Université Paul Sabatier - Bat. 3R4 - 118 route de Narbonne 31062 Toulouse Cedex 09, France


Accueil > Recherche > Équipe Interférométrie > Recherche > Interféromètre à jet de lithium

Theoretical works

The development of an atom interferometer requires theoretical works aiming at a better understanding of its operation. We have worked on several subjects :
- the index of refraction of gases for matter waves
- the fringe contrast in Mach-Zehnder atom interferometers
- an unified description of laser diffraction of atoms, using Bloch atomic states
- a possible test of the electric neutrality of atoms by atom interferometry
- phase noise on atom interference signals due to vibrations of the interferometer.

a) Index of refraction of gases for atom waves

We have studied theoretically this index of refraction and we have shown that the index of refraction diverges when the relative velocity tends toward zero, that the glory oscillations are the dominant observable feature and that they are not in phase for the real and imaginary parts. Finally, there are some open problems concerning the average over a thermal distribution of the gas and we are still working on these questions.

E. AUDOUARD, P. DUPLAA and J. VIGUÉ, " Glory and resonance effects in the index of refraction for atomic waves. ", Europhys. Lett. 32, 397-400 (1995) and erratum 37, 311 (1997)

C. CHAMPENOIS, E. AUDOUARD, P. DUPLAA and J. VIGUÉ, " Refractive index for atomic waves : theory and detailed calculations ", Journal-de-Physique-II 7, 523-541 (1997)

b) Understanding how an atom interferometer works

In a first step, we have studied the fringe contrast in Mach-Zehnder atom interferometers, with a calculation which included the effect of diffraction by the collimating slit. We have thus been able to describe the fringe contrast a function of several parameters, including the main alignment defects and we have been able to test most of the results of our calculations, with our lithium interferometer.

We have been interested by developing an unified formalism to describe Bragg diffraction by quasi-resonant laser standing wave. We have found that it is possible to treat all the well-known regimes (Bragg, Raman-nath, etc.) by using the basis of atomic Bloch states to describe [the motion of the atoms in the direction of the laser standing wave. This basis set was introduced to describe atomic motion near 1980 by Minogin et Lethokhov and several experiments have tested with ultra-cold the dynamics known as Bloch oscillations. The use of this basis set to describe Bragg diffraction is very interesting, in particular to understand the role of the various parameters (laser power density, interaction time, incidence angle) and to study higher diffraction orders.

C. CHAMPENOIS, M. BÜCHNER and J. VIGUÉ " Fringe contrast in three grating Mach Zehnder atomic interferometer ", Eur. Phys. J. D 5, 363-374 (1999)

C. CHAMPENOIS, M. BÜCHNER, R. DELHUILLE, R. MATHEVET, C. ROBILLIARD, C. RIZZO and J. VIGUÉ, " Atomic diffraction by a laser standing wave : analysis using Bloch states ", Eur. Phys. J. D 13, 271-278 (2000)

R. DELHUILLE, A. MIFFRE, B. VIARIS DE LESEGNO, M. BÜCHNER, C. RIZZO, G. TRÉNEC and J. VIGUÉ, " Fringe contrast in Mach-Zehnder atom interferometers ", Acta Physica Polonica B 33, 2157-71 (2002)

M. BÜCHNER, R. DELHUILLE, A. MIFFRE, C. ROBILLIARD, J. VIGUÉ and C. CHAMPENOIS, " Diffraction phases in atom interferometers ", Phys. Rev. A, 68, 013607 (2003)

c) Possible test the electric neutrality of atoms by atom interferometry

We have studied how one can measure by atom interferometry a possible non-zero electric charge carried by atoms. The principle of the experiment is just to apply a uniform electric field over the apparatus (but not on the diffraction region in order not to perturb the interferometer operation). Numerical estimates suggest that, with slow atoms, a very large sensitivity can be achieved, with the smallest detectable charge of the order of 10-21 qe (where qe is the electron charge). The same sensitivity has been achieved with neutrons, through a neutron optics/interferometry experiment. With atoms, the main difficulty will come from the electric polarizability, which is obviously considerably larger than for neutrons, and the atom electric polarizability will induce large phase-shifts in case of weak misalignments : because these phase-shifts are quadratic in the applied electric field while the searched effect is linear, these stray phase-shifts should not induce any error but they will limit the sensitivity.

C. CHAMPENOIS, M. BÜCHNER, R. DELHUILLE, R. MATHEVET, C. ROBILLIARD, C. RIZZO and J. VIGUÉ, " A novel method to test atom neutrality with a Mach-Zehnder atom interferometer ", Proc of Workshop Hydrogen Atom II, S. G. Karshenboim, F. Pavone, F. Bassani, T. W. Hänsch, M. Inguscio éditeurs, Springer Lecture Notes in Physics p 554 (2001)

R. DELHUILLE, C. CHAMPENOIS, M. BÜCHNER, R. MATHEVET, C. RIZZO, C. ROBILLIARD and J. VIGUÉ, " Atom interferometry : principles and applications to fundamental physics ", in Quantum Electrodynamics and the Physics of the Vacuum, QED 2000, AIP Conference Proceedings 564, G. Cantatore ed., p 192-199 (2001)

d) Phase noise on atom interference signals due to vibrations of the interferometer

Atom interferometers have a very large sensitivity to inertial effects. This sensitivity has been used to develop very sensitive accelerometers and gyrometers. But it also makes the interferometers very sensitive to vibrations.

In a Mach-Zehnder atom interferometer, vibrations displace and distort the rail holding the three diffraction gratings and we have developed a simple model of the dynamics of this rail, using elasticity theory, in order to describe their effects on the grating positions and the resulting phase noise induced on the interferometer signal.
This model provides an understanding of the contributions of the various frequencies to the phase noise and this model proves that the vibration induced rotations of the rail are the dominant effect in our experiment, because our rail is very stiff. We have tested the main predictions of our model in the case of our setup and our observations, in particular the decrease of the fringe visibility when the diffraction order increases, are well explained. This model can be used for an optimization of the design of atom interferometer.

A. MIFFRE, M. JACQUEY, M. BÜCHNER, G. TRENEC and J. VIGUÉ, "Vibration induced phase noise in Mach-Zehnder atom interferometers", submitted to Appl. Phys. B ; preprint available on http://hal.ccsd.cnrs.fr/ccsd-00022231.

A. MIFFRE, M. JACQUEY, M. BÜCHNER, G. TRENEC and J. VIGUÉ, " Phase noise due to vibrations in Mach-Zehnder atom interferometers", submitted to EuroPhysics Lett. ; preprint available on https://hal.ccsd.cnrs.fr/ccsd-00022285.