  In this article, we develop a numerical method to find optimal control pulses
that accounts for the separation of timescales between the variation of the
input control fields and the applied Hamiltonian. In traditional numerical
optimization methods, these timescales are treated as being the same. While
this approximation has had much success, in applications where the input
controls are filtered substantially or mixed with a fast carrier, the resulting
optimized pulses have little relation to the applied physical fields. Our
technique remains numerically efficient in that the dimension of our search
space is only dependent on the variation of the input control fields, while our
simulation of the quantum evolution is accurate on the timescale of the fast
variation in the applied Hamiltonian.
