Counter-diabatic driving in the classical $\beta$-Fermi-Pasta-Ulam-Tsingou chain

TL;DR

This paper explores the application of approximate counter-diabatic driving to classical systems, specifically the $eta$-FPUT chain, demonstrating its effectiveness in suppressing excitations and minimizing heating.

Contribution

It adapts and optimizes counter-diabatic driving techniques for classical nonlinear systems, providing a new approach to control excitations in the $eta$-FPUT chain.

Findings

Simple ACD forms effectively suppress excitations

ACD reduces system heating significantly

Performance is consistent across different system sizes

Abstract

Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing excitations in the system's state. In quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing protocols, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counter-diabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the $\beta$ Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. In particular, we modify an existing variational technique to optimize the approximate driving and then develop classical figures of merit to quantify the performance of the driving. We find that relatively simple forms for the ACD driving can dramatically suppress excitations regardless of system size. ACD driving in classical nonlinear oscillators could have many applications, from minimizing heating in bosonic gases to finding optimal local dressing protocols in interacting field theories.