The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ...The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.展开更多
We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator.Highly distinctive and unique geometric pa...We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator.Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons.These patterns are in excellent agreement with a simulation using the Tavis-Cummings model,and allow us to readily identify different parameter regimes for both qubits in the detuning space.This method could potentially be an important component in the overall spectroscopic toolbox for quickly characterizing certain collective properties of multiple cavity quantum electrodynamics(QED)coupled qubits.展开更多
文摘The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.
基金supported by the National Key Research and Development Program of China(2016YFA0301700)the National Natural Science Foundation of China(61922074,11674300,61674132,11625419 and 11804327)+2 种基金the Strategic Priority Research Program of the CAS(XDB24030601)the Anhui Initiative in Quantum Information Technologies(AHY080000)financial support by U.S.ARO through Grant No.W911NF1410346 and No.W911NF1710257。
文摘We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator.Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons.These patterns are in excellent agreement with a simulation using the Tavis-Cummings model,and allow us to readily identify different parameter regimes for both qubits in the detuning space.This method could potentially be an important component in the overall spectroscopic toolbox for quickly characterizing certain collective properties of multiple cavity quantum electrodynamics(QED)coupled qubits.
