Berry Phase for Evolution of Spinning Atoms under Rotating Magnetic Field

Professor Atsua Morinaga

Tokyo University of Science, Japan

In 1984, Berry predicted that in a cyclic adiabatic process, one in which slowly time-varying Hamiltonian returns to its original form via a circuit C, a quantum state may acquire a geometrical phase of – imΩ(C), where m is the spin component and Ω is the solid angle. The experimental identification of the Berry phase has been carried out in various fields of quantum physics. Furthermore, an evolving geometrical phase induces a shift of resonance frequency. To verify such a phase shift or frequency shift experimentally, the extra dynamical effect should be removed. For this purpose, a superposition state of the ground hyperfine levels of the |F’ = 1, m’ = -1> state with a negative Landé g-factor to the |F = 2, m=1> state with a positive g-factor of an alkaline atom is suitable because it becomes a magnetic-field-insensitive transition at the magic magnetic field. Using the atom interferometer comprised of this transition, we demonstrated the Berry phase for a whole rotation, a partial rotation of the direction of the magnetic field and the frequency shift induced by the Berry phase under the constant rotation of a magnetic field with frequency f  for angle θ from the rotation axis.

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