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arXiv:0907.3727 · Physical Review A

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

M. G. Kozlov, D. English, Dmitry Budker

Published Oct 9, 2009• 10 citations
arXivHTMLPDF

Abstract

Two-photon transitions between atomic states of total electronic angular-momentum ${J}_{a}=0$ 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 ${J}_{2\ensuremath{\gamma}}=1$ quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero 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-Einstein-statistics 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.

DOI
10.1103/physreva.80.042504

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Two-photon transitions between atomic states of total electronic angular-momentum Ja=0{J}_{a}=0Ja​=0 and Jb=1{J}_{b}=1Jb​=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 J2\ensuremathγ=1{J}_{2\ensuremath{\gamma}}=1J2\ensuremathγ​=1 quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero 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-Einstein-statistics 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.
We establish the existence of spin-statistic selection rules (SSSR) for multi-equal-photon transitions in atomic systems. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter ones are the direct consequence of Pauli exclusion principle. In this sense the SSSR play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. We established several SSSR for few-photon systems. 1) First rule (SSSR-1): two-equivalent photons involved in any atomic transition can have only even values of the total angular momentum J. This selection rule is an extension of the Landau-Yang theorem to the photons involved in atomic transitions. 2) second rule (SSSR-2): three equivalent dipole photons involved in any atomic transition can have only odd values of the total angular momentum J=1,3. 3) third rule (SSSR-3): four equivalent dipole photons involved in any atomic transition can have only even values of the total angular momentum J=0,2,4. We also suggest a method for a possible experimental test of these SSSR by means of laser experiments.
We establish the existence of spin-statistic selection rules (SSSRs) for multiphoton transitions with equal photons in atomic systems. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter are a direct consequence of the Pauli exclusion principle. In this sense, the SSSRs play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. We established several SSSRs for few-photon systems. (i) First rule: two equivalent photons involved in any atomic transition can have only even values of the total angular momentum, JJJ. This selection rule is an extension of the Landau-Yang theorem to the photons involved in atomic transitions. (ii) Second rule: three equivalent dipole photons involved in any atomic transition can have only odd values of the total angular momentum, J=1,3J=1,3J=1,3. (iii) Third rule: four equivalent dipole photons involved in any atomic transition can have only even values of the total angular momentum, J=0,2,4J=0,2,4J=0,2,4. We also suggest a method for a possible experimental test of these SSSRs by means of laser experiments.
We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ two-photon transition. Owing to the high sensitivity of the DDD state of atoms to a magnetic field, the splittings of the spectra of the DDD state are sufficiently large in a weak magnetic field of <10<10<10 G. We experimentally observe how in the hyperfine coupling in the 52D5/25{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}52D5/2​ state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum JJJ and nuclear spin III. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.
Atomic two-photon $J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0\ensuremath{\leftrightarrow}{J}^{\ensuremath{'}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ transitions are forbidden for photons of the same energy. This selection rule is related to the fact that photons obey Bose-Einstein statistics. We have searched for small violations of this selection rule by studying transitions in atomic Ba. We set a limit on the probability vvv that photons are in exchange-antisymmetric states: $v<1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.
The theory of how excited-state hyperfine structure can be determined using a magnetic field to decouple the nuclear and electronic angular momentum is presented. The initial excited state is assumed to have an anisotropic Zeeman sublevel population distribution, which can be conveniently created by a laser-induced multiphoton excitation of an unpolarized atom. The Zeeman sublevel populations are subsequently mixed by the hyperfine interaction. The degree of mixing is controlled by a magnetic field applied along the quantization axis. The relative Zeeman sublevel populations can be monitored by detecting the polarization of fluorescence emitted when the excited state radiatively decays. It is convenient to take the ratio of two time-integrated fluorescent signals measured for orthogonal linear polarizations, since this is independent of the excited-state number density. The plot of this ratio versus magnetic field is very well approximated by a Lorentzian curve whose half-width is proportional to the magnetic dipole hyperfine coupling constant. This method was used to determine the magnitude of the magnetic dipole constant of the cesium 8D3/2{\mathit{D}}_{3/2}D3/2​ state to be 3.92\ifmmode\pm\else\textpm\fi{}0.10 MHz, which is in excellent agreement with previous results.
Earlier research highlighted the absence of certain bright peaks in Autler-Townes laser excitation spectra of alkali-metal atoms and attributed this phenomenon to a specific architecture of adiabatic (or ``laser-dressed'') states in hyperfine (HF) components. Here we have studied the dressed states' properties in several two-photon excitation schemes where constructive and destructive interferences between HF excitation pathways limit the available two-photon transitions. The analysis reveals a mechanism by which this interference reduces the conventional two-photon selection rule for the total angular momentum FFF, from $\mathrm{\ensuremath{\Delta}}F=0,\ifmmode\pm\else\textpm\fi{}1$ to $\mathrm{\ensuremath{\Delta}}F\ensuremath{\equiv}0$. Our discovery presents a practical method for selectively controlling the populations of unresolvable HF FFF components of ns1/2n{s}_{1/2}ns1/2​ Rydberg states in alkali-metal atoms. Using numerical simulations with sodium and rubidium atoms, we demonstrate that by blocking the effects of HF interaction with a specially tuned auxiliary control-laser field, the deviations from the ideal selectivity of the HF components population can be lower than 0.010.01%0.01 for Na and 0.0010.001%0.001 for Rb atoms.