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Multiple scattering of matter waves: An analytic model of the refractive index for atomic and molecular gases

Mikhail Lemeshko, Břetislav Friedrich

We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines the Wentzel-Kramers-Brillouin (WKB) treatment of the long-range attraction with the Fraunhofer model treatment of the short-range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey et al. [Phys. Rev. Lett. 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two-dimensional ``hard core'' of the potential, is essential for obtaining a correct imaginary part of the refractive index.We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines the Wentzel-Kramers-Brillouin (WKB) treatment of the long-range attraction with the Fraunhofer model treatment of the short-range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey et al. [Phys. Rev. Lett. 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two-dimensional ``hard core'' of the potential, is essential for obtaining a correct imaginary part of the refractive index.

arXiv:1003.0854Physical Review AAug 18, 20103 citations

Averaged wave operators in the problem of scattering by a Brownian particle

S. E. Cheremshantsev

Journal of Mathematical SciencesApr 1, 19911 citation

Development of fluctuations in propagation of coherent light in a gas. II

F. A. Vorob'ev, R. I. Sokolovskiǐ

Russian Physics JournalJan 1, 19750 citations

Refractive Index for Atomic Waves: Theory and Detailed Calculations

C. Champenois, E. Audouard, P. Duplàa +1 more

This paper describes new theoretical results and calculations concerning the recently introduced index of refraction of a gas for atomic waves. More precisely, the motion of the atoms of the gas is taken into account and the equation describing the Doppler and Fizeau effects is introduced. The case where the atoms of the wave and the gas have spin 1/2 is also discussed and the rotatory power and circular dichroism of an optically pumped gas is calculated. Finally, the index of the rare gases for sodium waves is calculated. The results show how important it is to take into account glory scattering and Doppler averaging to make a meaningful comparison with experiments. The index appears to be very sensitive to the precise value of the quantum parameter B = 2μDeσ2 (in atomic unit). Using the available interaction potential curves, we obtained a reasonably good agreement between the measurements and the corresponding calculated values. However, some experimental results appear difficult to explain with the best available interaction potentials.This paper describes new theoretical results and calculations concerning the recently introduced index of refraction of a gas for atomic waves. More precisely, the motion of the atoms of the gas is taken into account and the equation describing the Doppler and Fizeau effects is introduced. The case where the atoms of the wave and the gas have spin 1/2 is also discussed and the rotatory power and circular dichroism of an optically pumped gas is calculated. Finally, the index of the rare gases for sodium waves is calculated. The results show how important it is to take into account glory scattering and Doppler averaging to make a meaningful comparison with experiments. The index appears to be very sensitive to the precise value of the quantum parameter B = 2μDeσ2 (in atomic unit). Using the available interaction potential curves, we obtained a reasonably good agreement between the measurements and the corresponding calculated values. However, some experimental results appear difficult to explain with the best available interaction potentials.

Journal de Physique IIApr 1, 199716 citations

Negative refraction for matter waves in multiple scattering theory

Florian Pinsker

Nov 13, 20140 citations

Refractive index for matter waves in ultracold gases

Vasili A. Kharchenko, A. Dalgarno

An analytical expression for the refractive index of atomic and molecular matter waves in ultracold gases is obtained. Asymptotic formulas for the refractive index are derived for high and low projectile velocities, and intermediate velocities are investigated with the eikonal approximation. The real and imaginary parts of the matter wave refractive index are expressed via the complex scattering length of elastic and superelastic collisions. It is shown that superelastic collisions dramatically influence the low-energy behavior of the refractive index. A discussion is given of proposed measurements of the real and imaginary parts of the scattering length using the interferometry of slow de Broglie waves.An analytical expression for the refractive index of atomic and molecular matter waves in ultracold gases is obtained. Asymptotic formulas for the refractive index are derived for high and low projectile velocities, and intermediate velocities are investigated with the eikonal approximation. The real and imaginary parts of the matter wave refractive index are expressed via the complex scattering length of elastic and superelastic collisions. It is shown that superelastic collisions dramatically influence the low-energy behavior of the refractive index. A discussion is given of proposed measurements of the real and imaginary parts of the scattering length using the interferometry of slow de Broglie waves.

Physical Review AJan 18, 200116 citations

On the statistical averaging procedure for the refractive index of matter waves

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