  Generation of irregular time series based on physical processes is
indispensable in computing and artificial intelligence. In this report, we
propose and experimentally demonstrate the generation of Schubert polynomials,
which is the foundation of versatile permutations in mathematics, via optical
near-field processes introduced in a photochromic crystal of diarylethene,
which 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 experimentally generated Schubert matrices,
corresponding to Schubert polynomials, via optical near-field density mapping.
The versatility and correlations of the generated patterns 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 by
physical processes or nanophotonics, paving the way toward future nano-scale
intelligence devices and systems.
