Study On Topological Property And Topological Quantum State Transfer In Micro-nano Optical System

Topological insulator is a new form of matter that behaves as an insulator in its interior while behaving as a metal on its boundary and has been one of the most intriguing research fields in condensed-matter physics.The significant difference between traditional insulators and topological insulators is the presence of the gapless edge states in the nontrivial phase region with a nontrivially topological index.Generally,the system undergoes a topological phase transition accompanied by the changes of topological numbers.In recent years,the realization of band structures with geometric and topological characteristics in cold atoms and Fermi systems has made great progress in experiments.However,analogous topological effects can be obtained by applying the geometrical and topological ideas to some micronano optical systems.Some micro-nano optical systems have become the wellestablished platforms for realizing various novel topological models and exploring topological effects due to the flexibility of adjustable parameters and the designability of the system structure,such as optical waveguides,circuit QED lattices and optomechanical systems.In addition,topological insulator also has many potential applications in quantum information processing and quantum computing,and topological quantum computing has become one of the important approaches for constructing fault-tolerant quantum computer.Topological edge states are protected by topological invariants and symmetries,several different quantum state transfer schemes are realized in various micro-nano optical systems by employing topologically protected edge states as channels,and the simulation and detection of various topological models can be easily implemented resorting to the properties of micro-nano optical systems.In this dissertation,based on some micro-nano optical devices,we investigate the energy band structure of Hermitian and non-Hermitian systems,topological phase,topological invariant and topological state transfer.The main research contents are as follows:i)We investigate the energy band structure and exceptional ring based on a twodimensional superconducting circuit lattice.In the case of a Hermitian Hamiltonian,by modulating the on-site potential,we find that the single Dirac point splits into four degenerate points.For the non-Hermitian situation,we find that the flat band is significantly destroyed by the presence of gain and loss and the introduction of long-range coupling makes the zero-energy flat band survive because of the protection of chiral symmetry.Meanwhile,the purely real spectrum can be transformed into the purely imaginary spectrum via modulating the parameters appropriately.Furthermore,when the nonreciprocal next-nearest-neighbor couplings are continuously modulated,the two exceptional rings become one and a Dirac-like point occurs inside the exceptional ring.ii)Based on a one-dimensional optomechanical lattice,we achieve the mapping of periodically modulated Su-Schrieffer-Heeger(SSH)model.We show the energy-eigenvalue spectrum and the winding number to demonstrate two topologically distinct phases of the SSH model.Specifically,we realize the photon-phonon conversion process via the topologically protected edge channel with a controllable conversion efficiency.By calculating the fidelities of the photon-phonon conversion,we find that our system is more robust against the on-site defect potential throughout the overall lattice sites than the edge lattice sites.Photon-phonon conversion can still be realized within a minor parameter range.Interestingly,the large defect added into the edge sites can induce additional quantum channels to achieve the photonphoton transfer and the phonon-phonon transfer.iii)We investigate the topological properties of the circuit-QED lattice system and find that,the system undergoes a topological phase transition accompanied by the changes of Chern numbers from 2 to-1.For different lattice sizes,we show the energy eigenvalue spectra and the probability distributions of edge states.Moreover,we reveal that,depending on the strictly adiabatic evolution of the time-dependent Hamiltonian,several different topological state transfers between the first two sites and the last two sites can be achieved by employing the topologically protected edge states as the transfer channels.Further,by using resonatorbased input-output process,we detect the photonic topological edge state by measuring the average photon number in the steady state.