On the entanglement and engineering phase gates without dynamical phases for a two-qubit system with Dzyaloshinski-Moriya interaction in magnetic field

Abstract

We calculate Berry phases and entanglement of adiabatic states for a two spin-1/2 system described by the Heisenberg model with Dzyaloshinski-Moriya (DM) interaction; one of the spins is driven by a time-varing rotating magnetic field and the other is coupled with a static magnetic field. This static magnetic field can be used for controlling as well as vanishing the Berry phases and entanglement of the system state. Besides, we show that the Berry phase and entanglement are not always exact but useful to detect energy levels approach. Additionally, we find that a nontrivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with the opposite direction of the static magnetic field, opposite signs of the exchange constant as well as DM interaction, and a phase shift of the rotating magnetic field. This unitary transformation presents a two-qubit geometric phase gate.