Asymmetric dynamical localization and precision measurement of BEC micromotion

We employ a Bose Einstein Condensate (BEC) based atom-optic kicked rotor to generate an asymmetrically localized momentum distribution that depends upon initial velocity of the BEC. Asymmetric features are shown to arise from the early-time dynamics induced by the broken parity symmetry and, asymptotically freeze as the dynamical localization stabilizes. The asymmetry in the momentum distribution critically depends upon the initial launch velocity and is sensitive to very small initial velocities ('micromotion') of the BEC. In this work, we also perform a precise measurement of the 'micromotion'. By utilizing the technique of measuring the early-time asymmetry of momentum distribution, we report measurement of micromotion down to (230 \pm 17 , \mu\text{m/s}).