Even-Order Aberration Cancellation in Quantum Interferometry

We report the first experimental demonstration of even-order aberration cancellation in quantum interferometry. The effect is a spatial counterpart of the spectral group velocity dispersion cancellation, which is associated with spectral entanglement. It is manifested in temporal interferometry by virtue of the multiparameter spatial-spectral entanglement. Spatially entangled photons, generated by spontaneous parametric down-conversion, were subjected to spatial aberrations introduced by a deformable mirror that modulates the wave front. We show that only odd-order spatial aberrations affect the quality of quantum interference.

Figure 1

Schematic of the experimental setup. Examples of aberrations induced by the deformable mirror are illustrated in the inset: the even-parity aberrations on the left are canceled, while the odd-parity ones on the right alter the shape of the interference pattern.

Figure 2

Coincidence-rate interference patterns when coma ($n=3$, $m=\pm 1$) along the $x$ axis (on the left) and along the $y$ axis (on the right) is imposed on the deformable mirror. Solid lines illustrate theoretical fitting with experimental parameters. The initial relative tilt between the deformable mirror (DM) and the flat mirror (FM) is used as an adjustable parameter to account for the imperfectness of experimental alignment between two arms. The shapes of adaptive mirror deformation producing selected aberrations are illustrated in the insets.

Figure 3

Interference patterns in the coincidence rate when astigmatism at 45° (left picture) and the aberration described by $n=4$, $m=4$ are dialed on the mirror. The intensity of the aberrations has been scanned from $0.2$ to $0.8\mu \mathrm{m}$ peak-to-valley deformation. The interference pattern is insensitive to the aberrations within experimental errors.