Measurement of the Spiral Spectrum of Entangled Two-Photon States

We implement an interferometric method to measure the orbital angular momentum (OAM) spectrum of photon pairs generated by spontaneous parametric down-conversion. In contrast with previous experiments, which were all limited by the modal capacity of the detection system, our method operates on the entire down-conversion cone and reveals the complete distribution of the generated OAM. In this geometry, new features can be studied. We show that the phase-matching conditions can be used as a tool to enhance the azimuthal Schmidt number and to flatten the spectral profile, allowing the efficient production of high-quality multidimensional entangled states.

Figure 1

Experimental setup used to generate entangled two-photon pairs and to measure its OAM spectrum. See details in the text.

Figure 2

(a) Normalized visibility of the HOM interference as a function of the rotation angle for a 2-mm crystal. The dots are experimental results and the curve the theoretical calculation. (b) Corresponding OAM spectrum obtained via Fourier transform. The bars are the experimental results and the curve the theoretical expectation. Notice the excellent agreement, where no fitting parameters are used.

Figure 3

Dependence of the azimuthal Schmidt number $K_{\mathrm{az}}$ on the phase-mismatch parameter $\phi$ for a 5-mm crystal. The inset shows the measured visibilities, where the inner curve (at $\phi =-9$) corresponds to the highest $K_{\mathrm{az}}$.

Figure 4

The effect of phase mismatch on the modal decomposition $P_l$. For negative $\phi$ the SPDC rings are open and the pair generation is more efficient. By adjusting the phase-matching conditions we can increase the Schmidt number and flatten the spectral profile, producing high-quality entangled states in a larger $l$ range.