A ferroelectric quantum phase transition inside a superconducting dome

SrTiO$_{3}$, a quantum paraelectric, becomes a metal with a superconducting instability after removal of an extremely small number of oxygen atoms. It turns into a ferroelectric upon substitution of a tiny fraction of strontium atoms with calcium. The exceptionally dilute superconductor and ferroelectric are both percolative orders, which may be accidental neighbors or intimately connected, as in the picture of quantum critical ferroelectricity. We find that in Sr$_{1-x}$Ca$_{x}$TiO$_{3-\delta}$ ($0.002