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arXiv:2210.13253 · Physical Review Letters

Effective Potential and Superfluidity of Microwave-Shielded Polar Molecules

Fulin Deng, Xing-Yan Chen, Xinyu Luo, Wenxian Zhang, Su Yi, Tao Shi

Published May 3, 2023• 33 citations
arXivHTMLPDF

Abstract

We analytically show that the effective interaction potential between microwave-shielded polar molecules consists of an anisotropic van der Waals-like shielding core and a modified dipolar interaction. This effective potential is validated by comparing its scattering cross sections with those calculated using intermolecular potential involving all interaction channels. It is shown that a scattering resonance can be induced under microwave fields reachable in current experiments. With the effective potential, we further study the Bardeen-Cooper-Schrieffer pairing in the microwave-shielded NaK gas. We show that the superfluid critical temperature is drastically enhanced near the resonance. As the effective potential is suitable for exploring the many-body physics of molecular gases, our results pave the way for studies of the ultracold gases of microwave-shielded molecular gases.

DOI
10.1103/physrevlett.130.183001

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We analytically show that the effective interaction potential between microwave-shielded polar molecules consists of an anisotropic van der Waals-like shielding core and a modified dipolar interaction. This effective potential is validated by comparing its scattering cross sections with those calculated using intermolecular potential involving all interaction channels. It is shown that a scattering resonance can be induced under microwave fields reachable in current experiments. With the effective potential, we further study the Bardeen-Cooper-Schrieffer pairing in the microwave-shielded NaK gas. We show that the superfluid critical temperature is drastically enhanced near the resonance. As the effective potential is suitable for exploring the many-body physics of molecular gases, our results pave the way for studies of the ultracold gases of microwave-shielded molecular gases.
Abstract Quantum gases of ultracold polar molecules have novel properties because of the strong dipolar forces between molecules. Current experiments shield the molecules from destructive collisions by engineering long-range repulsive interactions using microwave or static electric fields. These shielding methods produce interaction potentials with large repulsive cores that are not well described with contact potentials. In this paper we explore the anisotropic interaction potentials that arise for pairs of polar molecules shielded with static electric fields. We derive computationally inexpensive approximations for the potentials that are suitable for use in calculations of many-body properties. The interaction potentials for molecules shielded with static fields are substantially different from those that arise from microwave shielding and will produce quite different many-body physics.
We propose a novel scheme to realize the supersolid phase in ultracold gases of microwave-shielded polar molecules by engineering an additional anisotropy in inter-molecular dipolar interaction via an elliptically polarized microwave. It is shown through quantum Monte-Carlo calculations that the interplay of the anisotropies between the interaction and trapping potential gives rise to rich quantum phases. Particularly, it is found that the supersolid phase emerges in the parameter regime accessible to current experiments. Our study paves the way for exploring the properties of supersolid phases in ultracold gases of polar molecules.
Abstract Ultracold polar molecular gases provide a powerful platform for exploring quantum many-body physics with strong, long-range, and anisotropic interactions. In this work, we develop an extended Gross-Pitaevskii approach tailored to bosonic dipolar molecules under single-microwave shielding, incorporating their effective interactions and adapting the quantum fluctuation corrections. We benchmark this beyond-mean-field theory against exact path-integral Quantum Monte Carlo simulations. Focusing on the regime of positive scattering lengths, we find excellent agreement across a range of quantum phases, including superfluid, supersolid, and droplet states. We show that elliptic microwave polarization induces anisotropic superfluidity with direction-dependent sound velocities along each spatial axis—an effect absent in atomic dipolar gases. A quasi-one-dimensional theory captures roton softening and predicts roton instabilities tunable via ellipticity. While most experiments rely on double-microwave shielding to reduce losses, we demonstrate that single-shielded molecules already support rich and tunable many-body behavior. Our framework is readily extendable to the double-shielded case. This work establishes a versatile theoretical foundation for ultracold molecular gases and opens the door to future studies with more advanced shielding protocols.
Ultracold polar molecules with microwave shielding provide a powerful platform for exploring quantum many-body physics with strong, anisotropic interactions. We develop an extended Gross-Pitaevskii framework for bosonic molecules under single microwave shielding, incorporating effective interactions and quantum fluctuations, and benchmark it against exact Quantum Monte Carlo simulations. In the regime of positive scattering lengths, our approach captures superfluid, supersolid, and droplet phases with excellent accuracy. We show that elliptic microwave polarization induces direction-dependent superfluidity--absent in cylindrically symmetric systems. A quasi-1D theory reveals that roton softening and instabilities can be controlled via ellipticity, consistent with recent experiments. Furthermore, we find that the nature of the superfluid-to-supersolid transition is strongly influenced by the ellipticity: the transition is sharp at low ellipticity and continuous at higher values. This tunability offers a potential route for low entropy preparation of molecular supersolids via adiabatic ramps. While double shielding is often used experimentally, our results demonstrate that single-shielded molecules already offer rich, controllable behavior, laying the groundwork for future studies with more complex shielding schemes.
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.
Dual-microwave shielding has emerged as a powerful tool for stabilizing ultracold polar molecules while tuning their intermolecular interactions. However, the two microwave fields are generally not perfectly orthogonal in experiments. Such misalignment introduces an in-plane component of the linearly polarized microwave, whose frequency differs from that of the elliptically polarized field. This component prevents complete cancellation of the dipole-dipole interaction and, more critically, renders the single-molecule dressed state intrinsically time-dependent, so that the conventional time-independent scattering framework is no longer available. Here we develop a Floquet theory that yields an analytic effective potential and enables accurate scattering calculations for polar molecules in non-orthogonal dual microwave fields. We find that, though misalignment weakens the shielding moderately, inelastic losses remain strongly suppressed under experimentally relevant conditions. Meanwhile, misalignment provides additional tunability of the interaction anisotropy and strength, which has been directly applied to recent experimental observations on the gas-to-droplet transition~[Z. Shi \textit{et al}, arXiv:2508.20518 (2025)] and Fermi-surface deformation in microwave-shielded molecular gases~[S. Biswas \textit{et al}, arXiv:2602.22447]. The framework is not restricted to dual-microwave shielding and can be generalized straightforwardly to arbitrary multi-frequency driving, providing a versatile tool for manipulating ultracold polar molecules under complex microwave configurations.