Time-Reversal-Based Quantum Metrology with Many-Body Entangled States

Linear quantum measurements with independent particles are bounded by the Standard Quantum Limit (SQL) that can be overcome by inducing entanglement between the particles. However, the measurement precision is often limited by the final state readout, especially for more complex entangled many-body states with non-Gaussian probability distributions. An alternative is to use a time-reversal protocol to amplify small displacement of the entangled state. We implement such a time-reversal protocol through a controlled sign change in many-body Hamiltonian of atomic spins coupled to an optical cavity. With this approach, we demonstrate quantum measurement with non-Gaussian states with a precision improving in proportion to the particle number (Heisenberg scaling), at fixed distance of 12.6 dB from the ultimate Heisenberg Limit. Using a system of 350 neutral 171Yb atoms, this signal amplification through time-reversed interaction (SATIN) protocol achieves an improvement of 12 dB beyond the SQL in a Ramsey sequence. We also use the time-reversed Hamiltonian to experimentally investigate the relation between out-of-time-order correlators and metrological gain.