Symmetry-suppressed two-photon transitions induced by hyperfine interactions and magnetic fields

Abstract

Two-photon transitions between atomic states of total electronic angular momentum Ja = 0 and J b = 1 are forbidden when the photons are of the same energy. This selection rule is analogous to the Landau-Yang theorem in particle physics that forbids decays of vector particle into two photons. It arises because it is impossible to construct a total angular momentum J2γ = 1 quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with non-zero nuclear spin, the selection rule can be violated due to hyperfine interactions. Two distinct mechanisms responsible for the hyperfine-induced two-photon transitions are identified, and the hyperfine structure of the induced transitions is evaluated. The selection rule is also relaxed, even for zero-nuclear-spin atoms, by application of an external magnetic field. Once again, there are two similar mechanisms at play: Zeeman splitting of the intermediate-state sublevels, and off-diagonal mixing of states with different total electronic angular momentum in the final state. The present theoretical treatment is relevant to the ongoing experimental search for a possible Bose-Einsteinstatistics violation using two-photon transitions in barium, where the hyperfine-induced transitions have been recently observed, and the magnetic-field-induced transitions are being considered both as a possible systematic effect, and as a way to calibrate the measurement.

Spectroscopic Test of Bose-Einstein Statistics for Photons

“…As is also discussed in Ref. [14], magnetic fields can create a false-positive signal in a way similar to the hfi. A relatively large field (∼10 gauss) would be necessary to generate a false-positive signal at the present level of sensitivity.…”

“…A number of sources of systematic error must be considered. The Landau-Yang theorem is circumvented in the nonzero-nuclear-spin isotopes of barium, 137 Ba (11% natural abundance, I = 3/2) and 135 Ba, (6.6%, I = 3/2), by two manifestations of the hyperfine-interaction (hfi): hfi-induced splitting of the intermediate 6s6p 1 P 1 state, and hfi-induced mixing of states with J = 2 (primarily 6s7d 3 D 2 ) with the final 5d6d 3 D 1 state [14]. The amplitudes for both processes are comparable, and the rate, relative to an allowed transition (i.e., expressed in the same way as the limit parameter ν), is ∼ 10 −8 .…”

An overview of some experimental and theoretical aspects of fundamental symmetry violations in atoms

“…The experiment has resulted not only in the new stringent limit on possible violation of Bose statistics by photons [28], but also in the observation (and a theoretical analysis) of hyperfine-interaction enabled forbidden two-photon transitions [29].…”

Exclusion principle for photons: Spin-statistic selection rules for multiphoton transitions in atomic systems

“…1. Finally, in [11,12] it was shown that the SSSR-suppressed two-photon transitions are opened either by the hyperfine interaction or by an external magnetic field. The hyperfine interaction changes the value of the total angular momentum J e of an electron state in an atom, and in an external magnetic field the angular momentum, in principle, is not conserved.…”