Theoretical Study On The Dynamics Of Distant Systems In 1D Waveguides

Quantum networks are considered as the typical backbone of distributed quantum com-puting and quantum communication,which are composed of quantum nodes and quantum channels.Such quantum channels have the advantage of not only directly exchanging quan-tum information between nodes but also distributing entanglement over the whole network.The previous mentioned distribution of quantum states across the whole network can lead to non-local and non-classical in the network.These properties not only enable fundamental tests of the predictions of quantum theory,but also serve as the basis for quantum com-munication and quantum computation.Therefore,quantum networks allow users to perform quantum information tasks in ways which are not possible with current conventional technolo-gies.The implementation of quantam networks becomes a key challenge for quantum science.In many typical physical systems,superconducting circuit systems are stronger coupling and greater scalability than the usual cavity QED system,which makes the systems one of the leading platforms for implementing distributed quantum networks.Based on above facts,this thesis focuses on the non-local interaction in the quantum network system,and explore the dynamics of the non-local quantum network and related applications in the superconducting circuit system.In this cdissertation,the concepts and history of quantum networks are firstly introduced.By comparing with classical networks,we briefly review the characteristics,advantages and research significance of quantum networks,and introduce several existing physical platforms for realizing quantum networks.Secondly,we focus on the research status of superconducting circuits system,and introduce several circuits with different structures and their applications in quantum networks.Then,we review some physical concepts and basic theories that will be used in this thesis,such as basic concepts of the quantum state and coherent state,scattering theory and input/output relation,Markov master equation method.Later,we propose a single-photon.routing scheme which uses two distant atoms.Based on the quantum interference,the photon output can be controlled by adjusting the atomic detuning,distance and coupling strength without any classical field.Unlike the single-atom scheme,when the system satisfies the standing wave condition and specific symmetry,input photon can be perfectly redirected into the specified port.If the system has weak dissipation,it is necessary to select proper atomic detuning to achieve higher efficiency of photon routing.Finally,we propose an exact master equation to describe the distant resonators,and conclude that the physical origin of non-Markovianity is the retardation effects.When the distance can be neglected,the exact solution given by the master equation agrees well with Markovian solution.However,as the distance increases,the deviation from the Markovian situation gradually increases,and the retardation effects play a significant role in the dynam-ics.Similar to the Markovian case,the dark mode still exists in the long-time limit,but the retardation effect will directly affect the final average photon number of dark mode.