Testing the validity of Bose-Einstein statistics in molecules

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.