O * + c . c .
J int = [ ( S n , 1 S R * ) R R ] O L D * + c . c .
J int ( 2 ) = S n 1 S R * S R [ 1 i ] 1 2 ( S n 1 * [ 1 i ] + S n 2 * [ 1 i ] ) + c . c . = S n 1 S n 1 * + S n 1 * S n 1 .
J int = 2 B n 2 R 2 cos ( φ n 1 φ n 1 ) .
J int = S n , 1 S R * R R O R D * + c . c . = S n 1 S R * S R [ 1 i ] 1 2 ( S n 3 * [ 1 i ] + S n 4 * [ 1 i ] ) = S n 1 S n 3 * + c . c .
J int tot = 1 2 π 0 2 π ( cos β ) d ( β ) = 0 , β = Δ ϕ + Δ α , Δ ϕ = ϕ n , o ϕ n , o , Δ α = α n , 1 α n , 3 .

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