We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La1,55Sr0,45CuO4) and a cuprate insulator (La2CuO4), in which each layer is just one unit cells thick. We have studied the magnetic field and temperature dependence of the complex sheet conductance, <$E sigma ( omega )>, of these films. Experiments have been carried out at frequencies between 2 - 50 MHz using the single-spiral coil technique. We found that: the inductive response starts at <$E DELTA T~=~3> K lower temperatures than Re <$E sigma (T)>, which in turn is characterized by a peak close to the transition; this shift is almost constant with magnetic field up to 14 mT; <$E DELTA T> increases sharply up to 4 K at larger fields and becomes constant up to 8 T; the vortex diffusion constant D(T) is not linear with T at low temperatures as in the case of free vortices, but is rather exponential due to pinning of vortex cores, and (<$E nu>) the dynamic Berezinski - Kosterlitz - Thouless (BKT) transition temperature occurs at the point where <$E Y~=~(l sub omega "/" xi sub + ) sup 2~=~1>. Our experimental results can be described well by the extended dynamic theory of the BKT transition and dynamics of bound vortex - antivortex pairs with short separation lengths.

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