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Roentgen phase and Berry phase in atom interferometry

Kolloquium der Abteilung 4

Two topological phases were examined using the atom interferometers.

The first topological phase is the Roentgen phase which is a vector potential of a few milliradian making the polarizability of atoms and the magnetic field. We developed a symmetrical Ca atom interferometer with a milliradian phase resolution at an integration time of 5000 s. Electric fields, whose direction were parallel to the laser beams, were applied to the thermal atomic beam through the ITO transparent electrodes being orthogonal to the direction of the homogeneous magnetic field. Under the condition that the electric field was 1.9 kV/cm, the magnetic field was 20 mT, and the length of the interference zone was 17 mm, the Roentgen phase was measured to be 3.0 ± 2.1 mrad.

The other one is the Berry phase that a spinning particle acquires geometrically in a conical rotation of the magnetic field, besides the dynamical phase. For this purpose, we have developed a two-photon radio-frequency atom interferometer between the ground hyperfine levels with opposite signs of the g-factors, which is perfectly insensitive to the dynamical phase shift. We observed the Berry phase for a whole turn of the magnetic field, the frequency shift induced by Berry phase evolving linearly in time, according to Berry’s prediction. Finally, we demonstrated that the Berry phase is defined by a geodesic gauge for a noncyclic rotation of the magnetic field.