Fig. 2: Experimental implementation of one-dimensional quasicrystals via photonic quantum walks.

a, Simplified experimental setting for realizing photonic lattices via discrete-time quantum walks. Two unequally long optical fibre loops are connected by a variable beam splitter (VBS) that controls β. The non-Hermitian potential is realized by introducing controlled optical losses with acousto-optical modulators (AOMs). A phase modulator (PM) emulates the real part of the potential and creates the quasicrystalline order. Photodetectors measure the light intensity in both loops and hereby the time evolution of the quantum walk. b, The one-dimensional lattice (top) is implemented with a one-dimensional quantum walk (bottom) (equation (1)), based on a mesh lattice of beam splitters that is created with the coupled fibre loops (Supplementary Section 1). Gain and loss are incorporated at different lattice positions and in a two-step Floquet protocol, such that the skin effect modulation with anisotropic coupling with strength h (imaginary gauge field) is obtained. In a similar way, the potential (strength corresponds to amount of blue coloured filling) of the AAH model is realized via phase modulation (equation (2)) with a spatial phase gradient and alternating sign. The combined modulations realize the non-Hermitian Floquet AAH model based on a discrete-time quantum walk.