Time Reversed States in Barrier Tunneling

TL;DR

This paper explores quantum tunneling in mesoscopic systems, deriving an expression for current under the barrier and demonstrating measurable propagation, with implications for device applications and causality considerations.

Contribution

It introduces a general scheme to derive the quantum current under the barrier in arbitrary systems, validated through a 1D quantum ring example.

Findings

Propagation occurs under the barrier in mesoscopic systems

An expression for quantum current under the barrier is derived

Evanescent states are stable and suitable for device applications

Abstract

Tunneling, though a physical reality, is shrouded in mystery. Wave packets cannot be constructed under the barrier and group velocity cannot be defined. The tunneling particle can be observed on either sides of the barrier but its properties under the barrier has never been probed due to several problems related to quantum measurement. We show that there are ways to bypass these problems in mesoscopic systems and one can even derive an expression for the quantum mechanical current under the barrier. A general scheme is developed to derive this expression for any arbitrary system. One can use mesoscopic phenomenon to subject the expression to several theoretical and experimental cross checks. For demonstration we consider an ideal 1D quantum ring with Aharonov-Bohm flux $\Phi$, connected to a reservoir. It gives clear evidence that propagation occur under the barrier resulting in a current that can be measured non-invasively and theoretically cross checked. Time reversed states play a role but there is no evidence of violation of causality. The evanescent states are known to be largely stable and robust against phase fluctuations making them a possible candidate for device applications and so formalizing current under barrier is important.