Control of tunneling by adapted signals

Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an under-barrier motion of a particle such signal provides a "coherent" assistance of tunneling by the multi-quanta absorption resulting in a strong enhancement of the tunneling probability. The semiclassical approach based on trajectories in the complex time is developed for tunneling in a non-stationary field. Enhancement of tunneling occurs when a singularity of the signal coincides in position at the complex time plane with a singularity of the classical Newtonian trajectory of the particle. The developed theory is also applicable to the over-barrier reflection of particles and to reflection of classical waves (electromagnetic, hydrodynamic, etc.) from a spatially-smooth medium.