Probing ultracold Fermi atoms with a single ion

We show that the recently proposed ionic microscope setup [Kollath , Phys. Rev. A 76, 063602 (2007)] could be adapted to measure the local single-particle energy distribution of a degenerate Fermi gas in situ with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photoassociation rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photoassociation rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas.