Shortcuts to Adiabaticity Assisted by Counterdiabatic Born-Oppenheimer Dynamics

TL;DR

This paper introduces a new framework called CBOD for designing shortcuts to adiabaticity in complex quantum systems with different energy scales, using the Born-Oppenheimer approximation to simplify control protocols.

Contribution

The paper presents CBOD, a novel method leveraging the Born-Oppenheimer approximation to efficiently design STA in multi-scale quantum systems.

Findings

CBOD accurately reproduces exact results in coupled harmonic oscillators.

CBOD effectively applies to two-charged particle systems.

The method simplifies STA design in complex quantum systems.

Abstract

Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. We introduce Counterdiabatic Born-Oppenheimer Dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each subsystem. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.