  One of the most widely discussed features of the cuprate high Tc
superconductors is the presence of a pseudogap in the normal state. Recent
transport and specific heat measurements have revealed an abrupt transition at
the pseudogap critical point, denoted p*, characterized by a drop in carrier
density and a strong mass enhancement. In order to give more details about this
transition at p*, we performed low-temperature infrared spectroscopy in the
normal state of cuprate superconductors La2-xSrxCuO4 (LSCO) and
La1.8-xEu0.2SrxCuO4 (Eu-LSCO) for doping contents across the pseudogap critical
point p* (from p = 0.12 to 0.24). Through the complex optical conductivity we
can extract the spectral weight, K*, of the narrow Drude peak due the coherent
motion of the quasi-particles, and the spectral weight enclosed inside the
mid-infrared (MIR) band, KMIR, caused by coupling of the quasi-particles to
collective excitations of the many-body system. K* is smaller than a third of
the value predicted by band calculations, and KMIR forms a dome as a function
of doping. We observe a smooth doping dependence of K* through p*, and
demonstrate that this is consistent with the observed doping dependence of the
carrier density and the mass enhancement. We argue that the superconducting
dome is the result of the confluence of two opposite trends, namely the
increase of the density of the quasi-particles and the decrease of their
coupling to the collective excitations as a function of doping.
