Geometric phase of spin-1 in a rotating magnetic field

Xin Li

Chang-Tan Xu, J.-Q. Liang

Edmund Meyer, Russell Stutz, Laura C. Sinclair +3 more

Xiaoyan Zhang, Lian Hu

The quantum phase and the related fields have attracted considerable attention. The geometric phase of spin-1/2 particle in the magnetic field has been discussed comprehensively, but few of spin-1. In this paper, the exact solution of spin-1 was obtained by using rotational frame method. The problems of the Rabi oscillation, dynamical phase, and geometric phase were solved.

Apoorva G. Wagh, Veer Chand Rakhecha

M. Amniat-Talab, Hossein Rangani Jahromi

We investigate how to obtain a non-trivial geometric phase gate for a two-qubit spin chain, with Ising interaction in different magnetic fields. Indeed, one of the spins is driven by a time-varying rotating magnetic field, and the other is coupled with a static magnetic field in the direction of the rotation axis. This is an interesting problem both for the purpose of measuring the geometric phases and in quantum computing applications. It is shown that the static magnetic field does not change the adiabatic states of the system, and it does not affect the geometric phases, whereas it may be used to control the dynamic phases. In addition, by considering the exact two-spin adiabatic geometric phases, we find that a non-trivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with opposite directions of the magnetic fields, opposite signs of the interaction constant and the phase shift of the rotating magnetic field. In addition, in the non-adiabatic case, starting with a certain initial state, a cycle can be achieved and thus the Aharonov–Anandan phase is calculated.