  Recent experiments have shown that it is possible to create an in-plane
harmonic potential trap for a two-dimensional (2D) gas of exciton-polaritons in
a microcavity structure, and evidence has been reported of Bose-Einstein
condensation of polaritons accumulated in this type of trap. We present here
the theory of Bose-Einstein condensation (BEC) and superfluidity of the exciton
polaritons in a harmonic potential trap. Along the way, we determine a general
method for defining the superfluid fraction in a 2D trap, in terms of angular
momentum representation. We show that in the continuum limit, as the trap
becomes shallower the superfluid fraction approaches the 2D Kosterlitz-Thouless
limit, while the condensate fraction approaches zero, as expected.
