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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry Van Driel
  • Vol. 26, Iss. 4 — Apr. 1, 2009
  • pp: 797–804

Effect of high-dimensional entanglement of Laguerre–Gaussian modes in parametric downconversion

Daisuke Kawase, Yoko Miyamoto, Mitsuo Takeda, Keiji Sasaki, and Shigeki Takeuchi  »View Author Affiliations

JOSA B, Vol. 26, Issue 4, pp. 797-804 (2009)

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We calculate the coincidence count probabilities when the photon pairs entangled in orbital angular momentum generated via spontaneous parametric downconversion are measured by using holograms with an m-fold dislocation, considering the nonzero crystal length. We find that the coincidence probabilities related to azimuthal changes in hologram positions deviate significantly from a sinusoidal curve, which has often been assumed in simple analyses. It is found that the main cause of this effect is the high-dimensional entanglement in Laguerre–Gaussian modes. We also find that the crystal length causes the hologram positions to change for the maximum coincidence probabilities.

© 2009 Optical Society of America

OCIS Codes
(050.4865) Diffraction and gratings : Optical vortices
(270.5565) Quantum optics : Quantum communications
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: August 6, 2008
Revised Manuscript: February 5, 2009
Manuscript Accepted: February 25, 2009
Published: March 26, 2009

Daisuke Kawase, Yoko Miyamoto, Mitsuo Takeda, Keiji Sasaki, and Shigeki Takeuchi, "Effect of high-dimensional entanglement of Laguerre-Gaussian modes in parametric downconversion," J. Opt. Soc. Am. B 26, 797-804 (2009)

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  31. For the cases where the Rayleigh range of the pump is smaller than the crystal length, L can be considered the Rayleigh range.
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  35. This approximation is introduced to simplify the form of the mode function in position representation, which can be easily calculated numerically.
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  37. These parameters were determined for various experimental conditions.
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  39. Note that for ∣m∣>1 there are more than one values of the distance d from the dislocation to the optical axis for which the minimum coincidence probability becomes 0. For the plots in Fig. , we selected the smallest values (d/w0=0.35 for m=2 and 0.26 for m=3) that meet this criterion. We have confirmed that the shape of the plots are almost the same even when we select other values of d for which the minimum coincidence becomes 0.
  40. One can easily confirm this fact by using a simple model assuming the state of the source is given by ∣Ψ⟩=α∣0⟩I∣0⟩S+β∣1⟩I∣−1⟩S and the detection basis states are ∣ψ⟩S=sinδS∣0⟩S+cosδS∣−1⟩S and ∣ψ⟩I=sinδI∣0⟩I+cosδI∣1⟩I.
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