  Interacting quantum many-body systems constitute a fascinating playground for
researchers since they form quantum liquids with correlated ground states and
low-lying excitations, which exhibit universal behaviour. In fermionic systems,
such quantum liquids are realized in helium-3 liquid, heavy fermion systems,
neutron stars and cold gases. Their properties in the linear-response regime
have been successfully described by the theory of Fermi liquids. However,
non-equilibrium properties beyond this regime have still to be established and
remain a key issue of many-body physics. Here, we show a precise experimental
demonstration of Landau Fermi-liquid theory extended to the non-equilibrium
regime in a 0-D system. Combining transport and ultra-sensitive current noise
measurements, we have unambiguously identified the SU(2) and SU(4) symmetries
of quantum liquid in a carbon nanotube tuned in the universal Kondo regime. We
find that, while the electronic transport is well described by the free
quasi-particle picture around equilibrium, a two-particle scattering process
due to residual interaction shows up in the non-equilibrium regime. By using
the extended Fermi-liquid theory, we obtain the interaction parameter "Wilson
ratio" $R=1.9 \pm 0.1$ for SU(2) and $R=1.35 \pm 0.1$ for SU(4) as well as the
corresponding effective charges, characterizing the quantum liquid behaviour.
This result, in perfect agreement with theory, provides a strong quantitative
experimental background for further developments of the many-body physics.
Moreover, we discovered a new scaling law for the effective charge, signalling
as-yet-unknown universality in the non-equilibrium regime. Our method to
address quantum liquids through their non-equilibrium noise paves a new road to
tackle the exotic nature of quantum liquids out-of-equilibrium in various
physical systems.
