Ion trajectory analysis for micromotion minimization and the measurement of small forces

For experiments with ions conned in a Paul trap, minimization of micromotion is often essential. This is the case, for example, for experiments in quantum information science using trapped ions, in combined traps for neutral atoms and ions, and for precision measurements using trapped ions. In order to diagnose and compensate micromotion we have implemented a method that allows for nding the position of the radio-frequency (RF) null reliably and eciently, in principle, without any variation of direct current (DC) voltages. We apply a trap modulation technique and tomographic imaging to extract 3d ion positions for various RF drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical eect as opposed to ecient numerical minimization in a high-dimensional parameter space. The precise position determination of an harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with an accuracy of 135 yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well-suited to be used with surface-electrode traps.