Measurement of the Aharonov-Casher geometric phase with a separated-arm atom interferometer

Abstract

-In this letter, we report a measurement of the Aharonov-Casher (AC) geometric phase with our lithium atom interferometer. The AC phase appears when a particle carrying a magnetic dipole propagates in a transverse electric field. The first measurement of the AC phase was done with a neutron interferometer in 1989 by A. Cimmino et al. (Phys. Rev. Lett. 63, 380, 1989) and all the following experiments were done with Ramsey or Ramsey-Bordé interferometers with molecules or atoms. In our experiment, we use lithium atoms pumped in a single hyperfineZeeman sublevel and we measure the AC-phase by applying opposite electric fields on the two interferometer arms. Our measurements are in good agreement with the expected theoretical values and they prove that this phase is independent of the atom velocity.In 1984, Y. Aharonov, and A. Casher [1] discovered the geometric phase which is called by their name. This phase appears when a particle with a magnetic dipole interacts with an electric field perpendicular to both the particle velocity and to the magnetic dipole. This phase had also been discussed by J. Anandan [2], who did not remark its unusual properties. The Aharonov-Casher (AC) phase is the second example of a geometric phase, after the Aharonov-Bohm phase [3]. A third geometric phase predicted in 1993/1994 by X.-G. He, B.H.J. McKellar [4] and by M. Wilkens [5] is now named the He-McKellarWilkens (HMW) phase, and we have recently measured this phase [6,7]. This phase appears, if an electric dipole travels in a magnetic field B and if the scalar triple product of the dipole, B and the velocity vectors is not zero. All these phases belong to the general class of geometric phases discussed by M.V. Berry in 1984 [8,9] and they are very interesting because they strongly differ from dynamical phases: geometric phases modify the wave propagation in the absence of any force on the particle; they are independent of the modulus of the particle velocity but they change sign if the velocity is reversed.In the present letter, we describe measurements of the AC phase shift using a separated-arm 7 Li atom interferometer using Bragg diffraction on laser standing waves.The internal quantum state of the atom is the same in the two interferometer arms and we apply opposite electric fields and a common magnetic field on the two interferometer arms. The atom fringes are phase shifted by both the AC and the HMW phases. The AC phase is proportional to the atom magnetic dipole moment, thus depends on the magnetic sublevel, while the HMW phase is independent. By combining measurements made with the 7 Li atoms pumped in F = 2 either in m F = +2 or in m F = −2, we can extract both phases. In the following, we focus on the AC phase measurements. As explained below, this is the first AC phase measurement of this type and the sensitivity of our atom interferometer has enabled us to test the velocity dependence of this phase.Since its theoretical discovery, the AC phase has been tested in five different experiments [10][11][12][13]...

Relativistic dipole interaction and the topological nature for induced HMW and AC phases

“…In AC and HWM cases, the charges are magnetic dipole and electric dipole and the FCs are field configurations in which the vector product of the magnetic or electric dipole and the electric or magnetic field has a non-vanishing curl. These non-trivial phases cause interference effects which have been observed experimentally, the topological AB phase by Chambers [7] and by Tonomura et al [8], the topological AC phase by Cimmino et al [9] and the Toulouse group [10], and the topological HMW effect by the Toulouse group [11], and the Tokyo Atom Interferometry Group [12]. For the HMW effect, because no atom has an observable electric dipole moment, it is necessary to induce the electric dipole moment by applying an electric field [4].…”

Neutron Interferometry 2nd Edn

“…The Aharonov-Casher effect also must be considered in accurate electric dipole moment measurements of the neutron (Pendlebury et al 2004). A new experiment by the Toulouse atom interferometer group has observed the AC effect using Li atoms in a separated atom interferometer (Gillot et al 2014). This experiment is very similar geometrically to the neutron experiment.…”

Persistent Superfluid Flow Arising from the He-McKellar-Wilkens Effect in Molecular Dipolar Condensates

“…The He-McKellar-Wilkens phase has recently been experimentally measured, by Lepoutre et al [30], using an atom interferometer, for a field geometry equivalent to that proposed by Wei, Han and Wei [29]. The same group later reported the experimental observation of the Aharonov-Casher phase [31].…”

“…The He-McKellarWilkens phase has recently been experimentally measured, by Lepoutre et al [30], using an atom interferometer, for a field geometry equivalent to that proposed by Wei, Han and Wei [29]. The same group later reported the experimental observation of the AharonovCasher phase [31].Bose-Einstein condensates have been formed from atoms with large magnetic dipole moments such as 52 Cr [32,33] where B is the radial magnetic field from the line of monopoles.One might expect that a BEC of electric dipoles in a toroidal geometry, with the electric dipoles aligned perpendicular to the plane of the toroid could exhibit persistent flow due to φ HMW , if a line of magnetic monopoles passed through the centre of the toroid, as schematically shown in Fig. 1(a).…”