  The probability of a random walker to return to its starting point in
dimensions one and two is unity, a theorem first proven by G. Polya. The
recurrence probability -- the probability to be found at the origin at a time
t, is a power law with a critical exponent d/2 in dimensions d=1,2. We report
an experiment that directly measures the Laplace transform of the recurrence
probability in one dimension using Electromagnetically Induced Transparency
(EIT) of coherent atoms diffusing in a vapor-cell filled with buffer gas. We
find a regime where the limiting form of the complex EIT spectrum is universal
and only depends on the effective dimensionality in which the random recurrence
takes place. In an effective one-dimensional diffusion setting, the measured
spectrum exhibits power law dependence over two decades in the frequency domain
with a critical exponent of 0.56 close to the expected value 0.5. Possible
extensions to more elaborate diffusion schemes are briefly discussed.
