Berry Phase of Composite System Induced by Time-Dependent Interaction

The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system: one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system (qubit) is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.