Asymmetric dynamical localization and precision measurement of BEC micromotion

We show that a Bose-Einstein Condensate (BEC) launched with non-zero initial momentum into a periodically kicked optical lattice creates an asymmetrically localized momentum distribution in a moving frame with a small initial current. This asymmetric localization is investigated under two scenarios; (a) when the BEC is in motion in the laboratory frame and, (b) when the optical lattice is in motion in the laboratory frame. The 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 micromotion of BEC is measured using the early-time asymmetry. In this context, micromotion refers to the extremely low initial velocity of the BEC along the lattice direction. This originates from the jitter when the hybrid trap potential is turned off. By employing BEC in a kicked and moving optical lattice, the asymmetry in early-time dynamics is measured to precisely characterize and quantify the micromotion phenomena in the quantum system. Micromotion measurement has applications in quantifying systematic shifts and uncertainties in light-pulse interferometers.