Excess micromotion of trapped ions leads to several adverse effects, such as modulating the absorption spectrum, shifting the transition frequency, and causing extra motional heating of ions. Moreover, it is hard to deal with, if there is no rf null point in a Paul trap. In this paper, two methods are proposed to control these adverse effects introduced by excess micromotion. The first method can eliminate the spectral modulation effect while keeping the micromotion unaffected by phase modulating the related laser. The second one can control the amplitude of micromotion or compensate it completely to remove the frequency shift effects by applying ac voltage to the dc electrodes. With these two methods, we are not only able to control the micromotion amplitude in a Paul trap without rf null point, but also to realize effective sideband cooling and quantum state manipulating when ions still undergo large excess micromotion.

中文翻译：

---

控制保罗阱中射频相位误差引起的微动

捕获离子的过度微动会导致多种不利影响，例如调制吸收光谱、改变跃迁频率以及导致离子的额外运动加热。而且，如果保罗陷阱中没有射频零点，则很难处理。在本文中，提出了两种方法来控制由过度微动引起的这些不利影响。第一种方法可以消除光谱调制效应，同时保持微动不受相位调制相关激光的影响。第二种可以控制微动幅度或完全补偿微动幅度，通过向直流电极施加交流电压来消除频移效应。使用这两种方法，我们不仅能够在没有 rf 零点的情况下控制 Paul 阱中的微动幅度，