  We discuss a platform for the synthetic realization of key physical
properties of helical Tomonaga Luttinger liquids (HTLLs) with ultracold
fermionic atoms in one-dimensional optical lattices. The HTLL is a strongly
correlated metallic state where spin polarization and propagation direction of
the itinerant particles are locked to each other. We propose an unconventional
one-dimensional Fermi-Hubbard model which, at quarter filling, resembles the
HTLL in the long wavelength limit, as we demonstrate with a combination of
analytical (bosonization) and numerical (density matrix renormalization group)
methods. An experimentally feasible scheme is provided for the realization of
this model with ultracold fermionic atoms in optical lattices. Finally, we
discuss how the robustness of the HTLL against back-scattering and
imperfections, well known from its realization at the edge of two-dimensional
topological insulators, is reflected in the synthetic one-dimensional scenario
proposed here.
