  We show that multiple point contacts on a barrier separating two laterally
coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the
tunneling conductance. These quantum coherence effects provide new evidence for
the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a
two point contact, we identify coherent and incoherent regimes determined by
the relative magnitude of their separation and the temperature. We analyze both
regimes in the strong and weak tunneling amplitude limits as well as their
temperature dependence. We find that the tunneling conductance should exhibit
AB oscillations in the coherent regime, both at strong and weak tunneling
amplitude with the same period but with different functional form.
