Diffusion coefficiets of rubidium in buffer gases

In the article [2] we used the methods developed above for a precise measurement of spinwave decoherence in the absence of light i.e. during storage in quantum memory. If multiple spatial spinwave modes are to be utilized the dominant decoherence mechanism is diffusion of atoms in the buffer gas. The numerical values of the diffusion coefficients quoted in literature are widely scattered likely due to involved way they were measured which was typically 40 years ago. Therefore we decided it would be worthwhile to publish a method relying on modern tools widely accessible nowadays. The method enables quantifying diffusion in any single sealed cell, within pressure range that allows for observation of the Raman scattering. The method is based on calculating the spinwave decay rate by measuring the readout signal as a function of storage time. Spinwaves with large wavevector K are characterized by fast spatial variation of the phase of coherence between the ground states and thus easily decohere due to random movements of the atoms as they diffuse in the buffer gas. As this process continues the ground state coherence is spatially averaged, only zero-K wavevector spinwave survives and the only forward scattering is observed.

The dependence of the decay rate on the scattering angle and thus the spinwave wavevector K is found by observing the readout in the far field on a camera. A square dependence of the decay rate on the K vector length reassures proper measurement.

Due to the high importance of the decoherence process and the necessity of its precise characterization we developed an independent method to measure the diffusion coefficients based on observation of the spreading of initially localized optically pumped population imbalance in the cell [1]. This is a particularly simple concept. With a pulsed pump beam focused to a fraction of a millimeter we locally pump atoms to ground state of F=1. After a variable temporal delay we illuminate the entire cell tuned to F=1 à F’=2 transition and we image the shadow of pumped atoms onto a camera. Fourier analysis of the optical depth images enables calculating the decay time for various Fourier components. Final data processing follows the same trail as in prior method. Note however, that this method probes the population distribution, not the coherence and can be performed with high buffer gas pressure forbidding Raman scattering.

Using methods presented in [1] and [2] we confirmed some literature values. Both methods gave practically same results. In addition we measured the diffusion of Rubidium in Xenon for the first time directly. This result may help in recently popular biomedical imaging with hyperpolarized Xenon, which is obtained in spin exchange collisions with optically polarized rubidium.

Buffer gas Our experimental results D_0 [cm^2/s] Our theoretical results D_0 [cm^2/s] Some of previous experimental results  
Neon 0.19 0.15 0.11 [Shuker 2008], 0.18 [Vanier 1974], 0.31 [Franzen 1959, Arditi 1964], 0.48 [Franz 1965]  
Krypton 0.069 0.065 0.1 [Bouchiat 1972], 0.04 [Higginbottom 2012]  
Xenon 0.055 0.055 No experimental data  


  1. M. Parniak and W. Wasilewski , Direct observation of atomic diffusion in warm rubidium ensembles, Appl. Phys. B 116, 415-421 (2014)
  2. R. Chrapkiewicz , W. Wasilewski , and C. Radzewicz, How to measure diffusional decoherence in multimode Rubidium vapor memories?, Opt. Commun. 317, 1-6 (2014)
  3. M. Parniak, BSc degree work (PL)
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