Sequential quantum-enhanced measurement with an atomic ensemble

We propose a quantum-enhanced iterative (with K steps) measurement scheme based on an ensemble of N two-level probes which asymptotically approaches the Heisenberg limit δK∝R−K/(K+1), where R is the number of quantum resources. The protocol is inspired by Kitaev's phase estimation algorithm and involves only collective manipulation and measurement of the ensemble. The iterative procedure takes the shot-noise-limited primary measurement with precision δ1∝N−1/2 to increasingly precise results, δK∝N−K/2. We propose an implementation of the algorithm for the measurement of a magnetic field using a two-component atomic cloud of bosons