  The ability to create and investigate composite fermionic phases opens new
avenues for the investigation of strongly correlated quantum matter. We report
the experimental observation of a series of quantized conductance steps within
strongly interacting electron waveguides formed at the LaAlO$_3$/SrTiO$_3$
interface. The waveguide conductance follows a characteristic sequence within
Pascal's triangle: $(1, 3, 6, 10, 15, ...)\cdot e^2/h$, where $e$ is the
electron charge and $h$ is the Planck constant. The robustness of these steps
with respect to magnetic field and gate voltage indicate the formation of a new
family of degenerate quantum liquids formed from bound states of $n = 2, 3, 4,
...$ electrons. These experiments could provide solid-state analogues for a
wide range of composite fermionic phases ranging from neutron stars to
solid-state materials to quark-gluon plasmas.
