  We study the superfluid density of the $\pm$s-wave state of the minimal two
band model for the Fe-based superconductors and its evolution with impurity
concentration. We show that the impurity scattering of the strong coupling
limit induces the selfenergy of a generic form $Im \Sigma_{imp} (\omega)
\approx i \gamma + i \beta \omega$ beyond a critical impurity concentration
$\Gamma_{imp} > \Gamma_{crit}$. This form of $Im \Sigma_{imp} (\omega)$ causes
the temperature dependence of the superfluid density $[\rho_{s}(T) -
\rho_{s}(0)] \approx - \gamma T^2 -\beta T^3$. Combining with the full gap
behavior of $\rho_{s}(T)$ for lower impurity concentration $\Gamma_{imp} <
\Gamma_{crit}$, the $\pm$s-wave state produces a continuous evolution of
$\Delta \lambda(T)$: exponentially flat $\to T^3 \to T^2$ with increasing
impurity concentration that is consistent with the measurements of the Fe
pnictide superconductors such as $M$-1111 ($M$=La,Nd,Sm,Pr) and Ba-122 with
various dopings, except LaFePO which shows $\Delta \lambda(T) \propto T^{1.2}$
at low temperatures by recent experiment. Our results also demonstrate that the
density of states (DOS) measured by thermodynamic properties and the DOS
measured by transport properties can in general be different.
