Optimal control of the signal-to-noise ratio per unit time for a spin-1/2 particle

We investigate the maximum signal-to-noise ratio per unit time that can be achieved for a spin-1/2 particle subjected to a periodic pulse sequence. Optimal control techniques are applied to design the control field and the position of the steady state, leading to the best signal-to-noise performance. A complete geometric description of the optimal control problem is given in the unbounded case. We show the optimality of the well-known Ernst angle solution, which is widely used in spectroscopic and medical imaging applications, over a large control space allowing the use of shaped pulses.