We can design our system such that one atom randomly jumps from the coupled to the non coupled state by cyclic photon scattering processes. This leads to so called quantum jumps and random telegraph signals in the probe laser transmission (*see following data*).

- no atom couples ⇒ full transmission
- one atom couples ⇒ intermediate transmission
- both atoms couple ⇒ low transmission

*part a)*of the figure) shows a typical transmission trace when two atoms undergo quantum jumps inside our cavity.

However we can extract the maximum information from our system by employing a Bayesian update formalism which yields time-dependent probabilities for the atoms to be in the coupled or non coupled states. *Part b)* of the figure shows the result of such an analysis where p_{i}(t) denotes the probability to have i atoms in the coupled state.* Part c)* shows a digitized version of the data which can be concluded from* part b)*.

Read here how we use the knowledge gained from the Bayesian update formalism to manipulate the spin states of the atoms at will by a feedback loop.