Scheme for accelerating quantum tunneling dynamics

Anvar Khujakulov and Katsuhiro Nakamura
Phys. Rev. A 93, 022101 – Published 1 February 2016

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 the phase of the wave function throughout the fast-forward time range and is distinct from that of Masuda and Nakamura [Proc. R. Soc. A 466, 1135 (2010)], which enabled acceleration of only the amplitude of the wave function on the way. We apply the proposed method to the quantum tunneling phenomena and obtain the electromagnetic 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 δ-function barrier and (2) the opened Moshinsky shutter with a δ-function barrier just behind the shutter. We elucidate the tunneling current in the vicinity of the barrier and find a 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 Schrödinger equation, which accommodates a tunneling barrier.

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  • Received 14 August 2015

DOI:https://doi.org/10.1103/PhysRevA.93.022101

©2016 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Anvar Khujakulov1 and Katsuhiro Nakamura2,3

  • 1Department of Physics, Heinrich-Heine-University Düsseldorf, Universität strasse 1, 40225 Düsseldorf, Germany
  • 2Faculty of Physics, National University of Uzbekistan, Vuzgorodok, Tashkent 100174, Uzbekistan
  • 3Department of Applied Physics, Osaka City University, Sumiyoshi-ku, Osaka 558-8585, Japan

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Issue

Vol. 93, Iss. 2 — February 2016

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