Tunnelling across a potential barrier

Stefano De Leo, PIETRO P. ROTELLI

E. Arimondo, Sandro Wimberger

Tunneling as a quantum mechanical effect takes place in a classically forbidden region between two regions of classically allowed motion. While the term “dynamical tunneling” typically refers to tunneling of quantum states across dynamical barriers in classical phase space [1], the original problem simply intended tunneling across a potential barrier. Both types of tunneling are addressed in this chapter, with major focus on situations in which external forces make the studied systems intrinsically time-dependent and allow for a dynamical control of tunneling through potential barriers or across band gaps which are dynamically explored by the system.

Jose C. Martinez, E. Polatdemir

After many decades, our understanding of the tunneling time across a barrier at the theoretical and experimental levels remains unsatisfactory and subject to debate. We describe an electron interference experiment by which the tunneling time across a symmetric potential barrier can be obtained from the phase shift introduced by the barrier to the interference pattern. We compare these phase shifts as predicted by three competing views of the tunneling time.

Zhuangqi Cao, Cheng Yin

Daniela Mugnai, Anedio Ranfagni, Lawrence S. Schulman

D. Sokolovski, ALFRED Z. MSEZANE, Vasily R. Shaginyan

We exploit the analogy between tunnelling across a potential barrier and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly 'superluminal' behaviur of the tunnelling particle in the barrier. We demonstrate that 'superluminality' occurs when the value of the duration $\\tau$ spent in the barrier is uncertain, whereas when $\\tau$ is known accurately, no 'superluminal' behaviur is observed. In all cases only subluminal durations contribute to the transmission across the barrier.