Magnetic noise spectrum measurement by an atom laser in gravity

Bose-Einstein condensates of ultracold atoms can be used to sense fluctuations of the magnetic field by means of the transitions into untrapped hyperfine states. It has been shown recently that counting the outcoupled atoms can yield the power spectrum of the magnetic noise. We calculate the spectral resolution function which characterizes the condensate as a noise measurement device in this scheme. We use the description of the radio frequency outcoupling scheme of an atom laser which takes into account the gravitational acceleration. The three-dimensional and fully quantum mechanical approach leads to a position-dependent spectral resolution function which can be used to describe any spatial resolution of the atom detection scheme.