  Laser cooling typically requires one or more repump lasers to clear dark
states and enable recycling transitions. Here, we have achieved cooling of Be+
ions using a single laser beam, facilitated by one-dimensional heating through
micromotion. By manipulating the displacement from the trap's nodal line, we
precisely controlled the ion micromotion direction and speed, reaching up to
3144 m/s, which corresponds to a 7.1 GHz Doppler frequency shift in our
experiment. This approach eliminates the necessity of a 1.25 GHz offset repump
laser while keeping the Be+ ions cold in the perpendicular direction.
Measurements were taken using cooling laser detuning and imaging of ion
trajectories. Molecular dynamics simulations, based on machine learned
time-dependent electric field E(X, Y, Z, t) inside the trap, accurately
reproduced the experimental observation, illuminating the relationship between
the direction of micromotion and the trapping electric filed vector. This work
not only provides a robust method for managing the micromotion velocity of ions
but also sheds light on laser cooling complex systems that require multiple
repumping lasers. Additionally, it offers a method for controlling energy in
the context of ion-molecule collision investigations.
