Quantum theory of shuttling instability in a movable quantum dot array

TL;DR

This paper investigates the shuttling instability in a movable quantum dot array, extending previous models to broader parameters and interpreting results through Wigner distributions, highlighting the crossover nature of the instability.

Contribution

It extends prior work on quantum shuttling instability to a wider parameter regime and provides a direct interpretation using Wigner distributions.

Findings

Instability is a crossover phenomenon, not a sharp transition.

Numerical methods effectively analyze the quantum shuttling behavior.

Results generalize previous models to broader conditions.

Abstract

We study the shuttling instability in an array of three quantum dots the central one of which is movable. We extend the results by Armour and MacKinnon on this problem to a broader parameter regime. The results obtained by an efficient numerical method are interpreted directly using the Wigner distributions. We emphasize that the instability should be viewed as a crossover phenomenon rather than a clear-cut transition.