Universal Spectra of Coherent Atoms in a Recurrent Random Walk

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dc.creatorPugatch, R.
dc.creatorFirstenberg, O.
dc.creatorShuker, M.
dc.creatorDavidson, N.
dc.date2009-04-20
dc.date2009-04-22
dc.date.accessioned2026-07-07T13:06:44Z
dc.date.available2026-07-07T13:06:44Z
dc.descriptionThe 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.
dc.description5 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0904.3015
dc.identifierhttp://arxiv.org/abs/0904.3015
dc.identifierPhys. Rev. Lett. vol. 102, p. 150602 (2009)
dc.identifierdoi:10.1103/PhysRevLett.102.150602
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227876
dc.subjectStatistical Mechanics
dc.titleUniversal Spectra of Coherent Atoms in a Recurrent Random Walk
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