There is no fundamental limit to the precision of a classical measurement. The position of a meter’s needle can be determined with an arbitrarily small uncertainty. In the quantum realm, quantum fluctuations due to the Heisenberg principle limit the precision of any measurement. When the needle is replaced by a mesoscopic system, for instance a spin J evolving on a spherical dial, the Bloch sphere, the semi-classical spin coherent state quantum fluctuations lead to a measurement uncertainty scaling as 1/sqrt(J), the standard quantum limit (SQL). This is far from the ultimate Heisenberg limit (HL), which scales as 1/J. We present here an innovative approach, using interferometric measurements on mesoscopic Schrödinger-cat-like superpositions of Rydberg states to realize a single-atom electrometer measuring weak fields of the order of 1 mV/cm in a few tens of nanoseconds. The sensitivity of this method is beyond the SQL and we check that its uncertainty scales as the HL. The extreme sensitivity of this non-invasive space- and time-resolved field measurement could have many practical applications.