  In the ideal quantum Zeno effect, repeated quantum projective measurements
can freeze the coherent dynamics of a quantum system. However, in the weak
quantum Zeno regime, measurement back-actions can allow the sensing of
semi-classical field fluctuations. In this regard, we theoretically show how to
combine the controlled manipulation of a quantum two-level system, used as a
probe, with a sequence of projective measurements to have direct access to the
noise correlation function. We experimentally test the effectiveness of the
proposed noise sensing method on a properly engineered Bose-Einstein condensate
of $^{87}Rb$ atoms realized on an atom chip. We believe that our quantum
Zeno-based approach can open a new path towards novel quantum sensing devices.
