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.
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