Non-cascade random walks in solid-state high harmonic generation

Random walks-both classical and quantum-unlocked new possibilities in search algorithms and information processing. Although linear photonic systems, with flexible tunability and multiple degrees of freedom, have served as efficient carriers for random walks, they typically require cascaded implementations, presenting a potential limitation on realizing integrated photonic circuits. In this work, we demonstrate a non-cascade, high-dimensional random walk in the orbital angular momentum (OAM) space of light using solid-state high-harmonic spectroscopy. The crystal nonlinearity enables the simultaneous conversion of multiple photons into a series of harmonics with distinct colors and whose OAM distributions are determined by the symmetry of the crystal. This approach reveals the dynamics of photonic degrees of freedom in high-harmonic generation can be naturally framed as an ultrafast, high-dimensional random walk, paving the way for compact, highly stable photonic platforms tailored for solid-state information processing.