  A spatial potential trap is formed in a 6.0 {\mu}m Al(Ga)N nanowire by
varying the Al composition along its length during epitaxial growth. The
polariton emission characteristics of a dielectric microcavity with the single
nanowire embedded in-plane has been studied at room temperature. Excitation is
provided at the Al(Ga)N end of the nanowire and polariton emission is observed
from the lowest bandgap GaN region of the nanowire. Comparison of the results
with those measured in an identical microcavity with an uniform GaN nanowire
and having an identical exciton-photon detuning suggests evaporative cooling of
the polaritons as they are transported across the trap in the Al(Ga)N nanowire.
Measurement of the spectral characteristics of the polariton emission, their
momentum distribution, first-order spatial coherence and time-resolved
measurements of polariton cooling provide strong evidence of the formation of
an equilibrium Bose-Einstein condensate, a unique state of matter in solid
state systems, in the GaN region of the nanowire, at room temperature. An
equilibrium condensate is not formed in the GaN nanowire dielectric microcavity
without the spatial potential trap.
