We demonstrate how to use feedback to control the internal states of trapped
coherent ensembles of two-level atoms, and to protect a superposition state
against the decoherence induced by a collective noise. Our feedback scheme is
based on weak optical measurements with negligible back-action and coherent
microwave manipulations. The efficiency of the feedback system is studied for a
simple binary noise model and characterized in terms of the trade-off between
information retrieval and destructivity from the optical probe. We also
demonstrate the correction of more general types of collective noise. This
technique can be used for the operation of atomic interferometers beyond the
standard Ramsey scheme, opening the way towards improved atomic sensors.Comment: 9 pages, 6 figure