中文摘要：

从描述囚禁离子与驻波激光场相互作用的Jaynes-Cummings（J-C）模型出发,导出了囚禁离子谐振动单量子共振激发相互作用的非线性J-C模型.通过求解这一模型的系统状态随时间变化,数值研究了离子布居数反转的演化规律.结果表明,离子布居数反转演化的崩塌-复原周期与Lamb-Dick参数η和离子在驻波激光场中的位置有关,随着η参数的增大,离子布居数反转的崩塌-复原周期变短,当离子质心的位置从驻波激光场的波节移向波腹时,离子布居数崩塌-复原的周期变长.

英文摘要：

Starting from the Jaynes-Cummings （J-C） model describing the interaction of a trapped ion with a standing-wave laser field, we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excitated resonantly with 1-quantum vibrational mode. After solving the time-dependent states of this model, we study the evolution of population inversion for the ion numerically. It is shown that the period of the quantum collapse and revival of the population inversionis related with the Lamb-Dick parameter and the position of the ion in the standing-wave laser field. With the increasing of the parameter, it will decrease the period of the collapse and revival. When moving the ion from the node of the standing-wave laser to the antinode, the period of the collapse and revival becomes longer.