Effect of non-Markovian dynamics on weak ergodicity breaking and sensing precision

Determine the extent to which weak ergodicity breaking and the associated differences in sensing precision between time averaging and ensemble averaging of the time-integrated transmitted intensity—under a fixed energy budget—in laser-driven single-mode optical cavities persist or are modified when the dynamics are non-Markovian due to memory effects in the cavity response.

Background

The paper establishes weak ergodicity breaking (WEB) in optical sensing by analyzing time- versus ensemble-averaged measurements of the time-integrated transmitted intensity in a noisy, laser-driven single-mode optical cavity with Markovian (memoryless) dynamics. Under a fixed energy budget, ensemble averaging can significantly outperform time averaging for short measurement times, though ergodicity emerges as measurement time increases.

These results rely on Lévy’s arcsine laws, derived for Markovian processes. The authors note that resonators with memory in their nonlinear response would induce non-Markovian dynamics, for which arcsine laws are expected to be modified or to break down, thereby potentially changing the conclusions about WEB and sensing precision.