Euclidean resonance in a magnetic field

Abstract

An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed region, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. Such phenomenon, which occurs at the certain magnetic field, is called Euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance a long distance underbarrier motion is possible.

Coherent Control of Quantum Dynamics with Sequences of Unitary Phase-Kick Pulses

“…Many experimental studies have demonstrated the feasibility of kinetic control of quantum dynamics by applying sinusoidal driving potentials. Starting with the use of radiofrequency (rf) electromagnetic pulse sequences in nuclear magnetic resonance (NMR), rf-pulse techniques were subsequently applied to achieve coherent control in a wide range of systems, including applications to the renormalization of Landé g factors in atoms [103], the micromotion of single trapped ions [104], motion of electrons in semiconductor superlattices [105], resonance activation of Brownian particle out of a potential well modeling a current-biased Josephson tunnel junction in its zero-voltage state [1] (also analyzed by theoretical studies [106][107][108][109][110][111]) and dynamical suppression of interwell tunneling of a Bose-Einstein condensate (BEC) in a strongly driven periodic optical potential [112,113]. Several other experiments have also reported tunneling suppression [114,115], and recently dynamical localization and coherent suppression of tunneling have been demonstrated for light propagating in coupled waveguide arrays [116,117].…”

Cyclotron enhancement of tunneling

“…One can find the action (31) by a direct solution of the Hamilton-Jacobi equation (10). Since the condition (11) holds at all y, it follows from (10) that ∂σ(0, y) ∂y…”

“…See, for example, [10,11]. The expression in the square brackets is the Lagrangian in terms of imaginary time.…”