Generation and detection of non-Abelian matrix Berry phases through manipulation of electric confinement potential of a semiconductor quantum dot

TL;DR

This paper demonstrates how to generate and detect non-Abelian matrix Berry phases in semiconductor quantum dots using purely electrical manipulation of the confinement potential, highlighting their geometric nature and potential for quantum control.

Contribution

It introduces a method to produce and measure non-Abelian Berry phases electrically in quantum dots, expanding the toolkit for quantum information processing.

Findings

Matrix Berry phases can be generated by changing the quantum dot shape.

The phases are characterized by two geometric parameters.

Detection can be achieved through transport measurements.

Abstract

A matrix Berry phase can be generated and detected by {\it all electric means} in II-VI or III-V n-type semiconductor quantum dots by changing the shape of the confinement potential. This follows from general symmetry considerations in the presence of spin-orbit coupling terms. The resulting 2 x 2 matrix Berry phase can be characterized by two numbers of geometric origin. We investigate how these parameters depend on the shape and area of closed adiabatic paths. We suggest how the matrix Berry phase may be detected in transport measurements.