  We consider the tunneling current through a double point-contact Fabry-Perot
interferometer such as used in recent experimental studies of the fractional
quantum Hall plateau at filling fraction nu=5/2. We compare the predictions of
several different models of the state of the electrons at this plateau: the
Moore-Read, anti-Pfaffian, SU(2)_2 NAF, K=8 strong pairing, and (3,3,1) states.
All of these predict the existence of charge e/4 quasiparticles, but the first
three are non-Abelian while the last two are Abelian. We give explicit formulas
for the scaling of charge e/2 and charge e/4 quasiparticle contributions to the
current as a function of temperature, gate voltage and distance between the two
point contacts for all three models. Based on these, we analyze several
possible explanations of two phenomena reported for recent experiments by
Willett et al., namely halving of the period of the observed resistance
oscillations with rising temperature and alternation between the same two
observed periods at low temperatures as the area of the interference loop is
varied with a side gate. We conclude that the most likely explanation is that
the observed alternation is due to switching between even and odd numbers of
charge e/4 quasiparticles enclosed within the loop as a function of side gate
voltage, which is a clear signature of the presence of non-Abelian anyons.
However, there are important features of the data which do not have a simple
explanation within this picture. We suggest further experiments which could
help rule out some possible scenarios. We make the corresponding predictions
for future tunneling and interference experiments at the other observed second
Landau level fractional quantum Hall states.
