  Quadratic trapping potentials are widely used to experimentally probe
biopolymers and molecular machines and drive transitions in steered
molecular-dynamics simulations. Approximating energy landscapes as locally
quadratic, we design multidimensional trapping protocols that minimize
dissipation. The designed protocols are easily solvable and applicable to a
wide range of systems. The approximation does not rely on either fast or slow
limits and is valid for any duration provided the trapping potential is
sufficiently strong. We demonstrate the utility of the designed protocols with
a simple model of a periodically driven rotary motor. Our results elucidate
principles of effective single-molecule manipulation and efficient
nonequilibrium free-energy estimation.
