Manipulation of single electron spin in a GaAs quantum dot through the application of geometric phases: The Feynman disentangling technique

TL;DR

This paper analytically and numerically investigates how to manipulate a single electron spin in a GaAs quantum dot using geometric phases, revealing conditions for complete spin-flip via spin-orbit interactions.

Contribution

It provides exact analytical solutions for spin-flip probabilities in specific spin-orbit coupling scenarios and numerical analysis for mixed couplings using the Feynman disentanglement technique.

Findings

Spin-flip probability is higher with mixed spin-orbit couplings.

Complete spin-flip occurs only with symmetric Rashba and Dresselhaus couplings.

Analytical expressions are derived for special coupling cases.

Abstract

The spin of a single electron in an electrically defined quantum dot in a 2DEG can be manipulated by moving the quantum dot adiabatically in a closed loop in the 2D plane under the influence of applied gate potentials. In this paper we present analytical expressions and numerical simulations for the spin-flip probabilities during the adiabatic evolution in the presence of the Rashba and Dresselhaus linear spin-orbit interactions. We use the Feynman disentanglement technique to determine the non-Abelian Berry phase and we find exact analytical expressions for three special cases: (i) the pure Rashba spin-orbit coupling, (ii) the pure Dresselhause linear spin-orbit coupling, and (iii) the mixture of the Rashba and Dresselhaus spin-orbit couplings with equal strength. For a mixture of the Rashba and Dresselhaus spin-orbit couplings with unequal strengths, we obtain simulation results by solving numerically the Riccati equation originating from the disentangling procedure. We find that the spin-flip probability in the presence of the mixed spin-orbit couplings is generally larger than those for the pure Rashba case and for the pure Dresselhaus case, and that the complete spin-flip takes place only when the Rashba and Dresselhaus spin-orbit couplings are mixed symmetrically.