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Register a new userUniversal Spectra of Coherent Atoms in a Recurrent Random Walk
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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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In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between V and -V. If V is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the model accounts readily for the particles drift along the temperature gradient and recovers basic results of the conventional thermophoresis theory.
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