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:2607.03179

Effective potentials for polar molecules under non-orthogonal dual microwave fields

Fulin Deng, Xinyuan Hu, S K Yi, Tao Shi

Published Jul 3, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2607.03179

Related papers

Two- and many-body physics of ultracold molecules dressed by dual microwave fields

Fulin Deng, Xinyuan Hu, Wei-Jian Jin +2 more

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.

arXiv:2501.05210•Nature Communications•Dec 13, 2025•9 citations

Exploring molecular supersolidity via exact and mean-field theories: single microwave shielding

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

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.

arXiv:2509.18051•Sep 22, 2025•0 citations

Tuning interactions between static-field-shielded polar molecules with microwaves

Christopher J. Ho, Joy Dutta, Bijit Mukherjee +2 more

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.

cond-mat.quant-gasCross-listedarXiv:2602.03225•Physical Review Research•Feb 4, 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

Mapping the parameter space of double microwave shielding

Hubert J. Jóźwiak, Ian Stevenson, Sebastian Will +1 more

Double microwave shielding employs $σ^{+}$- and $π$-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 $10^{-18}$ cm$^{3}$/s-alongside robust interaction tunability using only moderate field strengths.

cond-mat.quant-gasCross-listedarXiv:2606.09636•Jun 9, 2026•0 citations

Double Microwave Shielding

Tijs Karman, Niccolò Bigagli, Weijun Yuan +3 more

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.

arXiv:2501.08095•PRX Quantum•May 20, 2025•24 citations
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.
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.
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.
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.
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.
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.