Geometric Phases Of Impurity Qubits And Their Manipulation In Bose-einstein Condensates

The impurity-doped Bose-Einstein condensate(BEC)is a typical hybrid quantum system which consists of a microscopic impurity atom and a macroscopic BEC.Such a micro-macro hybrid quantum system is providing a ideal platform for studying fundamental problems in quantum mechanics,generating and manipulating various quantum effects,and developing concepts in quantum information processing due to the quantum advantages of subsystems and the superb controllability of various interaction parameters,which can be combined to form more new advantages.In this thesis,I study the geometric phase of qubits in impurity-doped BEC in which the single impurity atom can act a qubit.The main results of the thesis are included as follows.1.The geometric phase of a single impurity qubit in a BEC.We present an analytical solution of the one-component impurity-doped BEC system,and obtain the analytical expression of the impurity qubit.It is indicated that the geometric phase of the impurity qubit can be controlled in terms of the initial-state parameters of the impurity-BEC system,the impurity-BEC coupling constant and the initial-state entanglement of the hybrid quantum system.It is found that the geometric phase of an impurity qubit in one evolution period would be zero when the system is initially in a“dark state”of the system.2.The geometric phase of two Rydberg impurity qubits in a BEC.We obtain a general analytical expression of the geometric phase of two Rydberg impurity qubits in a BEC for three types of different initial states of the system.The first case is that the two qubits is initially in a Bell-type entangled state without the initial entanglement between the qubits and BEC.The second case is that the initial state of the system is an entangled state among three components of two qubits and the BEC.The second case is that one qubit is initially entangled with the BEC without the initial entanglement between two qubits.It is indicated that the geometric phase of the qubits can be manipulated in terms of the initial-state parameters,the impurity-BEC coupling constant and the initial-state entanglement of the hybrid quantum system.It is found that both of the four independent free bases and four Bell bases of the two qubits are“dark state”of the system with respect to the geometric phase of the qubits.It is shown that the initial-state entanglement can be detected by measuring the geometric phase of the qubits.