A study of the Aharonov Casher physics of an entangled particle pair

Che-Chun Huang^1*, Seng Ghee Tan², Ching-Ray Chang¹

¹物理系, 國立台灣大學, 台北市, Taiwan
²光電物理系, 中國文化大學, 台北市, Taiwan

* Presenter:Che-Chun Huang, email:f06222009@ntu.edu.tw

Spin interference arising due to the electron phases have been studied for many years. The Aharonov-Bohm or the Altshuler-Aronov-Spivak effects described via the gauge potential the accumulation of the geometric phase for an electron traveling around the magnetic field. The Berry-Pancharatnam physics would in turn describe the generation of the geometric phase via the adiabatically cyclic evolution of the Hamiltonian. One example of which is the process of electron spin locking to the local magnetic fields as the electron propagates. By contrast, an electron precessing about the magnetic field acquires phases in the non-adiabatic manner. Likewise, in what is known as the Aharonov-Casher effect, phase is acquired by electron precessing about the effective magnetic field originating from the spin-orbit coupling.

While all the processes above produce the geometric phase, the dynamic phase is concomitantly generated. In our work, the electron phase is considered to comprise both the geometric and the dynamic. Our focus is on the bipartite states as well as their entanglement physics on the various electron phases. Our study is carried out in a square ring made out of the 2D spin-orbit materials, e.g. the Rashba spin-orbit coupling. In the quantum regime, the system would be a non-Abelian Aharonov-Casher as seen by the electron spin. As far as we know, there has been no previous study of the bipartite states and their entanglement effects on the total phase of a bi-partite pair in the Aharonov-Casher system. We have derived equations for bi-partite states composed of the Bell basis and described the generation and elimination of the geometric and the dynamic phases throughout the square ring. Interesting relations between the geometric and the dynamic phases have also been investigated for numerous initial states and the entanglement strength therein. Our results are thus a compilation of information pertaining to the behavior of electron phases in a non-Abelian system. In terms of applications, our results provide useful insights into the design of devices that could be used to feasibly generate and eliminate electron phases.

Keywords: Geometric phase, Aharonov Casher, Entanglement, Spin