  We present a theory of the linear and nonlinear optical characteristics of
the insulating phase of the Falicov-Kimball model within the self-consistent
mean-field approximation. The Coulomb attraction between the itinerant
d-electrons and the localized f-holes gives rise to a built-in coherence
between the d and f-states, which breaks the inversion symmetry of the
underlying crystal, leading to: (1) electronic ferroelectricity, (2)
ferroelectric resonance, and (3) a nonvanishing susceptibility for
second-harmonic generation. As experimental tests of such a built-in coherence
in mixed-valent compounds we propose measurements of the static dielectric
constant, the microwave absorption spectrum, and the dynamic second-order
susceptibility.
