  We establish new experiments to search for dark matter based on a model of a
light scalar field with a dilaton-like coupling to the electromagnetic field,
which is strongly motivated by superstring theory. We estimate the power of the
photon signal in the process of a non-resonant scalar-photon transition and in
a cavity resonator permeated by electric and magnetic fields. We show that
existing cavity resonators employed in the experiments like ADMX have a low but
non-vanishing sensitivity to the scalar-photon coupling. As a result, by
re-purposing the results of the ADMX experiment, we find new limits on the
scalar-photon coupling in the range of the scalar field masses from 2.7 to 4.2
$\mu$eV. We discuss possible modifications of this experiment, which enhance
the sensitivity to the scalar field dark matter. We also propose a broadband
experiment for scalar field dark matter searches based on a high-voltage
capacitor. The estimated sensitivity of this experiment exceeds by nearly two
orders in magnitude the sensitivity of the experiment based on molecular
spectroscopy.
