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arXiv:physics/9906025 · Physical Review Letters

Search for Exchange-Antisymmetric Two-Photon States

David P. DeMille, Dmitry Budker, Nathan D. Derr, E. Deveney

Published Nov 15, 1999• 38 citations
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Abstract

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 $v$ that photons are in exchange-antisymmetric states: $v<1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$.

DOI
10.1103/physrevlett.83.3978

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Atomic two-photon J=0\ensuremath↔J\ensuremath′=1J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0\ensuremath{\leftrightarrow}{J}^{\ensuremath{'}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1J=0\ensuremath↔J\ensuremath′=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×\else\texttimes\fi10\ensuremath−7v<1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}v<1.2\ifmmode×\else\texttimes\fi10\ensuremath−7.
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 ${J}_{2\ensuremath{\gamma}}=1$ 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.
A theoretical investigation of the three-photon transition rates $2\phantom{\rule{0.16em}{0ex}}{}^{1}{P}_{1}\ensuremath{\rightarrow}2\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\phantom{\rule{0.28em}{0ex}},1\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ and $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}2\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\phantom{\rule{0.28em}{0ex}},1\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ for the helium atom is presented. Photon energy distributions and precise values of the nonrelativistic transition rates are obtained with employment of correlated wave functions of the Hylleraas type. The possible experiments for the tests of the Bose-Einstein statistics for multiphoton systems are discussed.
We set a new upper limit of $1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ to the probability that two spin-0 16O{}^{16}\mathrm{O}16O nuclei are in forbidden exchange-antisymmetric states, testing the validity of fundamental principles of quantum mechanics. A newly designed difference-frequency spectrometer is used to look for the existence of these states. The experimental test was performed by tuning the spectrometer across a molecular transition of 12C16O2{}^{12}\mathrm{C}{}^{16}\mathrm{O}{}_{2}12C16O2​ belonging to the rovibrational band at $4.25\ensuremath{\mu}\mathrm{m}$, connecting the forbidden states (0000,J=25)({00}^{0}0,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}25)(0000,J=25) and (0001,J=26)({00}^{0}1,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}26)(0001,J=26).
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.