Metastable states of hydrogen: their geometric phases and flux densities

We discuss the geometric phases and flux densities for the metastable states of hydrogen with principal quantum number n=2 being subjected to adiabatically varying external electric and magnetic fields. Convenient representations of the flux densities as complex integrals are derived. Both, parity conserving (PC) and parity violating (PV) flux densities and phases are identified. General expressions for the flux densities following from rotational invariance are derived. Specific cases of external fields are discussed. In a pure magnetic field the phases are given by the geometry of the path in magnetic field space. But for electric fields in presence of a constant magnetic field and for electric plus magnetic fields the geometric phases carry information on the atomic parameters, in particular, on the PV atomic interaction. We show that for our metastable states also the decay rates can be influenced by the geometric phases and we give a concrete example for this effect. Finally we emphasise that the general relations derived here for geometric phases and flux densities are also valid for other atomic systems having stable or metastable states, for instance, for He with n=2. Thus, a measurement of geometric phases may give important experimental information on the mass matrix and the electric and magnetic dipole matrices for such systems. This could be used as a check of corresponding theoretical calculations of wave functions and matrix elements.

Longitudinal Atomic Beam Spin Echo Experiments: A possible way to study Parity Violation in Hydrogen

We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. Depending on the choice of the external fields the atoms may acquire both dynamical and geometrical quantum mechanical phases. As an example of the former, we show first in-beam spin rotation measurements on atomic hydrogen, which are in excellent agreement with theory. Additional calculations of the behaviour of the metastable 2S states of hydrogen reveal that the geometrical phases may exhibit the signature of parity-(P-)violation. This invites for possible future lABSE experiments, focusing on P-violating geometrical phases in the lightest of all atoms.

Parity Violation in Hydrogen and Longitudinal Atomic Beam Spin Echo I

We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. There the atoms acquire geometric (Berry) phases that exhibit a new manifestation of parity-(P-)violation in atomic physics. We provide analytical as well as numerical calculations of the behaviour of the metastable 2S states of hydrogen. The conditions for electromagnetic field configurations that allow for adiabatic evolution of the relevant atomic states are investigated. Our results provide the theoretical basis for the discussion of possible measurements of P-violating geometric phases in lABSE experiments.