  The characterization of mixtures of non-interacting, spectroscopically
similar quantum components has important applications in chemistry, biology,
and materials science. We introduce an approach based on quantum tracking
control that allows for determining the relative concentrations of constituents
in a quantum mixture, using a single pulse which enhances the
distinguishability of components of the mixture and has a length that scales
linearly with the number of mixture constituents. To illustrate the method, we
consider two very distinct model systems: mixtures of diatomic molecules in the
gas phase, as well as solid-state materials composed of a mixture of
components. A set of numerical analyses are presented, showing strong
performance in both settings.
