Arcsine laws of light

We demonstrate that the time-integrated light intensity transmitted by a coherently driven resonator obeys L'evy’s arcsine laws — a cornerstone of extreme value statistics. We show that convergence to the arcsine distribution is algebraic, universal, and independent of non-equilibrium behavior due to non-conservative forces or non-adiabatic driving. We furthermore verify, numerically, that the arcsine laws hold in the presence of frequency noise and in Kerr-nonlinear resonators supporting non-Gaussian states. The arcsine laws imply a weak ergodicity breaking which can be leveraged to enhance the precision of resonant optical sensors with zero energy cost, as shown in our companion manuscript [Ramesh {et al.}, Phys. Rev. Res. submitted (2024)]. Finally, we discuss perspectives for probing the possible breakdown of the arcsine laws in systems with memory.

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