Polarization coherence theorem

J. H. Eberly; X.-F. Qian; A. N. Vamivakas

doi:10.1364/OPTICA.4.001113

Abstract

Visibility $V$ and distinguishability $D$ quantify wave-ray duality: $V^{2} + D^{2} \leq 1$ . We join them to polarization $P$ via the Polarization Coherence Theorem, a tight equality: $P^{2} = V^{2} + D^{2}$ .

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References

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Publication

Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).
[Crossref]
J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]
T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]
A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]
X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]
An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).
C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]
X.-F. Qian, private communication.

2016 (2)

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

2015 (1)

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

2014 (1)

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

2003 (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]

1802 (1)

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

Adesso, G.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Al Qasimi, A.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Ali, H.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Alonso, M. A.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Baumgratz, T.

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Bera, M. N.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Cramer, M.

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Dhar, H. S.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Eberly, J. H.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Gutiérrez-Cuevas, R.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Howell, J. C.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Little, B. J.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Maholtra, T.

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Malhotra, T.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Plenio, M. B.

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Qian, X.-F.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

X.-F. Qian, private communication.

Singh, U.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Streltsov, A.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Vamivakas, A. N.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Wolf, E.

E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]

Wootters, W. K.

An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).

Young, Th.

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

Zurek, W. H.

An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).

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

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

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]

Phys. Rev. Lett. (3)

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Phys. Scripta (1)

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Other (3)

X.-F. Qian, private communication.

An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

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Figures (1)

Fig. 1.

Fig. 1. Double-slit interference setup. Classical light fields emerge from slits

a

and

b

and combine on screen

c

.

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Equations (12)

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F (r_{⊥}, z) = u_{a} (r_{⊥}, z) ϕ_{a} (q) + u_{b} (r_{⊥}, z) ϕ_{b} (q) .

I_{c} = I_{a} + I_{b} + 2 | ⟨ ϕ_{a}^{*} ϕ_{b} ⟩ | \cos [\arg (⟨ ϕ_{a}^{*} ϕ_{b} ⟩)],

V_{F} = \frac{I_{c}^{\max} - I_{c}^{\min}}{I_{c}^{\max} + I_{c}^{\min}} = \frac{2 | ⟨ ϕ_{a}^{*} ϕ_{b} ⟩ |}{I_{a} + I_{b}},

D_{F} = \frac{| I_{a} - I_{b} |}{I_{a} + I_{b}} .

V_{F}^{2} + D_{F}^{2} \leq 1 .

E = \hat{h} E_{h} + \hat{v} E_{v} .

W_{E} = [\begin{matrix} ⟨ E_{h}^{*} E_{h} ⟩ & ⟨ E_{v}^{*} E_{h} ⟩ \\ ⟨ E_{h}^{*} E_{v} ⟩ & ⟨ E_{v}^{*} E_{v} ⟩ \end{matrix}], P_{E} = \sqrt{1 - \frac{4 D e t W_{E}}{{(T r [W_{E}])}^{2}}} .

W_{F} = [\begin{matrix} ⟨ ϕ_{a}^{*} ϕ_{a} ⟩ & ⟨ ϕ_{b}^{*} ϕ_{a} ⟩ \\ ⟨ ϕ_{a}^{*} ϕ_{b} ⟩ & ⟨ ϕ_{b}^{*} ϕ_{b} ⟩ \end{matrix}], P_{F} = \sqrt{1 - \frac{4 D e t W_{F}}{{(T r [W_{F}])}^{2}}} .

P_{F}^{2} = 1 - 4 \frac{I_{a} I_{b} - | ⟨ ϕ_{a}^{*} ϕ_{b} ⟩ |^{2}}{{(I_{a} + I_{b})}^{2}} = \frac{{(I_{a} - I_{b})}^{2} + 4 | ⟨ ϕ_{a}^{*} ϕ_{b} ⟩ |^{2}}{{(I_{a} + I_{b})}^{2}} = \frac{{(I_{a} - I_{b})}^{2}}{{(I_{a} + I_{b})}^{2}} + 4 \frac{| ⟨ ϕ_{a}^{*} ϕ_{b} ⟩ |^{2}}{{(I_{a} + I_{b})}^{2}},

P_{F}^{2} \equiv D_{F}^{2} + V_{F}^{2} .

E_{h} = u_{a} H_{a} + u_{b} H_{b}, and E_{v} = u_{a} V_{a} + u_{b} V_{b} .

F = (\hat{s} \cdot E) = (\hat{s} \cdot \hat{h}) (u_{a} H_{a} + u_{b} H_{b}) + (\hat{s} \cdot \hat{v}) (u_{a} V_{a} + u_{b} V_{b}) = u_{a} [(\hat{s} \cdot \hat{h}) H_{a} + (\hat{s} \cdot \hat{v}) V_{a}] + u_{b} [(\hat{s} \cdot \hat{h}) H_{b} + (\hat{s} \cdot \hat{v}) V_{b}],

Abstract

References

2016 (2)

2015 (1)

2014 (1)

2003 (1)

1802 (1)

Adesso, G.

Al Qasimi, A.

Ali, H.

Alonso, M. A.

Baumgratz, T.

Bera, M. N.

Brosseau, C.

Cramer, M.

Dhar, H. S.

Eberly, J. H.

Gutiérrez-Cuevas, R.

Howell, J. C.

Little, B. J.

Maholtra, T.

Malhotra, T.

Plenio, M. B.

Qian, X.-F.

Singh, U.

Streltsov, A.

Vamivakas, A. N.

Wolf, E.

Wootters, W. K.

Young, Th.

Zurek, W. H.

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

Phys. Lett. A (1)

Phys. Rev. Lett. (3)

Phys. Scripta (1)

Other (3)

Cited By

Figures (1)

Equations (12)

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