He-McKellar-Wilkens Topological Phase in Atom Interferometry

Abstract

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...

Optical pumping of a lithium atomic beam for atom interferometry

“…and optical pumping has considerably improved the experimental accuracy by eliminating systematic errors due to the average over 8 sublevels [1].…”

He–McKellar–Wilkens-type effect, quantum holonomies and Aharonov–Bohm-type effect for bound states from the Lorentz symmetry breaking effects

“…Several experiments have been made in order to reproduce the field configuration of the He-McKellar-Wilkens effect [38][39][40].…”

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

“…We have built the present experiment to measure the HMW phase shift, using an arrangement inspired by the ideas of H. Wei et al [22], with opposite electric fields on the two interferometer arms and a common homogeneous magnetic field [6,23]. Figure 2 shows the interaction cell.…”

“…As explained in our papers [6,7,23], we eliminate interferometer phase drifts by alternating 6 field configurations, (V, I), (V, 0), (0, I), (−V, 0), (−V, I) and (0, 0) during each 20 second-long fringe scan. Least-square fits are used to extract the phase ϕ(V, I, m F ) corresponding to each field configuration and to an optical pumping in the F = 2, m F = +2 sublevel.…”

“…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.…”