Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

TL;DR

This paper explores how non-Abelian holonomies generated by spin-orbit coupling in n-type semiconductor quantum dots can be used for single electron control, highlighting the role of potential distortion in enabling Berry phases.

Contribution

It demonstrates that a distorted 2D harmonic potential can induce non-Abelian Berry phases in quantum dots with spin-orbit interactions, enabling electron manipulation.

Findings

Double degeneracy alone does not produce non-Abelian Berry phases.

Distorted harmonic potentials can generate non-Abelian Berry phases.

Optical measurements can test the presence of these Berry phases.

Abstract

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.