  We study the electrical transport properties of well-contacted ballistic
single-walled carbon nanotubes in a three-terminal configuration at low
temperatures. We observe signatures of strong electron-electron interactions:
the conductance exhibits bias-voltage-dependent amplitudes of quantum
interference oscillation, and both the current noise and Fano factor manifest
bias-voltage-dependent power-law scalings. We analyze our data within the
Tomonaga-Luttinger liquid model using the non-equilibrium Keldysh formalism and
find qualitative and quantitative agreement between experiment and theory.
