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arXiv:quant-ph/0611236 · Physical Review Letters

First Measurements of the Index of Refraction of Gases for Lithium Atomic Waves

Marion Jacquey, M Büchner, G. Trénec, J. Vigué

Published Jun 15, 2007• 18 citations
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Abstract

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.

DOI
10.1103/physrevlett.98.240405

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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.
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.
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.
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.
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.
We investigated the complex index of refraction in the x-ray regime of atoms in laser light. The laser (intensity up to 1013W∕cm2{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}1013W∕cm2, wavelength 800nm800\phantom{\rule{0.3em}{0ex}}\mathrm{nm}800nm) modifies the atomic states but, by assumption, does not excite or ionize the atoms in their electronic ground state. Using quantum electrodynamics, we devise an ab initio theory to calculate the dynamic dipole polarizability and the photoabsorption cross section, which are subsequently used to determine the real and imaginary part, respectively, of the refractive index. The interaction with the laser is treated nonperturbatively; the x-ray interaction is described in terms of a one-photon process. We numerically solve the resolvents involved using a single-vector Lanczos algorithm. Finally, we formulate rate equations to copropagate a laser and an x-ray pulse through a gas cell. Our theory is applied to argon. We study the x-ray polarizability and absorption near the argon KKK edge over a large range of dressing-laser intensities. We find electromagnetically induced transparency (EIT) for x rays on the Ar $1s\ensuremath{\rightarrow}4p$ pre-edge resonance. We demonstrate that EIT in Ar allows one to imprint the shape of an ultrafast laser pulse on a broader x-ray pulse (duration 100ps100\phantom{\rule{0.3em}{0ex}}\mathrm{ps}100ps, photon energy 3.2keV3.2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}3.2keV). Our work thus opens new opportunities for research with hard x-ray sources.