Observing Quantum Correlation of Photons in Laguerre-Gauss Modes Using the Gouy Phase

The effect of the Gouy phase, which is one of the geometrical phases of photons, is observed through quantum correlation in Laguerre-Gaussian (LG) modes. In an experiment, the relative phase of two different LG modes of measurement basis states is manipulated via the Gouy phase, and the observed coincidence count rates agree well with theoretical predictions. This result suggests that the Gouy phase can be used as a new tool to manipulate multidimensional photonic quantum states.

Figure 1

(a) Variation of beam diameter with propagation distance $z$ for a LG beam focused by a lens; (b) Plot of ${\Psi }_{00}$, ${\Psi }_{01}$ and ${\Psi }_{02}$ against $z$.

Figure 2

The experimental setup for observing quantum correlation using Gouy phase shift. The inset shows the hologram pattern as viewed from the BBO crystal.

Figure 3

Maps of the normalized coincidence count rates obtained by scanning hologram $H_I$. The distances between $H_S$ and $L_{S1}$ were (a) 250 mm, (b) 255 mm, (c) 257.5 mm, (d) 260 mm, (e) 262.5 mm, (f) 265 mm, and (g) 270 mm.

Figure 4

Dependence of ${\theta }_{\mathrm{map}}$ on the position of beam waist $z_{0S}$. The squares represent the measured data and the solid line represents the fitting result. The error bars are determined based on the assumption that the minimum (maximum) points exist in the areas 6.25% of the largest (smallest) coincidence counts in Fig. 3.