Geometric Phases for Mixed States in Trapped Ions

Abstract

The generalization of geometric phase from the pure states tothe mixed states may have potential applications in constructing geometricquantum gates. We here investigate the mixed state geometric phases andvisibilities of the trapped ion system in both non-degenerate and degeneratecases. In the proposed quantum system, the geometric phases are determinedby the evolution time, the initial states of trapped ions, and the initialstates of photons. Moreover, special periods are gained under which thegeometric phases do not change with the initial states changing of photonparts in both non-degenerate and degenerate cases. The high detectionefficiency in the ion trap system implies that the mixed stategeometric phases proposed here can be easily tested.