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arXiv:2510.04634 · Physical Review Research

Symmetry and self-bound droplets in dipolar molecular gases

D. Baillie

Published May 11, 2026• 1 citation
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Abstract

Recent experiments with degenerate molecular gases dressed by elliptically polarized microwave fields have enabled new control of dipolar interactions via engineered anisotropy. We reveal a symmetry structure of the dipolar interaction that generates degeneracies among the interaction parameters, enabling a classification of spatial symmetries and equilibrium shapes of the gases. Exploiting these symmetries, we analyze solutions including beyond-mean-field quantum fluctuations in the dilute gas regime and develop a complementary variational theory. We map out the phase diagram of self-bound droplets and characterize their widths, energies, and densities.

DOI
10.1103/l9wk-v25v

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We investigate how dipolar interactions between microwave-shielded polar molecules structure the self-bound droplets formed under variation of the interaction strength. We identify the transition from droplets to crystals as a finite-size first order transition. With droplet-ring states and transitional supersolid states we predict additional structure in the crystal and droplet phases, respectively. To describe this strongly correlated regime, and in particular the reconfiguration of quantum ground states, we design a variational Monte Carlo framework based on neural quantum states. It is especially suitable to describe ground states and almost degenerate states with very different configurations. Moreover, one can easily determine the superfluid fraction. Our results reveal the sequence of finite-size structures through which dipolar interactions reorganize molecular droplets into crystals.
We simulate a molecular Bose-Einstein condensate in the strongly dipolar regime, observing the existence of self-bound droplets, as well as their splitting into multiple droplets by confinement-induced frustration. Our quantum Monte Carlo approach goes beyond the limits of the established effective mean-field theories for dipolar quantum gases, revealing small droplets produced by strong dipolar interactions outside known stable regimes. The simulations include realistic molecular interactions and therefore have direct relevance for current and future experiments.
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We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquidlike density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.
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.