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Several decades after the discovery of superconductivity in bismuthates, thestrength of their electron-phonon coupling and its evolution with doping remainpuzzling. To clarify these issues, polycrystalline hole-dopedBa$_{1-x}$K$_{x}$BiO$_3$ ($0.1 \le x \le 0.6$) samples were systematicallysynthesized and their bulk- and microscopic superconducting properties wereinvestigated by means of magnetic susceptibility and muon-spinrotation/relaxation ($\mu$SR), respectively. The phase diagram ofBa$_{1-x}$K$_{x}$BiO$_3$ was reliably extended up to $x = 0.6$, which is stillfound to be a bulk superconductor. The lattice parameter $a$ increases linearlywith K-content, implying a homogeneous chemical doping. The low-temperaturesuperfluid density, measured via transverse-field (TF)-$\mu$SR, indicates anisotropic fully-gapped superconducting state with zero-temperature gaps$\Delta_0/k_\mathrm{B}T_c$ = 2.15, 2.10, and 1.75, and magnetic penetrationdepths $\lambda_0$ = 219, 184, and 279 nm for $x$ = 0.3, 0.4, and 0.6,respectively. A change in the superconducting gap, from a nearly ideal BCSvalue (1.76 $k_\mathrm{B}$$T_c$ in the weak coupling case) in the overdoped $x$= 0.6 region, to much higher values in the optimally-doped case, implies agradual decrease in electron-phonon coupling with doping.

Strong- to weak-coupling superconductivity in high-$T_c$ bismuthates: revisiting the phase diagram via $\mu$SR