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Cambridge University Press eBooks

Effect of external magnetic field on angular momenta distribution

Marcis P. Auzinsh, R. Ferber

Published Mar 30, 1995• 0 citations
Publisher
DOI
10.1017/cbo9780511564093.005

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The Berry phase for a variety of systems comprising of two angular momenta is discussed. These include the electron and proton in the ground state of the hydrogen atom (taking into account the hyperfine interaction), the positronium atom, the spin and orbital angular momenta of a single electron, muon capture by the deuteron in an external magnetic field, etc. Though the time scales involved, the underlying intrinsic Hamiltonians are quite different, as also the possible experimental probes, the geometric nature of the results for the Berry phase due to a time varying externally imposed magnetic field is found to be quite robust. Some indications are also put forward as to the possible interesting studies with time varying electric fields. The objective of this work is an attempt to broaden the scope of such studies in both the experimental and theoretical directions.
We calculate and analyze Feshbach resonance spectra for ultracold Yb(1S0)+Yb(3P2)\mathrm{Yb}({}^{1}{S}_{0})+\mathrm{Yb}({}^{3}{P}_{2})Yb(1S0​)+Yb(3P2​) collisions as a function of an interatomic potential scaling factor $\ensuremath{\lambda}$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\ensuremath{\lambda}$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.