Quantum Teleportation Via Photonic Faraday Rotation And Non-Markovian Effect On The Geometric Phase Of A Dissipative Qubit

This thesis is contributed to the study of two parts. In the first part, we propose a practical scheme for deterministically teleporting an arbitrary multipartite pure state, either product or entangled, using Faraday rotation of the photonic polarization in cavity QED system. In the second part, we study the geometric phase of a two-level atom coupled to an environment with Lorentzian spectral density.Firstly, we propose a practical scheme for quantum teleportation in cavity QED system. In quantum teleportation, using an EPR entangled pair as quantum channel, one can transfer one qubit quantum information via delivering two classical bits classical information from the sender to the receiver. Here we can accomplish this protocol by the single-photon input-output process regarding cavities. The interaction between the photons and optical cavities with atoms trapped in leads to the polarization direction of the reflected photon rotating an angle with respect to the input one, named Faraday rotation. Making use of the Faraday rotation, we could establish the entangled channel between photon pulse and the atom in the sender's hands. Based on the channel, a practical teleportation scheme using low-Q cavities and moderate atom-cavity couplings can be realized. The scalability of our scheme to realize the teleportation of an arbitrary multipartite pure state is also proved.Compared with previous proposals for teleportation with decaying cavities, there are some advantageous in ours. Firstly, our scheme could work very well even in the case of moderate Rabi frequencies, and achieve the teleportation perfectly and deter-ministically. Secondly, our scheme, based on the input-output process of single-photon pulses regarding cavities, works in low-Q cavities and only involves virtual excitation of the atoms, which is insensitive to both cavity decay and atomic spontaneous emis-sion. Besides, the Bell-state measurement is accomplished by the Faraday rotation plus product-state measurements, which could much relax the experimental difficulty to realize the Bell-state measurement by the CNOT operation. Finally, our scheme us-ing bipartite entangledment as quantum channels is more robust to decoherence than others based on multipartite entanglement.Secondly, we study the geometric phase of an open two-level atom interacting with an environment with Lorentzian spectral density. The non-Markovian effect on the geometric phase is explored analytically and numerically. In the weak coupling limit the lowest-order correction to the geometric phase is derived analytically and the general case is calculated numerically. It is found that the correction to the geometric phase is significantly large if the spectral width is small, and in this case the non-Markovian dynamics has a significant impact to the geometric phase. When the spectral width increases, the correction to the geometric phase becomes negligible, which shows the robustness of the geometric phase to the environmental white noises. The result shows that the geometric phase in this cavity QED system is fault-tolerant not only against the classical noise induced by the parameter fluctuation but also against the quantum noise. It is significant to the quantum information processing based on the geometric phase.