Study On The Quantum Phase Transition And Dynamics In Several Quantum Systems

The main target of quantum information science is to achievepractical quantum communication and quantum computation. But thequantum systems inevitably interact with the external environmentwhich would lead to the quantum system decoherence, in the actualquantum information processing. Therefore, in order to find a way toovercome decoherence phenomenon, systematic studies on thedynamics of open system become the major task of quantuminformation science. The quantum system shall present differentdynamical properties under different environments. The coherenceof the system that experiences a Markov process would losemonotonously if the environment meets the Born-Markovapproximation. However, for some environment models, the quantumcoherence of the systems can be temporarily restored because thoseenvironments have memory effects on the state information of thesystems. The property of non-Markovian is very common in the actualquantum information processing.In this paper, the dynamics of two typical environment modelswere studied in quantum information processing. By Using anon-Markovian measure based on the revivals of the volumes of thequantum states, we calculated the Non-Markovianity of spin channel under the common spin environment. We found that for theHeisenberg spin channel: the Non-Markovianity decreasesexponentially with the increase of the environment parameter,decreases with the increase of the temperature for thermal channel;we also found that because of the odd-even effect, theNon-Markovianity declines non-monotonously with the increase of thechannel length. Furthermore, oscillatory behaviors of theNon-Markovianity were demonstrated with the variation of themagneticfield, and we found that the non-Markovianity could beenhanced greatly due to some specific magneticfield for the groundstate channel. But for the XY model, the Non-Markovianity decreasesmonotonously with the increase of the environment parameter, thechannel length, and its Non-Markovianity is independent with thetemperature for thermal channel.Finally, for the coupled two-level atoms in a single cavity, wediscussed its quantum phase transition and the ground statecorrelation. Firstly, without the rotating-wave approximation, thequantum phase transition and the ground state correlation of themodel were investigated in the framework of meanfield approach.Then the normal-superradiant phase boundary was obtained byminimizing the scaled ground state energy. In addition, the pairwisequantum discord and the classical correlation were also calculated.