  We study experimentally the critical correlation in an ultra-cold Bose gas
with a temporal Talbot-Lau (TL) interferometer. Near the critical temperature,
we observe a bi-modal density distribution in an ultra-cold Bose gas after the
application of the TL interferometer. The measured fraction of the narrower
peak in the density distribution displays a clear peak within the critical
regime. The peak position agrees with the critical temperature calculated with
the finite-size and interaction corrections. The critical exponents are
extracted from the peak and they agree with the critical exponents for the
correlation length.
