Testing Critical Slowing Down as a Bifurcation Indicator in a Low-dissipation Laser System

A huge amount of research is devoted today to determine good indicators applicable on time series obtained from real systems that may anticipate a change in its behaviour [1] , [2] . A well-established indicator is the so-called "critical slowing down" (CSD). CSD is the asymptotic growth of the of the relaxation time of a kicked dynamical system when it is approaching a bifurcation [3] . In this contribution, we address the question whether CSD is always a good indicator of an incoming bifurcation in a system where a parameter is linearly changing in time. We answer by presenting a laser system with a time swept pump where CSD appears only after the bifurcation has already occurred, hence when it is too late to reverse its behavioural change. Furthermore, we show experimentally that a perturbation in the accessible control parameter is unable to provide any indication, nor on the occurrence of CSD nor on the bifurcation crossing.