Sideband Rabi spectroscopy of finite-temperature trapped Bose gases

We use Rabi spectroscopy to explore the low-energy excitation spectrum of a finite-temperature Bose gas of rubidium atoms across the phase transition to a Bose-Einstein condensate (BEC). To record this spectrum, we coherently drive the atomic population between two spin states. A small relative displacement of the spin-specific trapping potentials enables sideband transitions between different motional states. The intrinsic non-linearity of the motional spectrum, mainly originating from two-body interactions, makes it possible to resolve and address individual excitation lines. Together with sensitive atom-counting, this constitutes a feasible technique to count single excited atoms of a BEC and to determine the temperature of nearly pure condensates. As an example, we show that for a nearly pure BEC of N = 800 atoms the first excited state has a population of less than 5 atoms, corresponding to an upper bound on the temperature of 30 nK.