Minimum-Time Quantum Transport With Bounded Trap Velocity

We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system with bounded input. We completely solve the corresponding optimal control problem and obtain an interesting bang-bang solution, where the switching times are obtained from a transcendental equation. These results are expected to find applications in quantum information processing and atom interferometry.