Abstract: In the system composed of a two-level atom with a single-mode cavity, the density matrix and population of the atom in the excited state are obtained under the condition of normalization, and the quantum speedup formula of the system evolution is given. Longitudinal speedup and transverse speedup are used to describe the dynamics evolution process of the system, and influence of the coupling strength between the atom and cavity as well as the evolution time on the speedup of system evolution are analyzed numerically. Results show that the coupling between the atom and the cavity can speed up the longitudinal evolution of quantum state, and with the increase of evolution time, the transverse speedup of quantum state increases along with periodic oscillation.

Key words: quantum optics, dynamics evolution, quantum speedup, quantum speed limit time