  A novel symplectic algorithm is proposed to solve the Maxwell-Schr\"odinger
(M-S) system for investigating light-matter interaction. Using the fourth-order
symplectic integration and fourth-order collocated differences,
Maxwell-Schr\"odinger equations are discretized in temporal and spatial
domains, respectively. The symplectic finite-difference time-domain (SFDTD)
algorithm is developed for accurate and efficient study of coherent interaction
between electromagnetic fields and artificial atoms. Particularly, the
Dirichlet boundary condition is adopted for modeling the Rabi oscillation
problems under the semi-classical framework. To implement the Dirichlet
boundary condition, image theory is introduced, tailored to the high-order
collocated differences. For validating the proposed SFDTD algorithm,
three-dimensional numerical studies of the population inversion in the Rabi
oscillation are presented. Numerical results show that the proposed high-order
SFDTD(4,4) algorithm exhibits better numerical performance than the
conventional FDTD(2,2) approach at the aspects of accuracy and efficiency for
the long-term simulation. The proposed algorithm opens up a promising way
towards a high-accurate energy-conservation modeling and simulation of complex
dynamics in nanoscale light-matter interaction.
