Protecting atomic coherent spin states with weak measurements and feedback

Weak measurements provide new ways to observe and control quantum systems. Here we use weak non-destructive measurements in a feedback scheme to protect an atomic ensemble in a coherent superposition against a simple decoherence model. The feedback efficiency, defined as the ability to recover the coherence of the initial state, is studied versus the number of photons in the probe beam. This allows us to precisely characterize the trade-off between information retrieval and destructivity. The lifetime of the coherent spin state is increased by one order of magnitude when the correction cycle is iterated