Generation of Schubert polynomial series via nanometre-scale photoisomerization in photochromic single crystal and double-probe optical near-field measurements

Generation of irregular time series based on physical processes is indispensable in computing and artificial intelligence. In this report, we propose and demonstrate the generation of Schubert polynomials, which are the foundation of versatile permutations in mathematics, via optical near-field processes introduced in a photochromic crystal of diarylethene combined with a simple photon detection protocol. Optical near-field excitation on the surface of a photochromic single crystal yields a chain of local photoisomerization, forming a complex pattern on the opposite side of the crystal. The incoming photon travels through the nanostructured photochromic crystal, and the exit position of the photon exhibits a versatile pattern. We emulated trains of photons based on the optical pattern experimentally observed through double-probe optical near-field microscopy, where the detection position was determined based on a simple protocol, leading to Schubert matrices corresponding to Schubert polynomials. The versatility and correlations of the generated Schubert matrices could be reconfigured in either a soft or hard manner by adjusting the photon detection sensitivity. This is the first study of Schubert polynomial generation via physical processes or nanophotonics, paving the way for future nano-scale intelligence devices and systems.