  The structure and the statistical fluctuations of interfaces between
coexisting phases in the Asakura-Oosawa (AO) model for a colloid--polymer
mixture are analyzed by extensive Monte Carlo simulations. We make use of a
recently developed grand canonical cluster move with an additional constraint
stabilizing the existence of two interfaces in the (rectangular) box that is
simulated. Choosing very large systems, of size LxLxD with L=60 and D=120,
measured in units of the colloid radius, the spectrum of capillary wave-type
interfacial excitations is analyzed in detail. The local position of the
interface is defined in terms of a (local) Gibbs surface concept. For small
wavevectors capillary wave theory is verified quantitatively, while for larger
wavevectors pronounced deviations show up. For wavevectors that correspond to
the typical distance between colloids in the colloid-rich phase, the
interfacial fluctuations exhibit the same structure as observed in the bulk
structure factor. When one analyzes the data in terms of the concept of a
wavevector-dependent interfacial tension, a monotonous decrease of this
quantity with increasing wavevector is found. Limitations of our analysis are
critically discussed.
