Anomalous peak in the superconducting condensate density of cuprate high T_(c) superconductors at a unique critical doping state

The doping dependence of the superconducting condensate density, n_{s}^{o}, has been studied by muon-spin-rotation for Y_{0.8}Ca_{0.2}Ba_{2}(Cu_{1-z}Zn_{z})_{3}O_{7-\delta} and Tl_{0.5-y}Pb_{0.5+y}Sr_{2}Ca_{1-x}Y_{x}Cu_{2}O_{7}. We find that n_{s}^{o} exhibits a pronounced peak at a unique doping state in the slightly overdoped regime. Its position coincides with the critical doping state where the normal state pseudogap first appears depleting the electronic density of states. A surprising correlation between n_{s}^{o} and the condensation energy U_{o} is observed which suggests unconventional behavior even in the overdoped region.