Abstract
The geometric phase, in particular the Berry phase, in an entangledstate of five spin-1/2 particles is studied. A time-dependent magneticfield is applied to control the time evolution of the cluster. Using themethod of algebraic dynamics, we calculate the non-adiabatic geometricphase or Berry phase and the degeneracy energy levels when the magneticrotates around Z axis. Based on the exact analytical solutions, weshow how the Berry phase of the entangled state of this cluster dependson the external magnetic field parameters ω (the angular velocityof the rotating magnetic field) and θ (the angle between themagnetic field and Z axis).
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