  A new class of cost functionals for optimal control of quantum systems which
produces controls which are sparse in frequency and smooth in time is proposed.
This is achieved by penalizing a suitable time-frequency representation of the
control field, rather than the control field itself, and by employing norms
which are of $L^1$ or measure form with respect to frequency but smooth with
respect to time.
  We prove existence of optimal controls for the resulting nonsmooth
optimization problem, derive necessary optimality conditions, and rigorously
establish the frequency-sparsity of the optimizers. More precisely, we show
that the time-frequency representation of the control field, which a priori
admits a continuum of frequencies, is supported on only \textit{ finitely many}
frequencies.
  These results cover important systems of physical interest, including
(infinite-dimensional) Schr\"odinger dynamics on multiple potential energy
surfaces as arising in laser control of chemical reactions. Numerical
simulations confirm that the optimal controls, unlike those obtained with the
usual $L^2$ costs, concentrate on just a few frequencies, even in the
infinite-dimensional case of laser-controlled chemical reactions.
