  We consider the time-optimal control by magnetic fields of a spin 1/2
particle in a dissipative environment. This system is used as an illustrative
example to show the role of singular extremals in the control of quantum
systems. We analyze a simple case where the control law is explicitly
determined. We experimentally implement the optimal control using techniques of
nuclear magnetic resonance. To our knowledge, this is the first experimental
demonstration of singular extremals in quantum systems with bounded control
amplitudes.
