  Cooling down a trapped ion into its motional ground state is a central step
for trapped ions based quantum information processing. State of the art cooling
schemes often work under a set of optimal cooling conditions derived
analytically using a perturbative approach, in which the sideband coupling is
assumed to be the weakest of all the relevant transitions. As a result the
cooling rate is severely limited. Here we propose to use quantum control
technique powered with automatic differentiation to speed up the classical
cooling schemes. We demonstrate the efficacy of our approach by applying it to
find the optimal cooling conditions for classical sideband cooling and
electromagnetically induced transparency cooling schemes, which are in general
beyond the weak sideband coupling regime. Based on those numerically found
optimal cooling conditions, we show that faster cooling can be achieved while
at the same time a low average phonon occupation can be retained.
