Ergodicity in randomly perturbed quantum systems

The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here,we show howsuch a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at randomtimes while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically showhowthemost probable value of the probability for the system to be in a given state eventually deviates fromthe non-stochastic casewhen the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.