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Physical Review A

Suppressing reactivity in a degenerate Fermi molecular gas via the statistical potential

Yan-Peng Bai, Jing-Lun Li, Gao‐Ren Wang, Zhong-Bo Chen, Bo-Wen Si, Shu‐Lin Cong

Published Apr 21, 2022• 0 citations
Publisher

Abstract

We present a simple theoretical model used for describing the suppressing reactivity of an ultracold Fermi molecular gas in a degenerate regime via the statistical potential. The statistical potential originates from the symmetry properties of the wave function of identical particles, and is derived by using the density matrix. We use our theoretical model to well reproduce recent experimental results of a potassium-rubidium molecule gas in the deep quantum degenerate regime reported by De Marco et al. [Science 363, 853 (2019)]. The suppression of the chemical reaction rate observed in the experiment is quantitatively reproduced by using the $p$-wave scattering volume as an adjusting parameter. The strength of spatial correlation can be intuitively captured by the statistical potential.

DOI
10.1103/physreva.105.043314

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We present a simple theoretical model used for describing the suppressing reactivity of an ultracold Fermi molecular gas in a degenerate regime via the statistical potential. The statistical potential originates from the symmetry properties of the wave function of identical particles, and is derived by using the density matrix. We use our theoretical model to well reproduce recent experimental results of a potassium-rubidium molecule gas in the deep quantum degenerate regime reported by De Marco et al. [Science 363, 853 (2019)]. The suppression of the chemical reaction rate observed in the experiment is quantitatively reproduced by using the ppp-wave scattering volume as an adjusting parameter. The strength of spatial correlation can be intuitively captured by the statistical potential.
A recent experiment [L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate Fermi gas of polar molecules, Science 363, 853 (2019)] reported for the first time the preparation of a Fermi degenerate gas of polar molecules and observed a suppression of their chemical reaction rate compared to the one expected from a treatment assuming classical Maxwell-Boltzmann statistics. While it was hypothesized that the suppression in the ultracold regime had its roots in the Fermi statistics of the molecules, this argument is inconsistent with the fact that the Fermi pressure should set a lower bound for the chemical reaction rate. Here we develop a simple model of chemical reactions that occur via the formation and decay of molecular complexes. We indeed find that pure two-body molecule losses are unable to explain the observed suppression. Instead we extend our description beyond two-body physics by including multibody complex-molecule interactions. Although our model is able to quantitatively reproduce recent experimental observations, it requires parameters physically unlikely for direct microscopic interactions. The underlying processes, however, might emerge effectively from many-body or medium effects. A detailed understanding of the direct microscopic mechanisms responsible for these higher-order interaction processes is therefore still pending.
Experimental realization of a quantum degenerate gas of molecules would provide access to a wide range of phenomena in molecular and quantum sciences. However, the very complexity that makes ultracold molecules so enticing has made reaching degeneracy an outstanding experimental challenge over the past decade. We now report the production of a degenerate Fermi gas of ultracold polar molecules of potassium-rubidium. Through coherent adiabatic association in a deeply degenerate mixture of a rubidium Bose-Einstein condensate and a potassium Fermi gas, we produce molecules at temperatures below 0.3 times the Fermi temperature. We explore the properties of this reactive gas and demonstrate how degeneracy suppresses chemical reactions, making a long-lived degenerate gas of polar molecules a reality.
Cold Molecules A dilute atomic gas cooled down to very cold temperatures can enter the so-called quantum degenerate regime, where quantum properties of the gas come to the fore. This regime has been achieved for both bosonic and fermionic atoms, but molecules, with their many internal states, present a special challenge. De Marco et al. cooled a bulk gas of fermionic potassium-rubidium molecules to quantum degeneracy (see the Perspective by Zelevinsky). The authors first cooled atomic potassium and rubidium gases separately, then bound them together into potassium-rubidium molecules, and finally brought the molecules down to their ground state. The density profile of the molecular gas revealed the system's quantum nature, which in turn kept the gas stable by suppressing chemical reactions. Science , this issue p. [853][1]; see also p. [820][2] [1]: /lookup/doi/10.1126/science.aau7230 [2]: /lookup/doi/10.1126/science.aav9149
How does a chemical reaction proceed at ultralow temperatures? Can simple quantum mechanical rules such as quantum statistics, single partial-wave scattering, and quantum threshold laws provide a clear understanding of the molecular reactivity under a vanishing collision energy? Starting with an optically trapped near-quantum-degenerate gas of polar 40K87Rb molecules prepared in their absolute ground state, we report experimental evidence for exothermic atom-exchange chemical reactions. When these fermionic molecules were prepared in a single quantum state at a temperature of a few hundred nanokelvin, we observed p-wave-dominated quantum threshold collisions arising from tunneling through an angular momentum barrier followed by a short-range chemical reaction with a probability near unity. When these molecules were prepared in two different internal states or when molecules and atoms were brought together, the reaction rates were enhanced by a factor of 10 to 100 as a result of s-wave scattering, which does not have a centrifugal barrier. The measured rates agree with predicted universal loss rates related to the two-body van der Waals length.
Fermi statistics suppress the elastic collisions that rethermalize a Fermi gas during evaporative cooling, creating a fundamental low-temperature bottleneck for producing quantum degenerate gases. We show that, for shielded single-component ultracold dipolar molecular Fermi gases in the Wigner threshold regime, this bottleneck is governed by universal threshold laws fixed by the effective dimensionality of the gas. In this regime, Fermi suppression of rethermalization scales quadratically with temperature in 3D but only linearly in 2D. Consequently, the thermalization-to-loss ratio is more favorable in 2D than in 3D, and these results suggest that 2D geometries are better suited for reaching deep degeneracy. We also present ab initio close-coupling calculations that agree well with experimental measurements on Fermi degenerate gases of KRb molecules, supporting our conclusions.
We consider the quench of an atomic impurity via a single Rydberg excitation in a degenerate Fermi gas. The Rydberg interaction with the background gas particles induces an ultralong-range potential that binds particles to form dimers, trimers, tetramers, etc. Such oligomeric molecules were recently observed in atomic Bose-Einstein condensates. In this work, we demonstrate with a functional determinant approach that quantum statistics and fluctuations have observable spectral consequences. We show that the occupation of molecular states is predicated on the Fermi statistics, which suppresses molecular formation in an emergent molecular shell structure. At large gas densities this leads to spectral narrowing, which can serve as a probe of the quantum gas thermodynamic properties.