Ac Josephson current and supercurrent noise through one-dimensional correlated electron systems

ac Josephson effect in one-dimensional Tomonaga-Luttinger liquid (TLL) adiabatically connected to superconducting electrodes is theoretically investigated. It is found that density fluctuations due to repulsive electron-electron interactions in TLL inhibit Josephson oscillations, whereas they do not affect time-independent current part. We also show that the fluctuations reduce supercurrent noise caused by multiple Andreev reflections. This indicates that the quantum fluctuations in TLL disturb the superconducting phase coherence spreading across the junction.