  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, however, fundamental quantum fluctuations
due to the Heisenberg principle limit the measurement precision. The simplest
measurement procedures, involving semi-classical states of the meter, lead to a
fluctuation-limited imprecision at the standard quantum limit. By engineering
the quantum state of the meter system, the measurement imprecision can be
reduced down to the fundamental Heisenberg Limit (HL). Quantum-enabled
metrology techniques are thus in high demand and the focus of an intense
activity. We report here a quantum-enabled measurement of an electric field
based on this approach. We cast Rydberg atoms in Schr\"odinger cat states,
superpositions of atomic levels with radically different polarizabilites. We
use a quantum interference process to perform a measurement close to the HL,
reaching a single-shot sensitivity of 1.2 mV/cm for a 100 ns interaction time,
corresponding to 30 $\mu$V/cm/Hz^(1/2) at our 3 kHz repetition rate. This
highly sensitive, non-invasive space- and time-resolved field measurement
extends the realm of electrometric techniques and could have important
practical applications. Detection of individual electrons in mesoscopic devices
at a ~100 $\mu$m distance, with a MegaHertz bandwith is within reach.
