On the static effective Hamiltonian of a rapidly driven nonlinear system

TL;DR

This paper introduces a recursive, symbolic method for calculating the static effective Hamiltonian of rapidly driven nonlinear systems, applicable to both quantum and classical cases, enhancing computational capabilities.

Contribution

It provides a new recursive formula and diagrammatic tool for computing the effective Hamiltonian to arbitrary order, surpassing previous perturbation methods.

Findings

Enables symbolic calculation of effective Hamiltonians to high order

Applicable to both quantum and classical systems

Facilitates new insights in quantum engineering

Abstract

We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented to arbitrary order, thus overcoming limitations of existing time-dependent perturbation methods and allowing computations that were impossible before. We also provide a simple diagrammatic tool for calculation and treat illustrative examples. By construction, our method applies directly to both quantum and classical systems; the difference is left to a low-level subroutine. This aspect sheds light on the relationship between seemingly disconnected independently developed methods in the literature and has direct applications in quantum engineering.