Superfluid density ($n_s$) in the mixed state of an iron pnictide superconductor Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ is determined by muon spin rotation for a sample with optimal doping ($x=0.4$). The temperature dependence of $n_s$ is perfectly reproduced by the conventional BCS model for s-wave paring, where the order parameter can be either a single-gap with $Delta=8.35(6)$ meV [$2Delta/k_BT_c=5.09(4)$], or double-gap structure with $Delta_1=12$ meV (fixed) [$2Delta_1/k_BT_c=7.3$] and $Delta_2=6.8(3)$ meV [$2Delta_2/k_BT_c=4.1(2)$]. The latter is consistent with the recent result of angle-resolved photo-emssion spectroscopy. The large gap parameters ($2Delta/k_BT_c$) indicate extremely strong coupling of carriers to bosons that mediate the Cooper pairing.
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