基于波导QED的微波量子态传输与操控理论研究

Superconducting quantum circuits are considered as one of best candidates for quantum information processing. Waveguide QED, based on superconducting quantum circuits and one dimensional microwave transmission lines, recently becomes more important in superconducting quantum information processing. In this proposal, we will study the transport and manipulation of microwave quantum states in the microwave waveguide QED. We will derive theoretical models for the interaction between different superconducting quantum circuits and transmission lines, write out the interaction Hamiltonians between superconducting multilevel systems and transmission lines. We will develop input-output theories of the microwave photons in the systems of microwave waveguide QED, and study the transports of different nonclassical microwave quantum states (e.g., number states, weak coherent states). Based on the nonlinear quantum optics, we will derive the quantum optics models for the interaction between superconducting quantum circuits and several transmission lines, study the generation and the output for microwave nonclassical states (e.g., entangled states). We will design indirectional or chiral devices for the transport of single microwave photons, and also derive theoretical models for the transports of microwave states in a small quantum network based on microwave waveguide QED.

超导量子电路被认为是实现量子信息处理最有前景的系统之一。最近兴起的基于超导量子电路和一维微波传输线的波导QED在超导量子信息处理中变得越来越重要。本项目拟对基于超导量子电路的波导QED系统中微波量子态的操控与传输展开研究，具体包括：基于各种超导量子电路构建它们与波导耦合的波导QED系统理论模型，导出波导与多能级超导量子电路相互作用的哈密顿量；发展波导QED系统中微波光子的输入输出理论，研究各种非经典微波（如数态和弱相干态）光子的传输性质；基于非线性量子光学理论，导出超导量子电路与多个传输线耦合的非线性量子光学模型，研究微波非经典态（如纠缠态）的产生与输出；设计微波单光子定向传输器件，给出微波在基于微波QED系统的小型量子网络中的传输理论。

我们主要研究了微波波导的性质和波导与超导量子比特电路的相互耦合，提出了微波单光子态在微波波导中的受控单向传输理论，发现由多个超导量子比特构建的具有拓扑性质的多能级非线性量子系统可以用来提高并调控微波波导中单光子传输的单向散射与吸收。我们用多个耦合超导量子比特构建了具有拓扑保护性质的多能级超原子，发现此原子在波导中的亚辐射边缘态具有拓扑保护性。针对普通微波波导结构单一的弱点，构建了具有拓扑性能的波导，开辟了关于拓扑波导与物质相互作用的研究方向，发现拓扑波导不仅可以完美地传输单量子态而且也能够完好地传输任意的纠缠态。研究了利用超导量子比特构建的拓扑SSH模型和Kitaev模型与波导的耦合，发现微波波导环境能够改变量子物质的拓扑性质，也可用来调控拓扑态，进一步发现强耦合下拓扑耗散系统中仍可能有拓扑相变等。我们也系统地研究了量子微波波导的输入输出及其网络理论。与实验物理学家合作研究了微波波导对表面声波与超导量子比特耦合的探测，也研究了超导量子比特与受驱动微腔耦合系统在微波波导中的共振荧光问题。

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