Interacting spin pairs in rotational magnetic fields and geometric phase

张晓燕, 胡连

Chang-Tan Xu, J.-Q. Liang

Yu Shi

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.

Xiangyu Ge, Miki Wadati

The entanglement dependence of the geometric phase is studied in the case of two interacting spins under a time-independent magnetic field. A general entanglement-dependence geometric phase is formulated. This unification scheme covers the analyses by Sj\"oqvist for precessing spins and for isotropically interacting spins. From the general formula, the geometric phase is determined explicitly for an isotropic interaction and nonzero magnetic field.

Apoorva G. Wagh, Veer Chand Rakhecha