  We discuss continuous observation of the momentum of a single atom by
employing the high velocity sensitivity of the index of refraction in a driven
$\Lambda$-system based on electromagnetically induced transparency (EIT). In
the ideal limit of unit collection efficiency this provides a quantum limited
measurement with minimal backaction on the atomic motion. A feedback loop,
which drives the atom with a force proportional to measured signal, provides a
cooling mechanism for the atomic motion. We derive the master equation which
describes the feedback cooling and show that in the Lamb-Dicke limit the steady
state energies are close to the ground state, limited only by the photon
collection efficiency. Outside of the Lamb-Dicke regime the predicted
temperatures are well below the Doppler limit.
