  We investigate the generation of higher-order harmonics from a quantum optics
perspective via the interaction of a semiconductor with a coherent pump field
focusing on the regime where strong-field intraband excitations dominate. The
related Schr\"odinger equation for the system is solved approximately and the
classical and quantum characteristics of the fundamental light mode as well as
the higher frequency modes are analyzed. We find intricate but sufficiently
mild modifications of the fundamental mode and coherent displacements depending
on the position quadrature component of the driving laser field for the
harmonic modes within our approximations due to the intricate induced nonlinear
interactions. Similar to high-harmonic generation in atoms, all radiation field
modes are entangled, allowing for potential novel protocols for quantum
information processing with high photon numbers over a large range of
frequencies.
