Dynamics revealed by correlations of time-distributed weak measurements of a single spin

We show that the correlations in stochastic outputs of time-distributed weak measurements can be used to study the dynamics of an individual quantum object, with a proof-of-principle setup based on small Faraday rotation caused by a single spin in a quantum dot. In particular, the third-order correlation can reveal the 'true' spin decoherence, which would otherwise be concealed by the inhomogeneous broadening effect in the second-order correlations. The viability of such approaches lies in the fact that (i) in weak measurement the state collapse that would disturb the system dynamics occurs at a very low probability and (ii) a shot of measurement projecting the quantum object to a known basis state serves as a starter or stopper of the evolution without pumping or coherently controlling the system as otherwise required in conventional spin echo.