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Biphoton phase space correlations from Gouy phase measurements using double-slits

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 Publication date 2021
  fields Physics
and research's language is English




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Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy phase shifts (D. Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)) allowing for a non-destructive manipulation of photonic quantum states. In this work we exploit the relation between phase space correlations of biphotons produced by spontaneously parametric down conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double slit setup. Using an analytical approach based on a double-gaussian approximation for type-I SPDC biphotons, we show that measurements of Gouy phase differences provide information on their phase space entanglement variation, governed by the physical parameters of the experiment and expressed by the LN via covariance matrix elements.



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We show that the phase shift of {pi}/2 is crucial for the phase space translation covariance of the measured high-amplitude limit observable in eight-port homodyne detection. However, for an arbitrary phase shift {theta} we construct explicitly a different nonequivalent projective representation of R$^2$ such that the observable is covariant with respect to this representation. As a result we are able to determine the measured observable for an arbitrary parameter field and phase shift. Geometrically the change in the phase shift corresponds to the tilting of one axis in the phase space of the system.
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