Generalized acceleration theorem for spatiotemporal Bloch waves

TL;DR

This paper introduces a generalized acceleration theorem for spatiotemporal Bloch waves, enabling better understanding and control of quantum particles in periodic potentials under combined strong and weak forces, with potential experimental applications.

Contribution

It proposes a new representation for wave functions in periodic potentials that generalizes Bloch's acceleration theorem to include time-periodic forcing and weak probe forces.

Findings

Derived a generalized acceleration theorem for spatiotemporal Bloch waves

Demonstrated the potential for coherent wave-packet manipulation

Suggested experimental implementation in optical lattices

Abstract

A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and the temporal periodicity. It is shown that there exists a generalization of Bloch's famous acceleration theorem which grows out of this representation and captures the effect of a weak probe force applied in addition to a strong dressing force. Taken together, these elements point at a "dressing and probing" strategy for coherent wave-packet manipulation, which could be implemented in present experiments with optical lattices.