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Sideband cooling is a popular method for cooling atoms to the ground state ofan optical trap. Applying the same method to molecules requires a number ofchallenges to be overcome. Strong tensor Stark shifts in molecules cause theoptical trapping potential, and corresponding trap frequency, to dependstrongly on rotational, hyperfine and Zeeman state. Consequently, transitionfrequencies depend on the motional quantum number and there are additionalheating mechanisms, either of which can be fatal for an effective sidebandcooling scheme. We develop the theory of sideband cooling in state-dependentpotentials, and derive an expression for the heating due to photon scattering.We calculate the ac Stark shifts of molecular states in the presence of amagnetic field, and for any polarization. We show that the complexity ofsideband cooling can be greatly reduced by applying a large magnetic field toeliminate electron- and nuclear-spin degrees of freedom from the problem. Weconsider how large the magnetic field needs to be, show that heating can bemanaged sufficiently well, and present a simple recipe for cooling to theground state of motion.

Sideband cooling of molecules in optical traps