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Physical Review A

Testing the validity of Bose-Einstein statistics in molecules

Pablo Cancio Pastor, Iacopo Galli, Giovanni Giusfredi, Davide Mazzotti, Paolo De Natale

Published Dec 11, 2015• 19 citations

Abstract

The search for small violations of the validity of the symmetrization postulate and of the spin-statistics connection (SSC) has been addressed in the last four decades by experimental tests performed in different physical systems of identical fermions or bosons. In parallel and consequently, theories extending the quantum mechanics to a more general level have been proposed to explain such possible violations. In this paper, we present the most stringent test to a possible violation of the SSC under permutation of the bosonic $^{16}\mathrm{O}$ nuclei in the $^{12}\mathrm{C}^{16}\mathrm{O}_{2}$ molecule. An upper limit of $3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ for an SSC-anomalous ${\mathrm{CO}}_{2}$ molecule is obtained using saturated-absorption cavity ring-down spectroscopy in the SSC-forbidden $({00}^{0}1\ensuremath{-}{00}^{0}0) R$(25) rovibrational transition of $^{12}\mathrm{C}^{16}\mathrm{O}_{2}$ at a $4.25\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ wavelength. Quantum mechanics implications of this result are discussed in the frame of the $q$-mutator theory. Finally, the perspective of stringent experimental tests of the symmetrization postulate in molecules that contain three or more identical nuclei is discussed.

DOI: 10.1103/physreva.92.063820

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Physical Review Letters•Mar 5, 2001•38 citations

The search for small violations of the validity of the symmetrization postulate and of the spin-statistics connection (SSC) has been addressed in the last four decades by experimental tests performed in different physical systems of identical fermions or bosons. In parallel and consequently, theories extending the quantum mechanics to a more general level have been proposed to explain such possible violations. In this paper, we present the most stringent test to a possible violation of the SSC under permutation of the bosonic

^{16}\mathrm{O}

nuclei in the

^{12}\mathrm{C}^{16}\mathrm{O}_{2}

molecule. An upper limit of

3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}

for an SSC-anomalous

{\mathrm{CO}}_{2}

molecule is obtained using saturated-absorption cavity ring-down spectroscopy in the SSC-forbidden

({00}^{0}1\ensuremath{-}{00}^{0}0) R

(25) rovibrational transition of

^{12}\mathrm{C}^{16}\mathrm{O}_{2}

at a

4.25\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}

wavelength. Quantum mechanics implications of this result are discussed in the frame of the

q

-mutator theory. Finally, the perspective of stringent experimental tests of the symmetrization postulate in molecules that contain three or more identical nuclei is discussed.

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

{\mathrm{SO}}_{3},

{\mathrm{BH}}_{3},

and

{\mathrm{NH}}_{3}

could lead, to our knowledge, to the first test of the symmetrization postulate for spin-0 and spin-1/2 nuclei.

We investigated the spectrum of the

{}^{16}{\mathrm{O}}_{2}

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.

We set a new upper limit of $1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ to the probability that two spin-0

{}^{16}\mathrm{O}

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

{}^{12}\mathrm{C}{}^{16}\mathrm{O}{}_{2}

belonging to the rovibrational band at $4.25\ensuremath{\mu}\mathrm{m}$, connecting the forbidden states

({00}^{0}0,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}25)

and

({00}^{0}1,J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}26)

.