Environmental effects on quantum geometric phase and quantum entanglement

Günhan, Ali Can
We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP, is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GP; its stability decreases as the magnetic field strength increases. (By decrease in stability what we mean is the increase in the time rate of change of GP.) We showed that this decrease can be very rapid, and so it could be impossible to make use of it as a quantum logic gate in quantum information theory (QIT). To see if these behaviors differ in different environments, we analyze the same system for a fixed temperature environment which is under the influence of an electromagnetic field in a squeezed state. We find that the general dependence of GP on magnetic field does not change, but this time the effects are smoother. Namely, increase in magnetic field decreases the stability of GP also for in this environment; but this decrease is slower in comparison with the former case, and furthermore it occurs gradually. As a second problem we examine the entanglement of two atoms, which can be used as a two-qubit system in QIT. The entanglement is induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole-dipole interaction. The two atoms are assumed to be in ordinary vacuum and the third system is taken as influenced by a certain environment. We examined different types of environments. We show that the steady-state bipartite entanglement can be achieved in case the environment is a strongly fluctuating, that is a squeezed-vacuum, while it is not possible for a thermalized environment.


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Citation Formats
A. C. Günhan, “Environmental effects on quantum geometric phase and quantum entanglement,” Ph.D. - Doctoral Program, Middle East Technical University, 2008.