We propose a new sub-Doppler cooling scheme in trapped ion crystals in Paul traps which utilizes a Sisyphus-like cooling mechanism to simultaneously cool all the motional modes of the crystal. We use a hollow tweezer, tuned near resonance with the transition from the qubit manifold to a short-lived excited manifold, to generate a state-dependent tweezer potential. This tweezer also introduces a position dependent quench rate for the qubit states. The cooling scheme is completed by using a microwave field to drive the magnetic dipole transition between the qubit states, creating a Sisyphus-like cooling mechanism which is augmented by the position dependent effective lifetime. The optimal cooling parameters are determined exactly for one and two-ion crystals and we demonstrate rapid multi-mode cooling perpendicular to the optical axis using a single tweezer. Furthermore, we demonstrate that this cooling scheme is robust against small tweezer pointing and polarisation errors and does not affect the internal state of the other ions in the crystal. Finally, we will provide a brief outlook of future theoretical work using a non-gaussian ansatz for simulating larger crystals and the eventual experimental implementation of this scheme.
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