  We consider the interaction of a magnetically trapped Bose-Einstein
condensate of Rubidium atoms with the stationary microwave radiation field
sustained by a coplanar waveguide resonator. This coupling allows for the
measurement of the magnetic field of the resonator by means of counting the
atoms that fall out of the condensate due to hyperfine transitions to
non-trapped states. We determine the quantum efficiency of this detection
scheme and show that weak microwave fields at the single-photon level can be
sensed with an integration time on the order of a second.
