Controlling the rf phase error induced micromotion in Paul trap

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.