Enhanced micromotion compensation using a phase-modulated light field

We investigate sideband spectroscopy of a trapped ion using a probe laser phase modulated at the trap drive frequency. The enhanced sensitivity of our technique provides us 1000-fold improvement in our control of excess micromotion. It allows us to monitor the evolution of stray fields on a timescale of a few minutes and detect differential phases of $5\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{rad}$ between applied ac potentials. We also demonstrate the ability to suppress Doppler shifts from excess motion to well below the limit imposed by the intrinsic motion of the ion in its motional ground state. The technique we introduce can be readily implemented in any ion-trap system that utilizes sideband spectroscopy for micromotion compensation and can be seamlessly integrated into experiments in a fully automated way.