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'Lines are boring. We measure spirals!'

Quantum metrology studies the measurement as an essentially quantum process. Its goal is to understand and, whenever possible, overcome the fundamental limitations set by nature to the measurement performances, in particular to the sensitivity.

One of the main feature of quantum systems, entanglement, is extensively studied as a resource for improving the sensitivity in all the precise measurements, such as the one based on quantum interference, e.g. atomic clock, gravitational-wave-detector, etc.

If entangled, the different parts of a probing system are correlated in order to cancel their noise contribution to the measurement result. In this way one can improve the way the sensitivity scales with the total number, N, of probe particle, from the Shot-Noise limit 1/N^1/2 up to 1/N, scaling law known as the Heisenberg limit, until few years ago thought to be the ultimate limit on sensitive measurements.

A different, but complementary approach, is to exploit nonlinearity in the interaction between the probing and the measured systems. Such nonlinearity, can boost up the signal and if tailored to not contribute with extra noise, it can allow a scaling better than the Heisenberg limit. For example a 2nd order nonlinearity, meaning a 2-particle interaction between probing particles, can show up into a sensitivity scaling as 1/N^3/2 even without the use of entanglement.

We apply this nonlinear approach in our system of photons interacting with cold atoms. We study the nonlinearity in such quantum interface as a photon-photon interaction mediated by the presence of the atoms. In this way the atomic angular momentum can be probed under the condition described above and we can experimentally test the improved sensitivity scaling. We can observe super-Heisenberg scaling over two orders of magnitude in the probing photon number.