Time-optimal monotonically convergent algorithm with an application to the control of spin systems

We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the laser fluence. A standard algorithm designs a control field of fixed duration which both brings the system close to the target state and minimizes the laser fluence, whereas here we include in addition the optimization of the duration in the cost functional. We apply this new algorithm to the control of spin systems in Nuclear Magnetic Resonance. We show how to implement CNOT gates in systems of two and four coupled spins.