Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2504.21535 · Physical Review Letters

Universal Bound States with Bose-Fermi Duality in Microwave-Shielded Ultracold Molecules

Tingting Shi, Haitian Wang, Xiaoling Cui

Published Jan 9, 2026• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/hcwf-tk6c

Related papers

Interaction-induced dimension reduction for bound states in microwave-shielded ultracold molecules

Haitian Wang, Tingting Shi, Xiaoling Cui

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.

arXiv:2511.09856•Communications Physics•May 15, 2026•1 citation

Efimov Effect in Ultracold Microwave-Shielded Polar Molecules

Shayamal Singh, Chris H. Greene

A quantum-mechanical description is presented for the three-body physics of shielded dipolar molecules, including a prediction of observable Efimov physics. Despite the anisotropic and long-range nature of the interaction, shielding enables a regime in which universality emerges already at the two-body level and extends to the three-body sector, where Efimov physics emerges. On the negative side of the scattering-length resonance, computed trimer binding energies display the characteristic scaling expected for Efimov resonances. Finally, the sudden approximation can be used to create trimer bound states, starting from positive energy trap states as a way to create or detect these molecular trimers. Moreover, the three-body parameter expressed in dipolar units is found to be universal.

physics.atom-phCross-listedarXiv:2602.21433•Physical Review Letters•Feb 26, 2026•0 citations

Exploring supersolids of single-microwave shielded molecules via exact and mean-field theories

T. Arnone Cardinale, Thomas Bland, S. M. Reimann

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.

Communications Physics•Jun 2, 2026•1 citation

Universality in the microwave shielding of ultracold polar molecules

Joy Dutta, Bijit Mukherjee, Jeremy M. Hutson

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.

arXiv:2501.03170•Physical Review Research•May 19, 2025•10 citations

Self-Bound Droplets of Ultracold Dipolar Molecules under Tunable Double Microwave Shielding

Roger Melero, Jordi Boronat, Ferran Mazzanti

We use the Ground-State Path Integral Monte Carlo method to study a Bose-Einstein condensate of strongly interacting NaCs polar molecules under the action of a fully anisotropic double microwave shielding potential characterized by a linear and an elliptical polarization field. In particular, we analyze the ground state of the system and its structure as a function of the ellipticity angle $ξ$. While for the circularly polarized case ($ξ=0$) a gas phase is realized, one or more self-bound droplets are observed for small $|ξ|$'s above a threshold value near $3^\circ$. With increasing $ξ$, the observed droplets rapidly become tightly bound and are estimated to form a superfluid array. Our results compare favorably to the experimental observations in [Zhang et al., Nature \textbf{651}, 601 (2026)] for positive $ξ$, while moderate differences show up for $ξ<0$ where our simulations conform to the expected symmetries of the intermolecular potential.

arXiv:2607.06130•Jul 7, 2026•0 citations

Self-bound many-body states of quasi-one-dimensional dipolar Fermi gases: Exploiting Bose-Fermi mappings for generalized contact interactions

F. Deuretzbacher, Georg M. Bruun, C. J. Pethick +3 more

Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these systems provide a realization of a single-component one-dimensional Fermi gas with a generalized contact interaction. Using an exact duality between one-dimensional Fermi and Bose gases, we show that when the dipole moment is strong enough, bound many-body states exist, and we calculate the critical coupling strength for the emergence of these states. At higher densities, the Hartree--Fock approximation is accurate, and by combining the two approaches we determine the structure of the phase diagram. The many-body bound states should be accessible in future experiments with ultracold polar molecules.

arXiv:1306.0405•Physical Review A•Sep 10, 2013•10 citations
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.
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.
A quantum-mechanical description is presented for the three-body physics of shielded dipolar molecules, including a prediction of observable Efimov physics. Despite the anisotropic and long-range nature of the interaction, shielding enables a regime in which universality emerges already at the two-body level and extends to the three-body sector, where Efimov physics emerges. On the negative side of the scattering-length resonance, computed trimer binding energies display the characteristic scaling expected for Efimov resonances. Finally, the sudden approximation can be used to create trimer bound states, starting from positive energy trap states as a way to create or detect these molecular trimers. Moreover, the three-body parameter expressed in dipolar units is found to be universal.
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.
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 use the Ground-State Path Integral Monte Carlo method to study a Bose-Einstein condensate of strongly interacting NaCs polar molecules under the action of a fully anisotropic double microwave shielding potential characterized by a linear and an elliptical polarization field. In particular, we analyze the ground state of the system and its structure as a function of the ellipticity angle ξξξ. While for the circularly polarized case (ξ=0ξ=0ξ=0) a gas phase is realized, one or more self-bound droplets are observed for small ∣ξ∣|ξ|∣ξ∣'s above a threshold value near 3∘3^\circ3∘. With increasing ξξξ, the observed droplets rapidly become tightly bound and are estimated to form a superfluid array. Our results compare favorably to the experimental observations in [Zhang et al., Nature \textbf{651}, 601 (2026)] for positive ξξξ, while moderate differences show up for ξ<0ξ<0ξ<0 where our simulations conform to the expected symmetries of the intermolecular potential.
Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these systems provide a realization of a single-component one-dimensional Fermi gas with a generalized contact interaction. Using an exact duality between one-dimensional Fermi and Bose gases, we show that when the dipole moment is strong enough, bound many-body states exist, and we calculate the critical coupling strength for the emergence of these states. At higher densities, the Hartree--Fock approximation is accurate, and by combining the two approaches we determine the structure of the phase diagram. The many-body bound states should be accessible in future experiments with ultracold polar molecules.