Approaching the Heisenberg Limit with a time-reversal Hamiltonian *

Reaching the Heisenberg limit is one of the long-sought goals in Quantum Metrology. Non-Gaussian Entangled States (NGES) with a large amount of entanglement have been proposed to approach such a limit. However, NGES are fragile against decoherence and depend on the challenging requirement of having single-particle state resolution, halting experimental progress for application to atomic sensors with today's technology.

We present here the implementation of a robust Signal Amplification through Time-reversal Interaction (SATIN) protocol, which enabled to use of highly entangled states for quantum metrology. We obtained an angular resolution of 12.8 dB beyond the SQL for a system of 370 ytterbium-171 atoms (and 12.8 dB away from the Heisenberg limit), Heisenberg scaling with atom number, and a record-breaking phase-sensitive measurement of 11.8 dB beyond the SQL. We plan to transfer these NGESs to the optical-clock transition of ytterbium-171.