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Coherent spatial control of wave packet dynamics on quantum lattices

Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Rapid developments in microscopy and quantum engineering allow for preparing and monitoring wave-packet dynamics on quantum lattices with increasing spatial and temporal resolution. Motivated by these emerging research interests, we present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis points to the crucial role of spatial coherence and predicts a set of novel phenomena: noise can enhance the transient diffusivity and diffusion length of sufficiently extended initial states; A smooth Gaussian initial state spreads slower than a localized initial state; A standing or traveling initial state with large momentum spreads faster than a localized initial state and exhibits a noise-induced peak in the transient diffusivity; The change in the time-dependent diffusivity and diffusion length relative to a localized initial state follows a universal dependence on the Gaussian width. These theoretical predictions and the underlying mechanism of spatial coherence suggest the possibility of controlling the wave packet dynamics on quantum lattices by spatial manipulations, which will have implications for materials science and quantum technologies.