Scheme for accelerating quantum tunneling dynamics

TL;DR

This paper introduces an exact fast-forwarding scheme for quantum dynamics that accelerates both amplitude and phase of wave functions, applied to tunneling phenomena to enhance tunneling rates and analyze high-barrier scenarios.

Contribution

The proposed method uniquely accelerates both amplitude and phase in quantum dynamics, enabling rapid tunneling analysis and control, distinct from previous amplitude-only acceleration techniques.

Findings

Enhanced tunneling rates due to fast-forwarding

Derived electromagnetic fields for rapid barrier penetration

Asymptotic analysis for high barrier tunneling

Abstract

We propose a scheme of the exact fast-forwarding of standard quantum dynamics for a charged particle. The present idea allows the acceleration of both the amplitude and phase of the wave function throughout the fast-forward time range and is distinct from that of Masuda-Nakamura (e.g., Proc. R. Soc. A {\bf 466}, 1135 (2010)) which enabled acceleration of only the amplitude of the wave function on the way. We shall apply the proposed method to the quantum tunneling phenomena and obtain the electro-magnetic field to ensure the rapid penetration of wave functions through a tunneling barrier. Typical examples described here are: 1) an exponential wave packet passing through the delta-function barrier; 2) the opened Moshinsky shutter with a delta-function barrier just behind the shutter. We elucidate the tunneling current in the vicinity of the barrier and find the remarkable enhancement of the tunneling rate (: tunneling power) due to the fast-forwarding. In the case of a very high barrier, in particular, we present the asymptotic analysis and exhibit a suitable driving force to recover a recognizable tunneling current. The analysis is also carried out on the exact acceleration of macroscopic quantum tunneling with use of the nonlinear Schr\"odinger equation which accommodates a tunneling barrier.