Study On Localized Characteristics And Topological States Of Photons In Circuit QED Lattice System

Topological insulators are materials with novel properties,which have a different band structure from the traditional insulators.The topological insulators are insulating with band gap in their internal,while the surface is metallic state protected by time reversal symmetry.Topological insulators have become an important research field in condensed matter physics,which have important applications in spintronics and quantum computation.On the other hand,the theoretical and experimental investigations of nonHermitian topological systems have drawn more attentions.A series of novel phenomena have been found,such as bulk-boundary correspondence breaking,non-Hermitian skin effect,fractional topological number.The investigations of the topological and nonHermitian topological systems are mainly based on the solid-state electronic system initially and it is found that the boson particles such as photon and phonon have similar band structure with electron,which make it possible for quantum simulation in bosonic system.The circuit quantum electrodynamics(QED)lattice,as a typical quantum optical system for boson,due to the regime of ultrastrong coupling,the flexibility of adjustable parameters,and the designability of the system structure,has been widely applied to the topological quantum simulation in condensed matter physics.It is also easy to realize the detection of the topological phenomena resorting to the bosonic statistical properties of the circuit QED lattice system.In this dissertation,based on the circuit QED lattice system,we investigate the topological and nontopological states,localized states,and localized characteristics of photons.The main research contents are as follows:i)We investigate the continuous-time quantum walks of single particle in periodically driving incommensurate circuit QED lattice system.It is found that the dynamic process of the quantum walks is affected by the strength of incommensurate potentials and the driving periods of the system.In high-frequency regime,quantum walks of single particle can be highly localized as Anderson localization.We calculate the mean square displacement,which shows that the localized process of the quantum walks presents the zero power-law index distribution.By calculating the mean information entropy,we find that the next-nearest-neighbor interactions make a stricter high-frequency condition for the localization of the quantum walker.Moreover,assisted by the circuit QED latticebased cavity input-output process,the features of localized edge states can be obtained.ii)Based on the coupled circuit QED lattice system,we investigate the topological and nontopological photonic states induced by the interchain coupling.By calculating the energy eigenvalue spectrum and state distributions of the system,the behaviors of topological and nontopological photonic states can be clearly observed.With the increase of the coupling strength,we find that the topologically nontrivial interface states of the system gradually disappear and finally become two nontopological impurity states.Meanwhile,two new topologically nontrivial interface states appear next to the sites of two bound states.We present the phase diagram to illustrate the characteristics of phase transition of the system.Moreover,assisted by the circuit QED lattice-based cavity inputoutput process,we can obtain the properties of these photonic states by detecting the average photon number of the cavity filed.iii)Based on the non-Hermitian QED lattice system,we investigate the influence of the change of nonreciprocal coupling strengths on the energy eigenvalue spectrum.It indicates that the localized photonic states with special energy eigenvalues,such as the zero-energy edge states,and interface and bound states with pure imaginary energy eigenvalues,appear in the system with increase of the nonreciprocal coupling strengths.We show the states distributions in different topological regimes,and the change of these photonic states can be described by the interference patterns.Moreover,through investigation of the dynamic process of photonic states for arbitrary lattice site,we find that the nonreciprocal couplings break the trapping effect of the edge states,which present a gathering effect for the dynamic process of photonic states,and this effect is unaffected by the on-site defect potentials.