  The Tomonaga-Luttinger liquid (TLL) theory describes the low-energy
excitations of strongly correlated one-dimensional (1D) fermions. In the past
years, a number of studies have provided a detailed understanding of this
universality class. More recently, theoretical investigations that go beyond
the standard low-temperature, linear-response, TLL regime have been developed.
While these provide a basis for understanding the dynamics of the
spin-incoherent Luttinger liquid, there are few experimental investigations in
this regime. Here we report the observation of a thermally-induced,
spin-incoherent Luttinger liquid in a $^6$Li atomic Fermi gas confined to 1D.
We use Bragg spectroscopy to measure the suppression of spin-charge separation
and the decay of correlations as the temperature is increased. Our results
probe the crossover between the coherent and incoherent regimes of the
Luttinger liquid, and elucidate the roles of the charge and the spin degrees of
freedom in this regime.
