Kinematic Approach to the Geometric Phase of Entangled Qubits under Rashba Spin Orbit Coupling

Ying-Cheng Yang^1*, Seng Ghee Tan², Ching-Ray Chang¹

¹Department of Physics, National Taiwan University, Taipei, Taiwan
²Department of Optoelectric Physics, Chinese Culture University, Taipei, Taiwan

* Presenter:Ying-Cheng Yang, email:d09222002@ntu.edu.tw

We systematically investigate nonadiabatic geometric phases in single- and two-particle quantum systems subject to Rashba and Dresselhaus spin-orbit couplings using the kinematic approach. By preparing different initial states, including Bell states and uniform superposition states, and evolving them under Rashba, Dresselhaus, or combined spin-orbit Hamiltonians, we calculate both geometric and dynamical phases as functions of the propagation azimuthal angle. Using the arctan2(Y/X) function, we find that under specific conditions, the dynamic phase can be eliminated, which leads to characteristic discontinuities of 0 or π in the geometric phase. The analysis is divided into two parts. First, we examine how the geometric phase of entangled spin pairs depends on the propagation angle and on the ratio α/β, where α and β represent the Rashba and Dresselhaus coupling strengths, respectively. Second, we discuss the influence of open system effects on the geometric phase and its potential implications for geometric quantum computation. These results offer new insights into controllable phase engineering in spin-orbit-coupled quantum systems.

Keywords: geometric phase, Rashba spin–orbit coupling, geometric quantum computation