Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Glory and Resonance Effects in the Index of Refraction for Atomic Waves

E. Audouard, P. Duplàa, J. Vigué

Published Nov 10, 1995• 15 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/32/5/003

Related papers

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.

Journal de Physique II•Apr 1, 1997•16 citations

Glory Oscillations in the Index of Refraction for Matter Waves

Tony Roberts, Alexander D. Cronin, David A. Kokorowski +1 more

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.

arXiv:physics/0203008•Physical Review Letters•Oct 29, 2002•30 citations

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

Marion Jacquey, M Büchner, G. Trénec +1 more

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.

arXiv:quant-ph/0611236•Physical Review Letters•Jun 15, 2007•18 citations

Measurement of the refraction index for atom waves

Marion Jacquey, M Büchner, G. Trénec +1 more

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.

Annales de Physique•Jan 1, 2007•0 citations

Refining molecular potentials using atom interferometry

Robert C. Forrey, Li You, Vasili A. Kharchenko +1 more

We present a theoretical study of the index of refraction of argon for the propagation of sodium matter waves. The sensitivity of the index of refraction to the details of the molecular potential curve is analyzed. Our calculations reveal velocity-dependent oscillations in the index of refraction that may be detectable, particularly at low temperatures, in atom interferometry measurements. A procedure for refining molecular potential curves is outlined.

Physical Review A•May 1, 1997•15 citations

Atomic beam propagation effects: index of refraction and longitudinal tomography

David A. Kokorowski, Troy D. Hammond, Edward T. Smith +4 more

We present initial measurements of the dispersive index of refraction for sodium matter waves passing through argon. In addition, we describe a novel scheme for performing tomography on the longitudinal quantum state of particles in an atomic beam.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 1997•0 citations
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.
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 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 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.