Direct measurement of wavefunctions has attracted great interest and many different methods have been developed. However, the precision of current techniques is limited by the use of Fourier transform lenses. These measurements require to shear cut the part of particles with momentum P = 0, which greatly restricts the efficiency and application of the approaches. Here, a method to directly measure 2D photonic wavefunctions is proposed and experimentally demonstrated by combining the momentum weak measurement technology and the zonal wavefront restoration algorithm. Both the Gaussian and Laguerre-Gaussian wavefunctions are experimentally well reconstructed. This method avoids using the Fourier lens and post selection on the momentum P = 0. This is further applied to measure wavefronts with ultra-high spatial frequency and achieve a pixel resolution, which is difficult for traditional Shack-Hartmann wavefront sensing technologies. This work extends the ability of quantum measurement techniques and will be useful for high-resolution wavefront sensing.

Synthetic dimensions based on particles’ internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological phenomena. Exploring more synthetic dimensions is one of the paths toward higher dimensional physics. In this work, we design and experimentally control the coupling among synthetic dimensions consisting of the intrinsic photonic orbital angular momentum and spin angular momentum degrees of freedom in a degenerate optical resonant cavity, which generates a periodically driven spin-orbital coupling system. We directly characterize the system’s properties, including the density of states, energy band structures and topological windings, through the transmission intensity measurements. Our work demonstrates a mechanism for exploring the spatial modes of twisted photons as the synthetic dimension, which paves the way to design rich topological physics in a highly compact platform.

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Exceptional points (EPs), at which more than one eigenvalue and eigenvector coalesce, are unique spectral features of non-Hermiticity (NH) systems. They exist widely in open systems with complex energy spectra. We experimentally demonstrate the appearance of paired EPs in a periodical-driven degenerate optical cavity along the synthetic orbital angular momentum dimension with a tunable parameter. The complex-energy band structures and the key features of EPs, i.e., their bulk Fermi arcs, parity-time symmetry breaking transition, energy swapping, and half-integer band windings, are directly observed by detecting the wavefront angle–resolved transmission spectrum. Our results demonstrate the flexibility of using the photonic synthetic dimensions to implement NH systems beyond their geometric dimension and EP-based sensing.

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