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Universal Spectra of Coherent Atoms in a Recurrent Random Walk

  • Pugatch, R.
  • Firstenberg, O.
  • Shuker, M.
  • Davidson, N.
Published Article
Publication Date
Apr 22, 2009
Submission Date
Apr 20, 2009
DOI: 10.1103/PhysRevLett.102.150602
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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.

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