Quantum effects in small-capacitance single Josephson junctions

We have measured the current-voltage (I-V) characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02--0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction I-V curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance R₀^' of the SQUID arrays is much higher than the quantum resistance RK≡h/e²≈26kΩ. The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the I-V curves numerically in order to compare then with the experimental ones at R₀^'RK. The numerical calculation agrees with the experiments qualitatively. We also discuss the R₀^' dependence of the single-Josephson-junction I-V curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.