Engineering effective adiabatic evolution via suitable coupling to auxiliary systems

A quantum system driven by a time-dependent Hamiltonian H₀(t) can be engineered to evolve adiabatically [with respect to H₀(t)] by the addition of a counterdiabatic term H₁(t), as shown by Berry. The time dependence of H₀(t) gives rise to a curvature term in the comoving frame, described via a gauge field, that induces transitions between distinct states and whose influence is exactly cancelled byH₁(t) . Implementation of H₁(t) can be impractical, e.g., because H₁(t) is nonlocal. By using geometrical arguments, we explore alternative means to engineer adiabatic evolution via increasing the number of freedoms, and thus induce adiabatic evolution by using entirely local terms. As a specific example, we consider a system of locally interacting particles, for which we wish to engineer adiabatic evolution. We show that by coupling this system to an auxiliary one, we can achieve adiabatic evolution and maintain locality at the expense of increasing the number of degrees of freedom. We explore the required compatibility relations between the original and auxiliary systems and their couplings, and comment on their geometrical significance.