Imaginary Kapitza pendulum

We extend the theory of Kapitza stabilization within the complex domain, i.e., for the case of an imaginary oscillating potential. At a high oscillation frequency, the quasienergy spectrum is found to be entirely real valued; however, a substantial difference with respect to a real potential emerges, that is, the formation of a truly bound state instead of a resonance. The predictions of the Kapitza averaging method and the transition from a complex to an entirely real-valued quasienergy spectrum at high frequencies are confirmed by numerical simulations of the Schrodinger equation for an oscillating Gaussian potential. An application and a physical implementation of the imaginary Kapitza pendulum to the stability of optical resonators with variable reflectivity is discussed.