Quantum feedback cooling of two trapped ions

We present a sub-Doppler cooling scheme of a two-trapped-ion crystal by quantum feedback control method. In the scheme, we obtain the motional information by continuously measuring the spontaneous emission photons from one single ion of the crystal, and then apply a feedback force to cool the whole chain down.We derive the cooling dynamics of the cooling scheme using quantum feedback theory and quantum regression theorem. The result shows that with experimentally achievable parameters, our scheme can achieve lower temperature and faster cooling rate than Doppler cooling.