The Theoretical Schemes Of Simulating Abelian And Non-Abelian Gauge Fields In Superconducting Quantum Circuits

Many-body quantum systems can hardly be simulated by classical computers due to the exponential explosion of Hilbert space which cost enormous source of the memory and the time of the computation. Meanwhile, many quantum systems cannot be studied directly with the state-art-of-technology. Therefore, the concept of quantum simulation,simulating a target quantum system by a well-controlled artificial quantum system, is proposed. The superconducting quantum circuit is an artificial quantum systems with macroscopic size fabricated by the traditional electron-beam or optical lithography. Due to its controllability, flexibility, the ability of integration, and the cooperation of the strong photon-photon interaction via the strong coupling between qubits and transmission line resonators, superconducting quantum circuits is becoming a promising platform of quantum simulation. In this thesis, we focus on the quantum simulation by the superconducting quantum circuits, including following aspects:Firstly, we introduce the concepts of quantum simulation, the artificial quantum systems exploited to quantum simulation, and the basic knowledge of superconducting quantum circuits.Secondly, we introduce a scheme of implementing artificial Abelian gauge fields via the parametric conversion method in a ring of superconducting transmission line resonators(TLRs) coupled by grounding superconducting quantum interference devices(SQUIDs) proposed by Wang et al. The dynamic modulations of the SQUIDs can induce effective magnetic fields for the microwave photons in the TLR ring through the generation of the nontrivial hopping phases of the photon hopping between neighboring TLRs. To demonstrate the synthetic magnetic field, the realization and detection of the chiral photon flow dynamics in this architecture under the influence of decoherence are studied. They further propose a quantitative measure for the chiral property of the photon flow. Beyond the level of qualitative description, the dependence of the chiral flow on external pumping parameters and cavity decay are characterized.Thirdly, as Wang et al. considered the Abelian gauge field. we further archive theartificial non-Abelian gauge field via the dynamic modulation methods where double-mode TLRs and multi-frequency modulation are used. The double-mode TLRs have two photonic modes, i. e. spin-up and spin-down. Different from the Abelian case,the two photonic modes experience a SU(2) transformation after the circulation in closed loop, and the unitary transformation can be treat as the non-Abelian gauge field. We numerically simulate the chiral flow of the two photonic modes. Due to its flexibility, the chiral flow of the two photonic modes can be controlled independently, i. e. the photons of spin-up and spin-down either flow in one direction, or flow in opposite direction. This can be understood as a versatile spin Hall effect, and out scheme may pave an alternative way to the simulation of topological insulators.