# Fast forward of adiabatic control of tunneling states

## TL;DR

This paper presents a method to rapidly control and observe quantum tunneling states by using electromagnetic fields to accelerate the evolution of wave functions, enabling real-time analysis of transport properties under changing barriers.

## Contribution

It introduces an exact fast-forward scheme for adiabatic tunneling control using electromagnetic fields, extending previous work on transient phenomena to stationary states.

## Key findings

- Successfully accelerates the evolution of tunneling states
- Enables observation of transport coefficients during rapid barrier changes
- Provides explicit electric field protocols for maintaining stationary tunneling states

## Abstract

By developing the preceding work on the fast forward of transient phenomena of quantum tunneling by Khujakulov and Nakamura (Phys. Rev. {\bf A 93}, 022101 (2016) ), we propose a scheme of the exact fast forward of adiabatic control of stationary tunneling states with use of the electromagnetic field. The idea allows the acceleration of both the amplitude and phase of wave functions throughout the fast-forward time range. The scheme realizes the fast-forward observation of the transport coefficients under the adiabatically-changing barrier with the fixed energy of an incoming particle. As typical examples we choose systems with (1) Eckart's potential with tunable asymmetry and (2) double $\delta$-function barriers under tunable relative height. We elucidate the driving electric field to guarantee the stationary tunneling state during a rapid change of the barrier and evaluate both the electric-field-induced temporary deviation of transport coefficients from their stationary values and the modulation of the phase of complex scattering coefficients