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Physical Review Letters

Spectroscopic Test of the Symmetrization Postulate for Spin-0 Nuclei

Robert C. Hilborn, Candice L. Yuca

Published Apr 15, 1996• 74 citations
Publisher

Abstract

We have used diode laser absorption spectroscopy of the ``A'' band of molecular oxygen near 762 nm to provide a sensitive experimental test of the symmetrization postulate of quantum mechanics. We place an upper limit of $(0.8\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ on the probability of finding two identical ${}^{16}$O nuclei in an antisymmetric state. This is one of the first sensitive tests of the symmetrization postulate for spin-0 particles.

DOI
10.1103/physrevlett.76.2844

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Physica Scripta•Jan 1, 2001•5 citations
We have used diode laser absorption spectroscopy of the ``A'' band of molecular oxygen near 762 nm to provide a sensitive experimental test of the symmetrization postulate of quantum mechanics. We place an upper limit of (0.8\ifmmode±\else\textpm\fi1.3)\ifmmode×\else\texttimes\fi10\ensuremath−6(0.8\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}(0.8\ifmmode±\else\textpm\fi1.3)\ifmmode×\else\texttimes\fi10\ensuremath−6 on the probability of finding two identical 16{}^{16}16O nuclei in an antisymmetric state. This is one of the first sensitive tests of the symmetrization postulate for spin-0 particles.
We investigated the spectrum of the 16O2{}^{16}{\mathrm{O}}_{2}16O2​ molecule by high-sensitivity laser spectroscopy and searched for transitions involving states which are antisymmetric under the exchange of the nuclei. These states are forbidden by the symmetrization postulate of quantum mechanics. This is the first reported experiment to test the symmetrization postulate for integer-spin particles to high precision. Our data set an upper limit of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ to a possible violation of this postulate.
An accurate test of the symmetrization postulate of quantum mechanics has been performed on the spin-0 16O{}^{16}\mathrm{O}16O nuclei, by looking for transitions in the CO2{\mathrm{CO}}_{2}CO2​ spectra involving states which are antisymmetric in the exchange of the nuclei. Using high-sensitivity laser spectroscopy, a bound of $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ has been set to a possible violation of such postulate, with an improvement of more than 2 orders of magnitude with respect to the previous limit.
A high-finesse optical cavity was employed to perform highly sensitive spectroscopy of molecular oxygen at wavelengths near 763 nm. An equivalent absorption length of ∼1 km was obtained by a 26-cm-long optical cavity with a finesse of 6000. An extended cavity diode laser was frequency locked to the cavity, and pure absorption profiles were recovered by monitoring of the cavity transmission during continuous scans of the cavity resonance through O2 rotational lines, allowing a detailed investigation of the line shapes. Phase modulation of the laser at a frequency equal to the cavity free-spectral-range frequency was employed for detection of weak absorption signals inside the cavity. A minimum detectable absorption coefficient of 6.9×10-11 cm-1 Hz-1/2 was measured. Finally, a test of the symmetrization postulate in 16O nuclei was demonstrated.
We propose an experiment to look for possible small violations of the symmetrization postulate of quantum mechanics, in systems composed of three identical particles. Such violations could be detected by investigating the population of particular rotovibrational states of symmetrical molecules containing three identical nuclei. We discuss the symmetry properties of such states, and the implications of the symmetrization postulate and the spin statistics connection. A high-sensitivity spectroscopic investigation of simple molecules such as SO3,{\mathrm{SO}}_{3},SO3​, BH3,{\mathrm{BH}}_{3},BH3​, and NH3{\mathrm{NH}}_{3}NH3​ could lead, to our knowledge, to the first test of the symmetrization postulate for spin-0 and spin-1/2 nuclei.