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arXiv:2310.17812 · Physical Review Research

Prospects for thermalization of microwave-shielded ultracold molecules

Reuben R. W. Wang, John L. Bohn

Published May 6, 2024• 6 citations
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Abstract

Toward more efficient schemes for achieving deeply degenerate molecular Fermi gases, we study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng [] to obtain accurate two-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l022033

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Toward more efficient schemes for achieving deeply degenerate molecular Fermi gases, we study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng [] to obtain accurate two-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization. Published by the American Physical Society 2024
In the quest toward realizing novel quantum matter in ultracold molecular gases, we perform a numerical study of evaporative cooling in ultracold gases of microwave-shielded polar fermionic molecules. Our Monte Carlo simulations incorporate accurate two-body elastic and inelastic scattering cross sections, realistic modeling of the optical dipole trap, and the influence of Pauli blocking at low temperatures. The simulations are benchmarked against data from evaporation studies performed with ultracold NaK molecules, showing excellent agreement. We further explore the prospects for optimizing the evaporation efficiency by varying the ramp rate and duration of the evaporation trajectory. Our simulation shows that it is possible to reach <10<10%<10 of the Fermi temperature under optimal conditions even in the presence of two-body molecular losses.
We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization [Monroe et al., Phys. Rev. Lett. 70, 414 (1993)], which, for dipolar gases, is highly dependent on the dipole alignment axis. These methods are formulated to be easily applied in experimental contexts, even reducing to analytic expressions if the route to thermal equilibrium is governed by short-time dynamics. In the analytic case, collisional rethermalization is fully characterized by the dipole magnitude and orientation, scattering length, and thermalization geometry. These models compare favorably to Monte Carlo simulations and are shown to model well a recent experimental result on the rethermalization of polar molecular samples.
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.
Abstract Ultracold polar molecules offer strong electric dipole moments and rich internal structure, which makes them ideal building blocks to explore exotic quantum matter 1–9 , implement quantum information schemes 10–12 and test the fundamental symmetries of nature 13 . Realizing their full potential requires cooling interacting molecular gases deeply into the quantum-degenerate regime. However, the intrinsically unstable collisions between molecules at short range have so far prevented direct cooling through elastic collisions to quantum degeneracy in three dimensions. Here we demonstrate evaporative cooling of a three-dimensional gas of fermionic sodium–potassium molecules to well below the Fermi temperature using microwave shielding. The molecules are protected from reaching short range with a repulsive barrier engineered by coupling rotational states with a blue-detuned circularly polarized microwave. The microwave dressing induces strong tunable dipolar interactions between the molecules, leading to high elastic collision rates that can exceed the inelastic ones by at least a factor of 460. This large elastic-to-inelastic collision ratio allows us to cool the molecular gas to 21 nanokelvin, corresponding to 0.36 times the Fermi temperature. Such cold and dense samples of polar molecules open the path to the exploration of many-body phenomena with strong dipolar interactions.
The strong, tunable dipolar interactions of ultracold molecules make them a powerful platform for quantum many-body physics, but reaching degeneracy by evaporative cooling requires suppressing inelastic collisions. Microwave collisional shielding has enabled the preparation of degenerate Fermi gases and Bose-Einstein condensates of polar molecules, whereas static electric field shielding has been limited to fermionic species, which are less prone to inelastic loss. We demonstrate static-field Förster shielding of bosonic 23^{23}23Na87^{87}87Rb molecules, suppressing two-body loss by up to four orders of magnitude. Within a bound-state-free electric-field window, three-body loss is also strongly suppressed, enabling efficient evaporation. Evaporating with an efficiency of 2.09(9), we increase the phase-space density of the gas by two orders of magnitude, reaching degeneracy with 7200(1000) molecules. We observe self-bound droplets at the end of evaporation over a wide range of field strengths, emerging from either degenerate or non-degenerate parent gases. We perform Path Integral Monte Carlo simulations, which suggest that the observed droplets are filamentary in nature, and find good agreement with the experimentally observed droplet formation temperatures. Our results establish Förster shielding as a single-field route to prepare degenerate gases and self-bound droplets of bosonic polar molecules.
We develop double microwave shielding, which has recently enabled evaporative cooling to the first Bose-Einstein condensate of polar molecules [Bigagli , Nature , 289 (2024)]. Two microwave fields of different frequency and polarization are employed to effectively shield polar molecules from inelastic collisions and three-body recombination. Here, we describe in detail the theory of double microwave shielding. We demonstrate that double microwave shielding effectively suppresses two- and three-body losses. Simultaneously, dipolar interactions and the scattering length can be flexibly tuned, enabling comprehensive control over interactions in ultracold gases of polar molecules. We show that this approach works universally for a wide range of molecules. This opens the door to studying many-body physics with strongly interacting dipolar quantum matter.