Microwave-shielded ultracold molecules provide a powerful platform for exploring quantum physics driven by long-range interactions. However, few-molecule bound states in fully three-dimensional (3D) environments remains largely unexplored. Here we show that the tetratomic and hexatomic bound states of 3D ultracold molecules dressed by a single elliptic microwave field can be accurately described by effective one-dimensional (1D) models incorporating high-order angular fluctuations. We identify the validity region of such 1D description in the parameter plane of microwave field ellipticity and coupling strength. The hard-core character of 1D models enables a duality between bosonic and fermionic molecules in real and spectral space, while their momentum distributions remain distinct. Our results demonstrate an effective dimension reduction purely due to the intrinsic interaction anisotropy rather than any external confinement. Extending to large systems, our results suggest a self-bound single-molecule array as the ground state of both bosonic and fermionic molecular gases. The authors establish an effective 1D description for 3D ultracold molecules dressed by an elliptic microwave field. The revealed tetratomic and hexatomic bound states exhibit an unexpected Bose-Fermi duality and point to the formation of self-bound single-molecule array when extending to large systems of both bosonic and fermionic molecules.
Microwave-shielded ultracold molecules provide a powerful platform for exploring quantum physics driven by long-range interactions. However, few-molecule bound states in fully three-dimensional (3D) environments remains largely unexplored. Here we show that the tetratomic and hexatomic bound states of 3D ultracold molecules dressed by a single elliptic microwave field can be accurately described by effective one-dimensional (1D) models incorporating high-order angular fluctuations. We identify the validity region of such 1D description in the parameter plane of microwave field ellipticity and coupling strength. The hard-core character of 1D models enables a duality between bosonic and fermionic molecules in real and spectral space, while their momentum distributions remain distinct. Our results demonstrate an effective dimension reduction purely due to the intrinsic interaction anisotropy rather than any external confinement. Extending to large systems, our results suggest a self-bound single-molecule array as the ground state of both bosonic and fermionic molecular gases. The authors establish an effective 1D description for 3D ultracold molecules dressed by an elliptic microwave field. The revealed tetratomic and hexatomic bound states exhibit an unexpected Bose-Fermi duality and point to the formation of self-bound single-molecule array when extending to large systems of both bosonic and fermionic molecules.
We report universal bound states of microwave-shielded ultracold molecules that solely depend on the strengths of long-range dipolar interaction and microwave coupling. Under a highly elliptic microwave field, few-molecule scatterings in three dimensions are shown to be governed by effective one-dimensional (1D) models, which well reproduce the tetratomic bound state and the Born-Oppenheimer potential in three-molecule sector. For hexatomic systems comprising three identical molecules, we find a much deeper bound state than the tetratomic one, with binding energy exceeding twice the latter. Strikingly, these bound states display Bose-Fermi duality as facilitated by the effective 1D scattering with a large repulsive core from angular fluctuations. For large molecule ensembles, our results suggest the formation of elongated self-bound droplets with crystalline patterns in both bosonic and fermionic 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.
Ultracold diatomic molecules have achieved significant breakthroughs in recent years, enabling the exploration of quantum chemistry, precision measurements, and strongly correlated many-body physics. Extending ultracold molecular complexity to polyatomic molecules, such as triatomic and tetratomic molecules, has attracted considerable interest. However, the realization of ultracold polyatomic molecules remains technically challenging due to their complex energy-level structures. While only a few experiments have successfully demonstrated the formation of polyatomic molecules by magnetoassociation or electroassociation, here we present the first step toward producing tetratomic molecules through the development of a microwave association technique combined with microwave dressing. When the two lowest rotational states of the molecules are dressed by a microwave field, weakly bound tetramer states emerge in the entrance channel with free dark excited states ∣0⟩ and a dressed state ∣+⟩. The spectroscopy of these weakly bound tetramers is probed by another microwave field that drives transitions from the populated dressed states ∣+⟩. By precisely discriminating the complex hyperfine structure of the dark excited level ∣0⟩ from the dressed-state spectroscopy, the binding energy of the tetratomic molecules is measured and characterized. Our work contributes to the understanding of complex few-body physics within a system of microwave-dressed molecules and may open an avenue toward the creation and control of ultracold polyatomic molecules.
We investigate the two- and many-body physics of ultracold polar molecules dressed by dual microwaves with distinct polarizations. Using Floquet theory and multichannel scattering calculations, we identify a regime with the largest elastic-to-inelastic scattering ratio, which is favorable for performing evaporative cooling. Furthermore, we derive and subsequently validate an effective interaction potential that accurately captures the dynamics of microwave-shielded polar molecules (MSPMs). We also explore the ground-state properties of the ultracold gases of MSPMs by computing physical quantities such as gas density, condensate fraction, momentum distribution, and second-order correlation. It is shown that the system supports a weakly correlated expanding gas state and a strongly correlated self-bound gas state. Since the dual-microwave scheme introduces an additional control knob and is essential for creating ultracold Bose gases of polar molecules, our work pave the way for studying the two- and many-body physics of the ultracold polar molecules dressed by dual microwaves. The authors report on a Floquet-theoretical approach to microwave shielding of bosonic ultracold molecules. This clarifies the underlying mechanism behind recently developed dual-microwave schemes and identifies the optimal parameter regime for evaporation.
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.