  Understanding the effects of nonequilibrium on strongly interacting quantum
systems is a challenging problem in condensed matter physics. In dimensions
greater than one, interacting electrons can often be understood within
Fermi-liquid theory where low-energy excitations are weakly interacting
quasiparticles. On the contrary, electrons in one dimension are known to form a
strongly-correlated phase of matter called a Luttinger liquid (LL), whose
low-energy excitations are collective density waves, or plasmons, of the
electron gas. Here we show that spectroscopy of locally injected high-energy
electrons can be used to probe energy relaxation in the presence of such strong
correlations. For detection energies near the injection energy, the electron
distribution is described by a power law whose exponent depends in a continuous
way on the Luttinger parameter, and energy relaxation can be attributed to
plasmon emission. For a chiral LL as realized at the edge of a fractional
quantum Hall state, the distribution function grows linearly with the distance
to the injection energy, independent of filling fraction.
