囚禁单离子的量子阻尼运动
Quantum damping motion of a single trapped ion
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摘要: 用包含偶极和四极虚势能项的非厄米哈密顿算符来描述Paul阱中囚禁阻尼单离子在静电场下的量子运动.通过导出和分析系统的精确解,得到在PT对称和不对称情形下的不同实能谱与稳定量子态,以及PT不对称情形的虚能谱和衰减量子态,同时给出相应于不同态的参数区域和存活概率.结果发现该非厄米系统外场参数能惟一确定量子稳定态并导致波函数形态变化,据此提出非相干操控相应量子跃迁的方法.让量子态衰减导致的离子位置期待值的衰减与经典阻尼谐振子的衰减一致,得到虚势能参数与经典阻尼参数的对应关系.所得结果将进一步丰富具有广泛应用背景的囚禁离子动力学.Abstract: Classical motion of a single damped ion confined in a Paul trap is usually described by a damped harmonic oscillator model. We report the treatment of quantum damping motion of the system via a non-Hermitian Hamiltonian with dipole and quadrupole imaginary potential. By deriving and analyzing the exact solution of the system, we obtain the different real energy spectra and stable quantum states for the PT symmetry and asymmetry cases, as well as the imaginary spectrum and decaying quantum state for the PT asymmetry case. The corresponding imaginary energy parameter region and the survival probability are investigated. We find that the non-Hermitian system parameters of the external filed uniquely determine the quantum stable states and lead to the new characteristic of the morphology of wave function. Based on these properties, we propose a method of incoherently manipulating quantum transitions between the quantum stable states. By setting the decayed expectation value of ion position to be the same as the decayed displacement of the classical damped harmonic oscillator, we obtain the correspondence between the imaginary potential strength and the classical damping parameters. The results will enrich the quantum dynamics of the damped trapped ions, which may be useful in a wide application field.
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