  We investigate simultaneous state-insensitive trapping of a mixture of two
different atomic species, Caesium and Rubidium. The magic wavelengths of the
Caesium and Rubidium atoms are different, $935.6$ nm and $789.9$ nm
respectively, thus single-frequency simultaneous state-insensitive trapping is
not possible. We thus identify bichromatic trapping as a viable approach to
tune the two magic wavelengths to a common value. Correspondingly, we present
several common magic wavelength combinations appropriate for simultaneous
state-insensitive trapping of the two atomic species.
