Resonant Tunneling between quantum Hall states at filling ν = 1 and ν = 1/3

We study the problem of resonant tunneling between a Fermi liquid and the edge of a $\nu=1/3$ fractional quantum Hall state. In the limit of weak coupling, the system is adequately described within the sequential tunneling approximation. At low temperatures, however, the system crosses over to a strong coupling phase, which we analyze using renormalization group techniques. We find that at low temperatures a "perfect" can be achieved by tuning two parameters. This resonance has a peak conductance $G = e^2/2h$ and is a realization of the weak backscattering limit of the $g=1/2$ Luttinger liquid, as well as the non Fermi liquid fixed point of the two channel Kondo problem. We discuss several regimes which may be experimentally accessible as well as the implications for resonances recently observed in cleaved edge overgrowth structures.