中文摘要：

理论分析了单电子白旋与碳纳米管机械谐振器之间的耦合对系统动力学行为的影响。用一个主方程，通过半经典的方法具体研究了系统在有量子位一谐振器耦合和没有耦合时平均声子占有数随频率失谐的变化情况、在不同耦合强度时对比了系统在旋波近似和非旋波近似下平均声子占有数随频率失谐的变化情况。在有耦合的情况下，平均声子占有数在共振时，产生了一个分裂，而且在分裂峰值的附近出现了双稳态。通过对碳纳米管谐振器平均声子占有数的分析发现，旋波近似和非旋波近似在耦合强度较弱的情况下能够很好地吻合。当系统进入超强耦合时，旋波近似不再有效，此时非旋波项变得不可忽略。

英文摘要：

The dynamic behavior of system which influenced by the coupling between the single electron spin and carbon nanotube mechanical resonator was theoretically analyzed. By means of a master equation, average phonon occupation number as functions of the frequency detuning under the case with and without qubit-oscillator coupling was investigated via a semiclassical approach. The variation of average phonon occupation number as functions of the frequency detuning under the case with and without rotating-wave approximation was compared for different coupling strength. For coupling system, average phonon occupation number occurs a splitting phenomenmon when resonance, simultaneously, a bistable state was observed near the splitting peak. By analysing the average phonon occupation number of the carbon nanotubes resonator, it was found that rotating-wave and non-rotating-wave approximation can coincide with each other very well under the weak coupling strength. However, the non-rotating-wave approximation term must be considered in the ultrastrong coupling system due to the rotating-wave approximation is no longer effective.