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.Comment: 14 pages, 3 figures, published New Journal of Physic