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A recent experiment reported for the first time the preparation of a Fermidegenerate gas of polar molecules and observed a suppression of their chemicalreaction rate compared to the one expected from a purely classical treatment.While it was hypothesized that the suppression in the ultracold regime had itsroots in the Fermi statistics of the molecules, this argument is inconsistentwith the fact that the Fermi pressure should set a lower bound for the chemicalreaction rate. Therefore it can not be explained from standard two-body$p$-wave inelastic collisions. Here we develop a simple model of chemicalreactions that occur via the formation and decay of molecular complexes. Weindeed find that pure two-body molecule losses are unable to explain theobserved suppression. Instead we extend our description beyond two-body physicsby including effective complex-molecule interactions possible emerging frommany-body and effective medium effects at finite densities and in the presenceof trapping light. %Under this framework we observe that additionalcomplex-molecule collisions, which manifest as a net three-body molecularinteraction could give rise to the additional suppression. Although oureffective model is able to quantitatively reproduce recent experimentalobservations, a detailed understanding of the actual physical mechanismresponsible for these higher-order interaction processes is still pending.

Understanding chemical reactions in a quantum degenerate gas of polar molecules via complex formation