Theoretical Study On The Entanglement And Geometric Phase In Bipartite Systems

With the rapid development of quantum information and quantum computation,the quantum theory has attracted more and more attention as an important physical resource. Quantum entanglement,geometric phase and quantum feedback control have been studied extensively in theory.Furthermore,their wide applications were rediscovered as a new resource to manipulate the quantum system in various physical research field.In this thesis, the geometric phase and entanglement properties in a bipartite system have been discussed, respectively.This discussions lead to some interesting results,which shed light on understanding the physical implications of geometric phase and quantum entanglement,it also inspires us how they can be applied in quantum information experiment.The dissertation consists of seven chapters,and the main contents are given in Chapters 3 through 6.In Chapter 1 and Chapter 2,the background of our study and the importance of the investigation are introduced,the general situation of quantification of quantum information theory,entanglement,geometric phase,as well as quantum feedback control are briefly described. The geometric phase in a nonunitary,nonadiabatic,noncyclic system are described in detail.In Chapter 3,a detailed investigation on the Berry phase in a bipartite system which consists of two coupled spin-1/2 particles with an X-X-Z term coupling is introduced.The Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem are calculated.The results show that the Berry phase of the bipartite system is a weighted sum of the geometric phases of the subsystems.And with the coupling constants tend to infinity the phases go to zero,this confirms the prediction given by Yi previously (Phys.Rev.Lett.92,150406(2004)) with a specific subsystem-subsystem coupling.In Chapter 4,a few features of entanglement of two types of particles coupled through a nonlinear interaction are presented.It is shown that the entanglement created by the nonlinear interaction can reflect nonlinearity of the system.Possible observation of our prediction in a double-well trapped Bose-Einstein condensates is discussed.In Chapter 5,the effect of feedback control on geometric phase in a two-level dissipative system is studied.The dependence of the phase on the feed-back parameters are calculated and discussed.The results suggested that we can manipulate the phase by a properly designed feedback control.For small and large atomic dissipative rates with respect to the amplitude of the driving magnetic fieldμB₀,the geometric phase is a periodic function of the feedback parameters,the physics behind these features is also presented.In Chapter 6,the dynamics and entanglement of a two-level atom trapped in a cavity with a movable mirror is studied.The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom.This optical effect by showing the population of the atom in its internal degrees of freedom as a function of time is studied.On the other side,fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration,leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.Finally,the conclusions and discussions are presented.