The 2023 creation of a quantum degenerate mixture of fermionic 23^{23}Na40^{40}K ground-state molecules coexisting with a degenerate 40^{40}K atomic Fermi gas left its central collision physics unquantified: the observed suppression of atom–molecule elastic collisions was attributed to Pauli exclusion without any theoretical model, and the proposed route to deeper molecular degeneracy — evaporative cooling of the molecules by selectively removing high-energy 40^{40}K atoms — has never been tested. The open problem is to build a quantitative theory of Pauli-blocked atom–molecule elastic collisions and thermalization in this degenerate mixture, and to determine whether atom-bath evaporative cooling can drive the molecular gas below the achieved T/TF≈0.5T/T_{F}\approx0.5 despite Pauli blocking and loss channels (photoexcitation by trap lasers, inelastic and sticky collisions). Later work has measured Pauli suppression for molecule–molecule collisions and reached deeper degeneracy for pure molecular gases by microwave shielding, but the atom–molecule case remains untreated and is now explicitly identified as the route around the Pauli limit of pure-gas evaporation.

Background

Ultracold polar molecules — heteronuclear molecules such as 23^{23}Na40^{40}K held in their rovibrational ground state, which carry permanent electric dipole moments — are a leading platform for quantum simulation and controlled ultracold chemistry, but most applications require quantum degeneracy, meaning temperatures below the Fermi temperature TFT_{F} (the characteristic temperature scale below which the occupation of low-energy states by identical fermions becomes governed by the Pauli exclusion principle). Direct cooling of molecules is hard because inelastic collisions rapidly destroy them, so molecular degeneracy is usually reached by cooling the parent atoms first and then associating them into molecules. STIRAP (stimulated Raman adiabatic passage) is a coherent two-photon transfer technique used to move weakly bound Feshbach molecules — molecules formed near a Feshbach resonance, a magnetically tunable scattering resonance between two colliding particles — into their absolute ground state without heating. A Feshbach resonance arises when a bound molecular level crosses the collision threshold; it allows the scattering length and hence interaction strength to be tuned magnetically. In 2022–2023 the group of Jian-Wei Pan created the first quantum degenerate atom–molecule mixture: about 3×1043\times10^{4} fermionic 23^{23}Na40^{40}K ground-state molecules coexisting with about 3×1053\times10^{5} degenerate 40^{40}K atoms at roughly 120 nK, with molecular degeneracy T/TF≈0.4T/T_{F}\approx0.4–0.5 at creation and 0.5–0.6 after equilibration in the mixture (Cao et al., Phys. Rev. A 107, 013307 (2023), the source paper of this problem). Elastic atom–molecule collisions provide the thermalization mechanism for the molecules. Both the molecules and the atoms are fermions (bosonic 23^{23}Na plus fermionic 40^{40}K makes 23^{23}Na40^{40}K a fermion), and in the degenerate regime the Pauli exclusion principle suppresses elastic atom–molecule collisions through the degenerate occupation of 40^{40}K bath states — energy exchange with the more degenerate atoms is blocked because the relevant atomic final states are already occupied — in analogy with the suppression first measured for a purely atomic degenerate Fermi gas by DeMarco, Papp, and Jin (Phys. Rev. Lett. 86, 5409 (2001)). The source paper inferred an effective elastic collision cross section of 2.7(5)×10−11 cm22.7(5)\times10^{-11}\ \mathrm{cm}^{2} from the damping of molecular dipole oscillations (damping time τd=17\tau_{d}=17 ms with atoms versus τ0=46\tau_{0}=46 ms without), smaller than the classical-mixture value 6.4(12)×10−11 cm26.4(12)\times10^{-11}\ \mathrm{cm}^{2}, and attributed the reduction to Pauli suppression — while stating explicitly that its thermalization calculation "do[es] not consider the suppression of the elastic collisions due to the Pauli exclusion principle in the quantum degenerate regime, which is difficult to consider in the theoretical model". It inferred a Pauli-enhanced thermalization time of about 17 ms, still well below the molecular lifetime of about 85 ms in the mixture, and noted that STIRAP transfer excites collective oscillations of the molecular cloud (dipole and breathing modes) that can be suppressed by a one-dimensional optical lattice or better beam alignment. Because the paper's thermalization model leaves out this suppression, a quantitative theory of Pauli suppression for atom–molecule collisions and thermalization timescales in the degenerate regime remains open. The paper's outlook identifies as the route to deeper degeneracy evaporative cooling achieved by selectively removing high-energy 40^{40}K atoms and using atom–molecule elastic collisions; its feasibility is bounded by Pauli blocking and by molecule losses, the mechanisms of which the paper notes as a known difficulty of atom–molecule mixtures — photoexcitation by trap lasers, inelastic collisions, and sticky collisions (long-lived transient complexes that decay before separating). The outlook further lists, as longer-term applications, exploiting the mixture's many atom–molecule Feshbach resonances for strongly interacting regimes, angulon physics (a quasiparticle describing a rotating molecule dressed by many-body excitations), and adiabatic association of triatomic molecules.

Problem Statement

For the quantum degenerate mixture of fermionic 23^{23}Na40^{40}K ground-state molecules and a degenerate 40^{40}K atomic Fermi gas: (1) construct a quantitative theoretical description of Pauli suppression of atom–molecule elastic collisions in the degenerate regime — covering the suppression of the effective elastic cross section relative to the classical value and the thermalization timescale as functions of T/TFT/T_{F} and density — and test it against the measured effective cross section 2.7(5)×10−11 cm22.7(5)\times10^{-11}\ \mathrm{cm}^{2}, the inferred thermalization time of about 17 ms, and the molecular lifetime of about 85 ms reported for this mixture in the source experiment (Cao et al., Phys. Rev. A 107, 013307 (2023)); and (2) determine whether evaporative cooling of the molecules — implemented by selectively removing high-energy 40^{40}K atoms so that atom–molecule elastic collisions rethermalize the bath — can drive the molecular gas to deeper degeneracy than the achieved T/TF≈0.5T/T_{F}\approx0.5 despite Pauli blocking and the known loss channels (photoexcitation by trap lasers, inelastic and sticky collisions). A complete answer establishes the collision physics (1) well enough to predict, and then resolve, the atom-bath cooling outcome (2); the two components are one linked objective — understanding and exploiting elastic atom–molecule collisions in the degenerate mixture to deepen molecular degeneracy. Suppression of the STIRAP-induced collective excitations (for example by a 1D optical lattice or improved beam alignment) is an auxiliary experimental enabling task for reading out thermal equilibrium, and exploitation of the atom–molecule Feshbach resonances for strongly interacting regimes, angulon physics, or degenerate triatomic association is the downstream application that deeper degeneracy and interaction control would unlock, not part of the completion boundary.

References

  1. Jin Cao, Huan Yang, Zhen Su, Xin-Yao Wang, Jun Rui, Bo Zhao, Jian-Wei Pan, "Preparation of a quantum degenerate mixture of 23^{23}Na40^{40}K molecules and 40^{40}K atoms", Phys. Rev. A 107, 013307 (2023), DOI 10.1103/PhysRevA.107.013307, arXiv:2208.09620, https://arxiv.org/abs/2208.09620
  2. Junyu Lin, Annette N. Carroll, Phillip Martin, Calder Miller, Reuben R. W. Wang, Kevin Xu, John L. Bohn, Tim de Jongh, Jun Ye, "Fermi gas of polar molecules in the Pauli-blocked regime", arXiv:2606.14135 (2026), https://arxiv.org/abs/2606.14135
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