Cooper pair transport in 1D Josephson chains in the regime $E_C \ll E_J \approx T$.*

We investigated the current-voltage characteristics (IVC) of one-dimensional arrays of SQUIDs in an unusual regime of very small Josephson energies, $E_J \approx 100-500mK$, and even smaller charging energies, $E_C \approx 10mK$. The $E_C$ values were realized by shunting the $Al-Al_2O_3-Al$ Josephson junctions with a large capacitance to the ground. The zero-bias resistance of the 1D chains is dominated by the quasiparticle transport at $T>0.2K$; below this temperature, only the Cooper pair transport is observed. We have measured the current $I_S$ corresponding to the switching between the low-voltage ``phase-diffusion'' branch of the IVC and the high-voltage branch ($eV \approx n \cdot 2 \Delta $, where $n$ is the number of SQUIDs in the chain, and $\Delta $ is the superconducting gap). At $E_J=100mK$ and $T=50mK$, the extraordinary small values of $I_S \approx 10^{-13} A$ are 1000 times smaller than the Ambegaokar-Baratoff critical current $I_C$. The IVC remains hysteretic in this regime, which indicates that dissipation in the chain is weak. The mechanisms of dissipation will be discussed.