Quantum tunneling in the time periodic double well potential

TL;DR

This paper models and numerically investigates quantum tunneling in a time-periodic double-well potential, demonstrating controllable tunneling rates via modulation parameters, unlike in stationary potentials.

Contribution

It introduces a numerical algorithm for solving the Schrödinger equation in a time-periodic double-well potential and shows how modulation controls tunneling.

Findings

Tunneling occurs only in time-periodic potentials, not stationary ones.

Tunneling rate depends on modulation frequency.

Adjusting modulation parameters controls tunneling rate.

Abstract

We present the mathematical model and numerical calculation results for the tunneling of the wave function in a time-periodic double-well potential. The bi-quadratic potential of a double-well form is used. Based on a mathematical model of the time evolution of the wave function, a numerical algorithm has been developed and a program has been created for solving the Schr\"odinger equation, which describes the time evolution of the particle's wave function. As a result of numerical modeling, modulation regimes have been obtained at which tunneling took place. In a stationary double well potential, no tunneling was observed. On the contrary, in the time periodic potential, tunneling was observed, the rate of which depended on the modulation frequency. Adjusting the modulation parameters, it is possible to control the particle wave function tunneling rate.