Abstract

Orbital angular momentum (OAM) entangled photons propagating through non-Kolmogorov turbulence are studied by numerical simulations. Here, the paper uses the multiphase screen model, especially focusing on the influences of the azimuthal mode and the turbulence parameters (i.e., the generalized exponent, the outer scale of turbulence, and the inner scale of turbulence) on entanglement evolution in the weak scintillation regime. The results indicate that the azimuthal mode, the generalized exponent, and the outer scale of turbulence have obvious influences on OAM entanglement. However, the influence of the turbulence inner scale on OAM entanglement can be ignored.

© 2016 Optical Society of America

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References

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2015 (1)

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

2014 (3)

A. H. Ibrahim, F. S. Roux, and T. Konrad, “Parameter dependence in the atmospheric decoherence of modally entangled photon pairs,” Phys. Rev. A 90, 052115 (2014).
[Crossref]

F. S. Roux, “The Lindblad equation for the decay of entanglement due to atmospheric scintillation,” J. Phys. A 47, 195302 (2014).
[Crossref]

J. S. Xiang, “Fast and accurate simulation of the turbulent phase screen using fast Fourier transform,” Opt. Eng. 53, 016110 (2014).
[Crossref]

2013 (4)

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

T. Brűnner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

M. V. Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled two-photon beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
[Crossref]

2011 (3)

2010 (1)

2009 (2)

W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17, 17829–17836 (2009).
[Crossref]

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E 80, 046609 (2009).
[Crossref]

2008 (3)

G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25, 225–230 (2008).
[Crossref]

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101, 050501 (2008).
[Crossref]

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref]

2006 (1)

B. J. Smith and M. G. Raymer, “Two-photon wave mechanics,” Phys. Rev. A 74, 062104 (2006).
[Crossref]

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

2004 (2)

2002 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref]

2001 (2)

M. Bourennane, A. Karlsson, and G. Björk, “Quantum key distribution using multilevel encoding,” Phys. Rev. A 64, 012306 (2001).
[Crossref]

A. Mair, G. W. A. Vaziri, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

1998 (1)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

1997 (1)

M. S. Belenkii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

1995 (3)

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389–404 (1995).
[Crossref]

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[Crossref]

1994 (2)

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

1992 (1)

1988 (1)

Aiello, A.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref]

Alonso, J. R. G.

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

Bailey, D. H.

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389–404 (1995).
[Crossref]

Barnett, S.

Beland, R. R.

R. R. Beland, “Some aspects of propagation through weak isotropic non-Kolmogorov turbulence,” Proc. SPIE 2375, 6–16 (1995).
[Crossref]

Belenkii, M. S.

M. S. Belenkii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Bishop, K. P.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Björk, G.

M. Bourennane, A. Karlsson, and G. Björk, “Quantum key distribution using multilevel encoding,” Phys. Rev. A 64, 012306 (2001).
[Crossref]

Bourennane, M.

M. Bourennane, A. Karlsson, and G. Björk, “Quantum key distribution using multilevel encoding,” Phys. Rev. A 64, 012306 (2001).
[Crossref]

Brown, J. M.

M. S. Belenkii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Brun, T. A.

J. R. G. Alonso and T. A. Brun, “Protecting orbital-angular-momentum photons from decoherence in a turbulent atmosphere,” Phys. Rev. A 88, 022326 (2013).
[Crossref]

Brunner, T.

T. Brűnner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

Buchleitner, A.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

Cheng, W.

Courtial, J.

Cunha Pereira, M. V.

M. V. Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled two-photon beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

Dang, A.

Dayton, D.

Dipankar, A.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E 80, 046609 (2009).
[Crossref]

Elie, E. R.

Eliel, E. R.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref]

Filpi, L. A. P.

M. V. Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled two-photon beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

Flatté, S. M.

Forbes, A.

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
[Crossref]

Franke-Arnold, S.

Fugate, R. Q.

M. S. Belenkii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Gavel, D. T.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

Gbur, G.

Gibson, G.

Guo, H.

Haus, J. W.

Hooft, G. W.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref]

Ibrahim, A. H.

A. H. Ibrahim, F. S. Roux, and T. Konrad, “Parameter dependence in the atmospheric decoherence of modally entangled photon pairs,” Phys. Rev. A 90, 052115 (2014).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
[Crossref]

Johansson, E. M.

E. M. Johansson and D. T. Gavel, “Simulation of stellar speckle imaging,” Proc. SPIE 2200, 372–383 (1994).
[Crossref]

Karis, S. J.

M. S. Belenkii, S. J. Karis, J. M. Brown, and R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997).
[Crossref]

Karlsson, A.

M. Bourennane, A. Karlsson, and G. Björk, “Quantum key distribution using multilevel encoding,” Phys. Rev. A 64, 012306 (2001).
[Crossref]

Kawase, D.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101, 050501 (2008).
[Crossref]

Keating, D. D. B.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Konrad, T.

A. H. Ibrahim, F. S. Roux, and T. Konrad, “Parameter dependence in the atmospheric decoherence of modally entangled photon pairs,” Phys. Rev. A 90, 052115 (2014).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
[Crossref]

Kyrazis, D. T.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Leonhard, N. D.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

Liu, Z.

Luo, B.

Ma, Y.

Mair, A.

A. Mair, G. W. A. Vaziri, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

Marchiano, R.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E 80, 046609 (2009).
[Crossref]

Martin, J. M.

McLaren, M.

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
[Crossref]

Miyamoto, Y.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101, 050501 (2008).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref]

Monken, C. H.

M. V. Cunha Pereira, L. A. P. Filpi, and C. H. Monken, “Cancellation of atmospheric turbulence effects in entangled two-photon beams,” Phys. Rev. A 88, 053836 (2013).
[Crossref]

B.-J. Pros, C. H. Monken, E. R. Elie, and J. P. Woerdman, “Transport of orbital-angular-momentum entanglement through a turbulent atmosphere,” Opt. Express 19, 6671–6683 (2011).
[Crossref]

Oemrawsingh, S. S. R.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref]

Ou, B.

Padgett, M.

Pas’ko, V.

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

Pierson, B.

Pors, J. B.

J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. Hooft, and J. P. Woerdman, “Shannon dimensionality of quantum channels and its application to photon entanglement,” Phys. Rev. Lett. 101, 120502 (2008).
[Crossref]

Preble, A. J.

D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
[Crossref]

Pros, B.-J.

Raymer, M. G.

B. J. Smith and M. G. Raymer, “Two-photon wave mechanics,” Phys. Rev. A 74, 062104 (2006).
[Crossref]

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Roux, F. S.

F. S. Roux, “The Lindblad equation for the decay of entanglement due to atmospheric scintillation,” J. Phys. A 47, 195302 (2014).
[Crossref]

A. H. Ibrahim, F. S. Roux, and T. Konrad, “Parameter dependence in the atmospheric decoherence of modally entangled photon pairs,” Phys. Rev. A 90, 052115 (2014).
[Crossref]

A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, “Orbital-angular-momentum entanglement in turbulence,” Phys. Rev. A 88, 012312 (2013).
[Crossref]

T. Brűnner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
[Crossref]

F. S. Roux, “Infinitesimal-propagation equation for decoherence of an orbital-angular-momentum-entangled biphoton state in atmospheric turbulence,” Phys. Rev. A 83, 053822 (2011).
[Crossref]

Sagaut, P.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E 80, 046609 (2009).
[Crossref]

Sasaki, K.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101, 050501 (2008).
[Crossref]

Sedmak, G.

Shatokhin, V. N.

N. D. Leonhard, V. N. Shatokhin, and A. Buchleitner, “Universal entanglement decay of photonic-orbital-angular-momentum qubit states in atmospheric turbulence,” Phys. Rev. A 91, 012345 (2015).
[Crossref]

Smith, B. J.

B. J. Smith and M. G. Raymer, “Two-photon wave mechanics,” Phys. Rev. A 74, 062104 (2006).
[Crossref]

Spielbusch, B.

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Swarztrauber, P. N.

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389–404 (1995).
[Crossref]

Takeda, M.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101, 050501 (2008).
[Crossref]

Takeuchi, S.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101, 050501 (2008).
[Crossref]

Tang, H.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2002).
[Crossref]

Tyson, R. K.

van Exter, M. P.

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D. T. Kyrazis, J. Wissler, D. D. B. Keating, A. J. Preble, and K. P. Bishop, “Measurement of optical turbulence in the upper troposphere and lower stratosphere,” Proc. SPIE 2120, 43–55 (1994).
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[Crossref]

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A. Mair, G. W. A. Vaziri, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref]

New J. Phys. (1)

T. Brűnner and F. S. Roux, “Robust entangled qutrit states in atmospheric turbulence,” New J. Phys. 15, 063005 (2013).
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Phys. Rev. A (8)

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[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Source produces a pairs of OAM-entangled qubits, whose wave fronts get deteriorated as they propagate through a series of phase screens along the (horizontal) z axis toward a detector.
Fig. 2.
Fig. 2. Comparisons between Eq. (11) and statistical mean of the structure function obtained from samples of 1000 phase screens generated with the spectral method. The black color is the results of Eq. (11), while the red represents the sample average results. The value of the Fried parameter is r0=3.18  cm.
Fig. 3.
Fig. 3. Concurrence as a function of ratio ω0/ρ0 when both the photons propagate through turbulence. In (a) l=1, in (b) l=3, in (c) l=5, and in (d) l=7.
Fig. 4.
Fig. 4. Concurrence as a function of ratio ω0/ρ0 for different values of the azimuthal modes.
Fig. 5.
Fig. 5. Concurrence as a function of ratio ω0/ρ0 for different values of the generalized exponent.
Fig. 6.
Fig. 6. Concurrence as a function of ratio ω0/ρ0 for different values of the turbulence outer scale with α=3.6.
Fig. 7.
Fig. 7. Concurrence as a function of ratio ω0/ρ0 for different values of the turbulence inner scale with α=3.6.

Equations (12)

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|ψin=12(|A|B+|A|B),
MpLG=Nr||exp(iφ)(1+it)p(1it)p+||+1LP||(2r21+t2)exp(r21it),
N=(p!2||+1π(p+||)!)1/2.
δn(x)=n1,
φ(x)=k00Δzδn(x)dz,
Φn(κ,z)=A(α)C˜n2(κ2+κ02)α/2exp(κ2/κm2),3<α<4,
A(α)=Γ(α1)cos(απ/2)/(4π2),
Φn(κ)=0.033Cn2κ11/3.
φFFT(m,n)=m=N/2N/21n=N/2N/21h(m,n)Δκ2πk2Φn(κx,κy)Δzei(mm/N+nn/N)ΔκΔκ,
φLow(m,n)=m=Nx/2Nx/21n=Ny/2Ny/21h(m,n)Δκ2πk2Φn(κx,κy)Δzei(mm/NxN+nn/NyN)ΔκΔκ.
Dφ(r)=6.16r05/3[35(L02π)5/3(rL0/4π)5/6Γ(11/6)K5/6(2πrL0)].
ρ0=(A(α)B(α)C˜n2k2L)1α2,

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