Rare Earth Ion Coupling Implements Attention-Like Reservoir Computing

Abstract: We present a physical computing paradigm that harnesses the intrinsic nonlinear dynamics of rare earth doped core shell nanoparticles as a computational substrate. By directly exploiting cross relaxation and energy transfer upconversion processes, the system realizes a state dependent transfer function whose effective decay rate evolves with the instantaneous Er3+ population, which mathematically analogous to gating and attention mechanisms in recurrent neural networks. The three spectrally resolved emission channels inherently span disparate timescales, endowing the reservoir with native multitimescale feature extraction without auxiliary engineering. Under the reservoir computing framework, the coupled three channel system achieves a total memory capacity exceeding fourfold that of a single ion reservoir; capacity decomposition further reveals that the nonzero cross memory capacity is a direct signature of many body Tm3+@Er3+ coupling. On the Mackey Glass and Santa Fe chaotic benchmarks, the system attains normalized mean squared errors of 1.2x10-3 and 2.1x10-2, respectively, with only 125 virtual nodes. These results establish rare earth nanoparticles as a compelling platform for compact and hardware integrable neuromorphic computing, and introduce "inward evolution", the deliberate exploitation of intra material quantum dynamics, as a generalizable design principle for next generation physical computing systems.