Fine Theoretical Physics Institute Seminar

The process of quantum tunneling through a static potential barrier is well described by the theory of Wentzel, Kramers, and Brillouin. When, due to external electric field ξ(t), the barrier is nonstationary the tunneling scenario becomes very delicate. First of all, an electron can absorb a number of quanta of the external field and to tunnel in a more transparent part (with a higher energy) of the barrier. This process is known as photon-assisted tunneling. The probability of this process can be calculated by the method of classical trajectories in complex time. In this case analytical properties of the function ξ(t), which can be sinusoidal or of a pulsed type, in the complex plane of time play a crucial role. In addition to photon-assisted tunneling, which has no conflict with intuition, there is another under-barrier process which is counter-intuitive and is called Euclidean resonance. A new branch of the wave function is created under the barrier due to nonstationary conditions. As a result, the tunneling probability strongly enhances and can be not exponentially small even for almost classical barriers. Remarkable, that an electron loses its energy under the barrier. Classical trajectories in complex time are also applicable to description of Euclidean resonance. Analytical methods and a direct numerical solution of Schroedinger equation are used to study photon-assisted tunneling and Euclidean resonance. The above phenomena can be used for control of tunneling: in scanning tunneling microscopy, for selective destruction of chemical bonds, in nanostructures, etc.

PACS numbers: 74.25.Nf, 74.40.+k, 74.72.Hs