  We calculate the bound plasmonic modes of a quantum metamaterial slab,
comprised of multiple quasi two dimensional electron gas (Q2DEG) layers, whose
thickness is much smaller than the optical wavelength. For the first order
transverse magnetic (TM) optical and the surface plasmonic modes we find
propagation constants which are independent of both the electron density and of
the scattering rates in the Q2DEGs. This leads to extremely long propagation
distances. In a detailed case study of a structure comprising a slab of
GaAs/AlGaAs multiple quantum well (MQW) material, we find propagation lengths
of 100s of mm. In addition, the electric field enhancement associated with the
plasmonic resonance is found to be sufficient to induce the condition of strong
coupling between the slab modes and the intersubband transitions in the MQWs.
