  Coupled-wire constructions offer particularly simple and powerful models to
capture the essence of strongly correlated topological phases of matter. They
often rely on effective theories valid in the low-energy and strong coupling
limits, which impose severe constraints on the physical systems where they
could be realized. We investigate the microscopic relevance of a class of
coupled-wire models and their possible experimental realization in cold-atom
experiments. We connect with earlier results and prove the emergence of
fractional quantum Hall states in the limit of strong inter-wire tunneling.
Contrary to previous studies relying on renormalization group arguments, our
microscopic approach exposes the connection between coupled-wire constructions
and model wavefunctions in continuum Landau levels. Then, we use exact
diagonalization methods to investigate the appearance of these fractional
quantum Hall states in more realistic settings. We examine the parameter
regimes where these strongly correlated phases arise, and provide a way to
detect their appearance in cold-atom experiments through standard
time-of-flight measurements. Motivated by this experimental probe, we finally
propose a realization of our model with cold-atom in spin-dependent optical
lattices. Our estimates show that the previous fractional quantum Hall phases
lie within experimentally accessible parameter regimes, giving a viable route
towards their experimental study.
