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arXiv:2501.03170 · Physical Review Research

Universality in the microwave shielding of ultracold polar molecules

Joy Dutta, Bijit Mukherjee, Jeremy M. Hutson

Published May 19, 2025• 10 citations
arXivHTMLPDF

Abstract

Microwave shielding is an important technique that can suppress the losses that arise from collisions of ultracold polar molecules. It has been instrumental in achieving molecular Bose-Einstein condensation (BEC) for NaCs []. We demonstrate that microwave shielding is universal, in the sense that the two-body collision properties of different molecules are very similar when expressed in suitable reduced units of length and energy. This applies to rate coefficients for inelastic scattering and loss, to scattering lengths, and to the properties of two-molecule bound states. We also explore the small deviations from universality that arise at very large Rabi frequencies. In general, the collision properties are near-universal except when the Rabi frequency exceeds a few percent of the molecular rotational constant. The universality extends to elliptically polarized microwaves and to combinations of multiple fields. Our results indicate that the methods that have been used to achieve BEC for NaCs can be transferred directly to most other polar molecules.

DOI
10.1103/physrevresearch.7.023164

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Microwave shielding is an important technique that can suppress the losses that arise from collisions of ultracold polar molecules. It has been instrumental in achieving molecular Bose-Einstein condensation (BEC) for NaCs []. We demonstrate that microwave shielding is universal, in the sense that the two-body collision properties of different molecules are very similar when expressed in suitable reduced units of length and energy. This applies to rate coefficients for inelastic scattering and loss, to scattering lengths, and to the properties of two-molecule bound states. We also explore the small deviations from universality that arise at very large Rabi frequencies. In general, the collision properties are near-universal except when the Rabi frequency exceeds a few percent of the molecular rotational constant. The universality extends to elliptically polarized microwaves and to combinations of multiple fields. Our results indicate that the methods that have been used to achieve BEC for NaCs can be transferred directly to most other 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.
Double microwave shielding employs σ+σ^{+}σ+- and πππ-polarized microwave fields, tuned close to the lowest rotational transition, to engineer a long-range repulsive barrier between polar molecules. By preventing molecules from reaching the short range, this technique suppresses detrimental two-body losses and recently enabled the realization of molecular Bose-Einstein condensates and self-bound droplets. Yet, the optimal operating regimes of the shielding mechanism remain largely unexplored. Here, by leveraging the underlying universality of the scattering problem, we systematically map the four-dimensional microwave parameter space-spanned by the detunings and intensities of the two fields-to identify configurations that maximize both shielding efficiency and interaction tunability. We define optimal operating regimes as configurations that are strictly free of field-linked bound states while sufficiently suppressing two-body losses to exceed typical lifetimes of ultracold samples. In these regimes, we evaluate the elastic-to-inelastic collision ratios required for efficient evaporative cooling and explore the accessible tuning range of the effective dipolar interactions. Finally, to identify the best platforms for future quantum simulation experiments, we conduct a global survey of candidate molecular species under realistic field constraints. We identify heavy, strongly dipolar molecules as the most promising candidates, demonstrating that they can achieve extreme loss suppression-reaching two-body loss rates as low as 10−1810^{-18}10−18 cm3^{3}3/s-alongside robust interaction tunability using only moderate field strengths.
Recent years have witnessed tremendous progress in creating and manipulating ground-state ultracold polar molecules.However, the two-body loss regardless of the chemical reactivities is still a hurdle for many future explorations.Here, we investigate the loss suppression of nonreactive bosonic 23 Na 87 Rb molecules with a circularly polarized microwave blue detuned to the rotational transition.We achieve suppression of the loss by 2 orders of magnitude with the lowest two-body loss rate coefficient reduced to 3 × 10 -12 cm 3 =s.Meanwhile, the elastic collision rate coefficient is increased to the 10 -8 cm 3 =s level.The large good-to-bad collision ratio has allowed us to carry out evaporative cooling of 23 Na 87 Rb with an efficiency of 1.7(2), increasing the phase-space density by a factor of 10.With further improvements, this technique holds great promises for creating a Bose-Einstein condensate of ultracold polar molecules.
The ability to tune interparticle interactions is one of the main advantages of using ultracold quantum gases for quantum simulation of many-body physics. Current experiments with ultracold polar molecules employ shielding with microwave or static electric fields to prevent destructive collisional losses. The interaction potential of microwave-shielded molecules can be tuned by using microwaves of two different polarisations, while for static-field-shielded molecules the tunability of interactions is more limited and depends on the particular species. In this work, we propose a general method to tune the interactions between static-field-shielded molecules by applying a microwave field. We carry out coupled-channel scattering calculations in a field-dressed basis set to determine loss rate coefficients and scattering lengths. We find that both the s-wave scattering length and the dipole length can be widely tuned by changing the parameters of the microwave field, while maintaining strong suppression of lossy collisions.
A combined experimental and theoretical study is carried out on the three-body recombination process in a gas of microwave-shielded polar molecules. For ground-state polar molecules dressed with a strong microwave field, field-linked bound states can appear in the intermolecular potential. We model three-body recombination into such bound states using classical trajectory calculations. Our results show that recombination can explain the enhanced loss rates observed at small microwave detunings in trapped samples of bosonic NaCs [Bigagli et al., Nat. Phys. 19, 1579-1584 (2023)NPAHAX1745-247310.1038/s41567-023-02200-6]. Specifically, our calculations reproduce the experimentally measured three-body loss rates across a wide range of microwave Rabi couplings, detunings, and temperatures. This work suggests that for bosonic shielded molecular systems in which the two-body loss is sufficiently suppressed and a field-linked bound state is present, the dominant loss process will be three-body recombination.
We propose a method to suppress collisional loss in strongly dipolar, rotationally excited ultracold molecules using a combination of static (dc) and microwave (ac) electric fields. By tuning two excited pair molecular rotational states into a Förster resonance with a dc field, simultaneously driving excited rotational transitions with an ac field removes all long-range bound states, allowing near complete suppression of all two- and three-body collisional loss channels. While permitting tunable dipolar and anti-dipolar interactions, this bound-state-free ac/dc scheme is not subject to photon-changing collisions that are the primary source of two-body loss in shielding with two microwave fields, used to achieve the first molecular Bose-Einstein condensate [Bigagli et al., Nature 631, 289 (2024)]. Using NaCs as a representative example for strongly dipolar molecules, close-coupling calculations are performed to show that bound-state-free shielding can achieve ratios of elastic-to-loss rates ≳106\gtrsim 10^{6}≳106 at 100 nK, with currently accessible ac and dc field generation technologies. This work opens new opportunities for realizing large, long-lived samples of strongly interacting degenerate molecular gases with tunable long-range interactions.