Transverse distinguishability of entangled photons with arbitrarily shaped spatial near- and far-field distributions

Abstract

Entangled photons generated by spontaneous parametric down conversion inside a nonlinear crystal exhibit a complex spatial photon count distribution. A quantitative description of this distribution helps with the interpretation of experiments that depend on this structure. We developed a theoretical model and an accompanying numerical calculation that includes the effects of phase matching and the crystal properties to describe a wide range of spatial effects in two-photon experiments. The numerical calculation was tested against selected analytical approximations. We furthermore performed a double-slit experiment where we measured the visibility V and the distinguishability D and obtained D 2 + V 2 = 1.43. The numerical model accurately predicts these experimental results.

The photon: the role of its mode function in analyzing complementarity

“…This effect originates from the phase matching condition and the unusual pump mode. Since our experimental results are in complete agreement with the corresponding numerical simulations [21] we can identify the signal-idler pairs belonging to the same mode. Only these photons have to obey the principle of complementarity as discussed in Sec.…”

“…In order to bring this difference out most clearly we have enlarged these structures in the right column of Fig.4 and emphasize that they are perfectly reproduced in the simulations of Ref. [21].…”

“…The top and the bottom of the ring belong to two different modes with either one or two maxima. This property has immediate consequences on our double-slit experiment with entangled photons [16,20,21] and, in particular, on the principle of complementarity.…”

“…Without the slit-aperture a maximum value of V 2 + D 2 ≈ 1.4 was determined experimentally [17] and theoretically [21] as a consequence of the unfair sampling. However, even in the presence of the vertical slit-aperture violations of the inequality, Eq.…”

Complementarity in single photon interference – the role of the mode function and vacuum fields

“…In experiments with higher order modes as e.g. TEM 01 [18] this analogy could be observed indirectly, too. Photons from the same coherent mode are not distinguishable and distinguishable photons belong always to different modes.…”