  The topological Kondo (TK) model has been proposed in solid-state quantum
devices as a way to realize non-Fermi liquid behaviors in a controllable
setting. Another motivation behind the TK model proposal is the demand to
demonstrate the quantum dynamical properties of Majorana fermions, which are at
the heart of their potential use in topological quantum computation. Here we
consider a junction of crossed Tonks-Girardeau gases arranged in a
star-geometry (forming a Y -junction), and we perform a theoretical analysis of
this system showing that it provides a physical realization of the topological
Kondo model in the realm of cold atom systems. Using computer-generated
holography, we experimentally implement a Y-junction suitable for atom
trapping, with controllable and independent parameters. The junction and the
transverse size of the atom waveguides are of the order of 5 micrometers,
leading to favorable estimates for the Kondo temperature and for the coupling
across the junction. Since our results show that all the required theoretical
and experimental ingredients are available, this provides the demonstration of
an ultracold atom device that may in principle exhibit the topological Kondo
effect.
