Research On Extraordinary Topological Physics Induced By Artificial Gauge Field In Superconducting Quantum Circuits

Compared with conventional condensed matter materials and natural atomic systems,the energy level structures of superconducting quantum circuits can be designed and tuned with great flexibility.Moreover,individual superconducting quantum circuit elements can be integrated to form large-scaled arrays based on current microelectronic technology.These advantages make superconducting quantum circuit one of the ideal platforms of simulating certain lattice models in condensed matter physics.Currently,one of the focus problems in quantum simulations is the simulation of artificial gauge fields.The main reason is that,magnetic field plays an important role in condensed matter physics.However,The strength of the realized effective magnetic field can hardly be realized in conventional condensed matter physics.Thus,It is very important to realize the artificial gauge field and to explore the influence of it on topological physics.Based on the above motivation,in this thesis,the scheme for implementing an artificial gauge field in superconducting quantum circuits was introduced.Based on the current parametric coupling technology in superconducting quantum circuits,the experiments of superconducting quantum circuits have realized tunable strength and phase.Then,by using the parametric conversion coupling method,in principle,the time-and site-resolved tunable hopping constants in the proposed architecture can be established,thus providing an ideal platform for investigating the higher-order topological phase transitions induced by continuously varying magnetic field.The numerical calculation further shows that the higher-order topology of the lattice,which manifests itself through the existence of the zero energy corner modes,exhibit exotic and rich dependence on the imposed magnetic field and the inhomogeneous hopping strength.To probe the proposed magnetic-field-induced topological phase transition,the response of the lattice to corner site pumping was studied in the steady state limit.On the other hand,a circuit quantum electrodynamics realization of the complex NonAbelian gauge field was proposed.Going beyond and develop the non-Abelian AharonovBohm(AB)caging concept by considering the particle localization in a one-dimensional multi-component rhombic lattice with non-Abelian background gauge field.In contrast to its Abelian counterpart,the non-Abelian AB cage depends on both the form of the nilpotent interference matrix and the initial state of the lattice.This phenomena is the consequence of the non-Abelian nature of the gauge potential and,thus,has no Abelian analog.Meanwhile,the non-Abelian AB caging can be unambiguously demonstrated through the pumping and the steady-state measurements of only a few sites on the lattice.In conclusion,in this thesis,the effectively quantum simulation of the higher-order topological phase transition induced by artificial Abelian gauge field and non-Abelian AB caging induced by artificial non-Abelian gauge field in superconducting quantum circuit by using the parametric coupling method was disussed.The quantum simulators presented in this paper make full advantage of the tunability,flexibility and integratibility of superconducting circuits and are expected to advance the application of superconducting quantum circuits in the field of topological photonics.