Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass

TL;DR

This paper investigates how a particle in a one-dimensional lattice responds to an external force, revealing oscillations in effective mass that can be observed in cold atom experiments.

Contribution

It introduces a modified Bloch state approach to describe the transient acceleration response of particles in lattices under sudden external forces.

Findings

Particle acceleration oscillates around the effective mass prediction.

Oscillations are observable over Bloch timescales in cold atom experiments.

Neglecting Zener tunneling, the theory accurately describes initial dynamics.

Abstract

We study the behaviour of the expectation value of the acceleration of a particle in a one-dimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states that include the interband mixing induced by the force. This approach allows us to understand the behaviour of the wavepacket, which responds with a mass that is initially the bare mass, and subsequently oscillates around the value predicted by the effective mass. If Zener tunneling can be neglected, the expression obtained for the acceleration of the particle is valid over timescales of the order of a Bloch oscillation, which are of interest for experiments with cold atoms in optical lattices. We discuss how these oscillations can be tuned in an optical lattice for experimental detection.