We have experimentally and analytically studied the dynamics of a bistable device prepared in the vicinity of an unstable state of the middle branch of the hysteresis cycle.
We investigate the temporal aspects of absorptive two-photon optical bistability described by a semiclassical theory in the limit of a fully developed hysteresis cycle and when all decay rates have comparable magnitude. We show by multiple time-scale perturbation analysis that near the high-transmission branch the behavior of the system is governed by an equation for the field amplitude which determines the long-time evolution of the system, whereas, near the low-transmission branch all dynamical variables vary on the long time scale, and it is possible to describe the transition between the two stable branch by simple equations.
We report on the switching dynamics of a bistable device in the case when a holding power maintains the system in a stable state of the lower branch and a pulse address of finite duration (T) brings it close to the unstable state of the middle branch. For a critical pulse duration (Tc) the pulse exactly brings the device in the unstable state where it would indefinitely remain in the absence of fluctuations. For pulse duration close to Tc the device switches up to the upper branch (T>Tc) or relaxes to the initial state (T<Tc) after a lethargy time which follows a logarithmic law {1,2}.