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arXiv:physics/0203008 · Physical Review Letters

Glory Oscillations in the Index of Refraction for Matter Waves

Tony Roberts, Alexander D. Cronin, David A. Kokorowski, David E. Pritchard

Published Oct 29, 2002• 30 citations
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Abstract

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N2 over a wide range of sodium velocities. We observe glory oscillations--a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.

DOI
10.1103/physrevlett.89.200406

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We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N2 over a wide range of sodium velocities. We observe glory oscillations--a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.
We have performed the first detailed calculation of the index of refraction of a gas (argon) for an atomic wave (sodium). The index depends rapidly on the wave vector k r describing the relative motion and exhibits two interesting effects: Breit-Wigner-type resonances at very low k r values, and intense glory oscillations over a large range of k r values. A recent experiment has measured this index of refraction, and our calculation using a very accurate sodium-argon potential and taking into account the thermal motion of argon, agrees quite well with the experimental result.
We report the first measurements of the index of refraction of gases for lithium waves. Using an atom interferometer, we have measured the real and imaginary parts of the index of refraction n for argon, krypton, and xenon as a function of the gas density for several velocities of the lithium beam. The linear dependence of (n-1) with the gas density is well verified. The total collision cross section deduced from the imaginary part of (n-1) is in very good agreement with traditional measurements of this quantity. Finally, the real and imaginary parts of (n-1) and their ratio rho exhibit glory oscillations, in good agreement with calculations.
We have developed a Mach-Zehnder atom interferometer which uses elastic diffraction of lithium atom on laser standing waves for the coherent manipulation of the atom wave. The interference signal is of sufficient quality to achieve a phase sensitivity near 10 milliradians/. With this apparatus, we have recently measured the index of refraction of several gases for lithium waves. The interference signals give access to the real and imaginary parts of () and we have tested the linear dependence of these two quantities with gas density. The measured values of () are in good agreement with calculations and they exhibit glory oscillations, as predicted by theory.
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.
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.