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We propose a new monotonically convergent algorithm which can enforcespectral constraints on the control field (and extends to arbitrary filters).The procedure differs from standard algorithms in that at each iteration thecontrol field is taken as a linear combination of the control field (computedby the standard algorithm) and the filtered field. The parameter of the linearcombination is chosen to respect the monotonic behavior of the algorithm and tobe as close to the filtered field as possible. We test the efficiency of thismethod on molecular alignment. Using band-pass filters, we show how to selectparticular rotational transitions to reach high alignment efficiency. We alsoconsider spectral constraints corresponding to experimental conditions usingpulse shaping techniques. We determine an optimal solution that could beimplemented experimentally with this technique.

Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field