We perform infrared conductivity measurements on a series of CaCuO$_2$/SrTiO$_3$ heterostructures made by the insulating cuprate CaCuO$_2$ (CCO) and the insulating perovkite SrTiO$_3$ (STO). We estimate the carrier density of various heterostructures, with different level of hole doping from the integral of the optical conductivity and we measure the corresponding degree of correlation by estimating the ratio between the Drude weight and the integral of the infrared spectrum. The analysis demonstrates a large degree of correlation, which increases as the doping is reduced. The experimental results can be reproduced by Dynamical Mean-Field Theory calculations which strongly support the role of correlations in the CCO/STO heterostructures and their similarities with the most common cuprate superconductors. Our results suggest that cuprate superconductors can be looked at as natural superlattices, where the properties of the CuO$_2$ conducting planes and charge reservoir blocks can be completely disentangled.
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