The principle of the equivalence of gravitational and inertial mass is one of the cornerstones of general relativity. Considerable efforts have been made and are still being made to verify its validity. A quantum-mechanical formulation of gravity allows for non-Newtonian contributions to the force which might lead to a difference in the gravitational force on matter and antimatter. While it is widely expected that the gravitational interaction of matter and of antimatter should be identical, this assertion has never been tested experimentally. With the production of large amounts of cold antihydrogen at the CERN Antiproton Decelerator, such a test with neutral antimatter atoms has now become feasible. For this purpose, we have proposed to set up the AEGIS experiment at 0168-583X/$ -see front matter Ó 2007 Published by Elsevier B.V.

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Using an atom interferometer, we have measured the static electric polarizability of 7 Li α = (24.33 ± 0.16) × 10 −30 m 3 = 164.19 ± 1.08 atomic units with a 0.66% uncertainty. Our experiment, which is similar to an experiment done on sodium in 1995 by D. Pritchard and co-workers, consists in applying an electric field on one of the two interfering beams and measuring the resulting phaseshift. With respect to D. Pritchard's experiment, we have made several improvements which are described in detail in this paper: the capacitor design is such that the electric field can be calculated analytically; the phase sensitivity of our interferometer is substantially better, near 16 mrad/ √ Hz; finally our interferometer is species selective so that impurities present in our atomic beam (other alkali atoms or lithium dimers) do not perturb our measurement. The extreme sensitivity of atom interferometry is well illustrated by our experiment: our measurement amounts to measuring a slight increase ∆v of the atom velocity v when it enters the electric field region and our present sensitivity is sufficient to detect a variation ∆v/v ≈ 6 × 10 −13 .

We summarise the scientific and technological aspects of the Search for Anomalous Gravitation using Atomic Sensors (SAGAS) project, submitted to ESA in June 2007 in response to the Cosmic Vision 2015-2025 call for proposals. The proposed mission aims at flying highly sensitive atomic sensors (optical clock, cold atom accelerometer, optical link) on a Solar System escape trajectory in the 2020 to 2030 time-frame. SAGAS has numerous science objectives in fundamental physics and Solar System science, for example numerous tests of general relativity and the exploration of the Kuiper belt. The combination of highly sensitive atomic sensors and of the laser link well adapted for large distances will allow measurements with unprecedented accuracy and on scales never reached before. We present the proposed mission in some detail, with particular emphasis on the science goals and associated measurements and technologies.

Abstract. In this paper, we describe in detail the BMV (Biréfringence Magnétique du Vide) experiment, a novel apparatus to study the propagation of light in a transverse magnetic field. It is based on a very high finesse Fabry-Perot cavity and on pulsed magnets specially designed for this purpose. We justify our technical choices and we present the current status and perspectives. PACS. PACS-key discribing text of that key -PACS-key discribing text of that key

We report the first experimental test of the topological phase predicted by He and McKellar and by Wilkens in 1993: this phase, which appears when an electric dipole propagates in a magnetic field, is connected to the Aharonov-Casher effect by electric-magnetic duality. The He-McKellarWilkens phase is quite small, at most 27 mrad in our experiment, and this experiment requires the high phase sensitivity of our atom interferometer with spatially separated arms as well as symmetry reversals such as the direction of the electric and magnetic fields. The measured value of the HeMcKellar-Wilkens phase differs by 31% from its theoretical value, a difference possibly due to some as yet uncontrolled systematic errors.PACS numbers: 03.65. Vf; 03.75.Dg; 39.20.+q In quantum mechanics, propagation can be modified without any force, the first example being the AharonovBohm effect [1] discovered in 1959: a magnetic field shifts the fringes of an electron interferometer, even if the field vanishes on the electron paths. This was the discovery of topological phases [2], which differ considerably from ordinary dynamic phases because they are independent of the particle velocity and non-reciprocal, i.e. they change sign when propagation is reversed. In 1984, Aharonov and Casher [3] discovered another topological phase, which appears in a matter wave interferometer operated with a particle carrying a magnetic dipole, the interferometer arms encircling a line of electric charges. In 1993, He and McKellar [4] applied electricmagnetic duality [5] to the Aharonov-Casher phase, thus exhibiting a topological phase when the particle carries an electric dipole and the interferometer arms encircle a line of magnetic monopoles: this phase appeared as speculative but a possible experiment was rapidly proposed by Wilkens [6]. Whereas the Aharonov-Bohm and Aharonov-Casher (AC) effects were rapidly tested by experiments [7][8][9][10][11][12], no experimental test of the HeMcKellar-Wilkens (HMW) phase has been available so far. Here, we report the first experimental attempt to detect the HMW phase, with results in reasonable agreement with theory. The HMW phase is the last member of the family of topological phases when free particles propagate in electromagnetic fields [13,14]: one might expect similar phases for higher order electromagnetic multipoles but the calculated values for quadrupoles [15] are so small that their detection is presently out of reach. [19], in which the particle propagates in a superposition of two spin states: this type of interferometer is ideal for the detection of a spindependent phase and it provides an excellent cancelation of systematic errors. The use of a Ramsey interferometer for the HMW phase would require the production of a quantum superposition of states with opposite electric dipole moments, which is feasible if states of opposite parity are quasi-degenerate [14], a situation which does not exist with ground state atoms. Consequently, the HMW phase must be measured by alternating field configurations a...

The effective hyperfine Hamiltonian is studied in the case of homonuclear diatomic molecules, using irreducible tensorial algebra. The second order perturbation terms due to the magnetic dipole and electric quadrupole Hamiltonian are calculated in a compact form. These calculations are applied to the B state of molecular iodine : the experimental values of the scalar and tensorial spin-spin coupling constants are interpreted. Moreover it is shown that the recently published magnetic octupole coupling value for the B state is unrealistic and also that some other terms must be introduced in the hyperfine Hamiltonian

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