Abstract

We present an innovative method to address the relation between the purity of type-I polarization entangled states and the spatial properties of the pump laser beam. Our all-optical apparatus is based on a spatial light modulator, and it offers unprecedented control on the spatial phase function of the entangled states. In this way, we demonstrate quantitatively the relation between the purity of the generated state and the spatial field correlation function of the pump beam.

© 2012 Optical Society of America

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  1. P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
    [CrossRef]
  2. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
    [CrossRef]
  3. W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
    [CrossRef]
  4. C. I. Osorio, G. Molina-Terriza, B. G. Font, and J. P. Torres, Opt. Express 15, 14636 (2007).
    [CrossRef]
  5. G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres, Opt. Express 15, 14636 (2007).
    [CrossRef]
  6. P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
    [CrossRef]
  7. S. Cialdi, D. Brivio, and M. G. A. Paris, Appl. Phys. Lett. 97, 041108 (2010).
    [CrossRef]
  8. R. Rangarajan, M. Goggin, and P. Kwiat, Opt. Express 17, 18920 (2009).
    [CrossRef]
  9. S. Cialdi, F. Castelli, I. Boscolo, and M. G. A. Paris, Appl. Opt. 47, 1832 (2008).
    [CrossRef]
  10. S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
    [CrossRef]
  11. H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
    [CrossRef]
  12. S. Cialdi, D. Brivio, and M. G. A. Paris, Phys. Rev. A 81, 042322 (2010).
    [CrossRef]
  13. A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
    [CrossRef]

2011 (3)

W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
[CrossRef]

S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

2010 (2)

S. Cialdi, D. Brivio, and M. G. A. Paris, Phys. Rev. A 81, 042322 (2010).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Appl. Phys. Lett. 97, 041108 (2010).
[CrossRef]

2009 (2)

R. Rangarajan, M. Goggin, and P. Kwiat, Opt. Express 17, 18920 (2009).
[CrossRef]

H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
[CrossRef]

2008 (1)

2007 (2)

2005 (1)

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

1999 (1)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

1995 (1)

P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Appelbaum, I.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Bennink, R. S.

W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
[CrossRef]

Boscolo, I.

Breuer, H. P.

H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
[CrossRef]

Brivio, D.

S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Phys. Rev. A 81, 042322 (2010).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Appl. Phys. Lett. 97, 041108 (2010).
[CrossRef]

Castelli, F.

Cialdi, S.

S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Phys. Rev. A 81, 042322 (2010).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Appl. Phys. Lett. 97, 041108 (2010).
[CrossRef]

S. Cialdi, F. Castelli, I. Boscolo, and M. G. A. Paris, Appl. Opt. 47, 1832 (2008).
[CrossRef]

Deyanova, Y.

Eberhard, P. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Font, B. G.

Goggin, M.

Goodman, D. S.

W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
[CrossRef]

Grice, W. P.

W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
[CrossRef]

Hendrych, M.

Kwiat, P.

Kwiat, P. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Laine, E. M.

H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
[CrossRef]

Lee, P. S. K.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Mattle, C.

P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Minardi, S.

Molina-Terriza, G.

Osorio, C. I.

Paris, M. G. A.

S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Phys. Rev. A 81, 042322 (2010).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Appl. Phys. Lett. 97, 041108 (2010).
[CrossRef]

S. Cialdi, F. Castelli, I. Boscolo, and M. G. A. Paris, Appl. Opt. 47, 1832 (2008).
[CrossRef]

Piilo, J.

H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
[CrossRef]

Rangarajan, R.

Ryan, A. T.

W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
[CrossRef]

Smirne, A.

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

Tesio, E.

S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
[CrossRef]

Torres, J. P.

Vacchini, B.

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

van Exter, M. P.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Waks, E.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Weinfurter, H.

P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

White, A. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

Woerdman, J. P.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

Zeilinger, A.

P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Cialdi, D. Brivio, and M. G. A. Paris, Appl. Phys. Lett. 97, 041108 (2010).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (6)

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A 72, 033803 (2005).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. G. Eberhard, Phys. Rev. A 60, R773 (1999).
[CrossRef]

W. P. Grice, R. S. Bennink, D. S. Goodman, and A. T. Ryan, Phys. Rev. A 83, 0238102 (2011).
[CrossRef]

S. Cialdi, D. Brivio, E. Tesio, and M. G. A. Paris, Phys. Rev. A 83, 042308 (2011).
[CrossRef]

S. Cialdi, D. Brivio, and M. G. A. Paris, Phys. Rev. A 81, 042322 (2010).
[CrossRef]

A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, and M. G. A. Paris, Phys. Rev. A 84, 032112 (2011).
[CrossRef]

Phys. Rev. Lett. (2)

P. G. Kwiat, C. Mattle, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef]

H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup. The dashed part is used to measure the Fourier transform of the pump beam, and it is not present during measurements on the PDC output.

Fig. 2.
Fig. 2.

Purity (visibility) as a function of α for a beam with spot of 220 μm. The phase function imposed by the SLM is given by Φa=ϕ0αθ+. Error bars on the experimental values are within the points. The solid black line is the theoretical prediction.

Fig. 3.
Fig. 3.

Spatial field correlations of the pump beam and purity of the entangled output in three relevant cases: (first row) collimated pump beam of 220 μm, (second row) divergent pump beam of 220 μm, and (third row) pump beam with two peaks. We report the spatial profile of the pump (left column), its Fourier transform (right column), and the visibility as a function of β (right column). The phase function imposed by the SLM is given by Φa=ϕ0α0θ++βθ. Error bars on the experimental values are within the points. The solid black lines are the theoretical predictions (which include the effects of the walk-off in the two-peaks case).

Equations (5)

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|Ψ=12dθsdθisinc(12ΔkL)F(Δk)[|H,θs|H,θi+eiΦ(θs,θi)|V,θs|V,θi],
Δk=kpkscos[(θ0+θs)/no]kicos((θ0+θi)/no)kθ0(θs+θi)=kθ0θ+,Δk=kssin[(θ0+θs)/no]kisin[(θ0+θi)/no]k(θsθi)=kθ,
Φ(θ,θ+)=ϕ0+α0θ++Φa.
p=dθ+dθ|sinc(γθ+)|2|F(kθ)|2cosΦ(θ+,θ),
p=dθ|F(kθ)|2cosβθAp*(x+βk)Ap(x)x,

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