Large oxygen-isotope shift above the quantum critical point of Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$

We have studied the oxygen-isotope effect on the superconducting transition temperature $T_{c}$ in overdoped Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ with $x$ = 0.10, 0.20, and 0.25. We find the oxygen-isotope exponent $\alpha_{O}$ to be small ($\sim$0.02) for $x$ = 0.10 but substantial ($\sim$0.1) for $x$ = 0.20 and 0.25. The doping level above which $\alpha_{O}$ increases sharply coincides with a quantum critical point where the normal-state pseudogap starts to diminish. The present isotope-effect experiments provide direct and quantitative constraints on the pairing mechanism of high-temperature superconductivity in cuprates.