Chaotic instantons and enhancement of tunneling in double-well system with polychromatic perturbation

TL;DR

This paper develops an analytical chaotic instanton approach to describe how polychromatic perturbations enhance tunneling in a double-well quantum system, with results validated by numerical simulations.

Contribution

It introduces a novel analytical method using chaotic instantons to predict tunneling enhancement under polychromatic perturbations in nonlinear quantum systems.

Findings

Analytical formula for quasienergy level splitting derived.

Numerical results agree well with analytical predictions.

Polychromatic perturbations significantly enhance tunneling effects.

Abstract

Chaotic instanton approach allows to describe analytically the influence of the polychromatic perturbation on quantum properties of nonlinear systems. Double well system with single, multiple and polychromatic kicked perturbation is considered in the paper to compare quantitative analytical predictions with the results of numerical calculations. Chaotic instantons are responsible for the enhancement of tunneling far away from the exact (avoided) level crossings in framework of the approach used. Time-independent averaged system is used for regular approximation of the chaotic instanton solution in order to take into account its contribution to the ground quasienergy doublet splitting. Formula for the ground quasienergy levels' splitting was derived averaging trajectory action in the stochastic layer in the framework of chaotic instanton approach. Results of quasienergy spectrum numerical calculations and simulations for tunneling dynamics are in good agreement with the obtained analytical predictions.