Shortcuts to adiabaticity assisted by counterdiabatic Born-Oppenheimer dynamics

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 sub-system. 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.