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:2406.06412 · Physical Review Letters

Bose-Einstein Condensates of Microwave-Shielded Polar Molecules

Wei-Jian Jin, Fulin Deng, Su Yi, Tao Shi

Published May 27, 2025• 9 citations
arXivHTMLPDF

Abstract

We investigate the ground-state phases of ultracold gases composed of bosonic microwave-shielded polar molecules (MSPMs). Using a translational symmetry-breaking variational ansatz with Jastrow correlations, we characterize the many-body correlations arising from the large shielding core of the two-body potential in a dense gas. We show that the molecular gases are always stabilized by the shielding potential and support a self-bound gas phase and an expanding gas phase. Furthermore, we find that, analogous to liquid ^{4}He, the condensate fraction is significantly reduced when the size of the shielding core of the two-body potential becomes comparable to the intermolecular distance. For experimental detection, we also identify a bimodal feature in the momentum distribution. Our work invalidates the application of the Gross-Pitaevskii equation to molecular gases and establishes a universal framework to reveal the many-body correlations in dense molecular gases.

DOI
10.1103/b8y9-yvz9

Related papers

Quantum Phases for Finite-Temperature Gases of Bosonic Polar Molecules Shielded by Dual Microwaves

Wei Zhang, Kun Chen, Su Yi +1 more

We investigate the finite-temperature phase diagram of polar molecules shielded by dual microwave fields using the path integral Monte Carlo method combined with the worm algorithm. We determine the critical temperature T c for Bose-Einstein condensations (BECs) and identify two distinct phases below T c : the expanding gas (EG) phase and the self-bound gas (SBG) phase. We further analyze the temperature and interaction-strength dependence of the condensate and superfluid fractions. Notably, in contrast to dilute atomic BECs, the SBG phase displays a low condensate fraction and a high superfluid fraction, resembling the behavior of strongly correlated 4 He superfluids. These significant many-body correlations arise from the interplay between long-range dipole-dipole interactions and the short-range shielding potential. Furthermore, we demonstrate that the aspect ratio of the gas provides a characteristic geometric signature to accurately determine the EG-to-SBG transition, robust against external trapping potentials. Our findings provide unbiased and numerically exact results to guide upcoming experiments with polar molecules.

arXiv:2503.02644•PRX Quantum•Aug 26, 2025•5 citations

Phases of a Bose-Einstein condensate of microwave-shielded dipolar molecules

Chiara J. Polterauer, Robert E. Zillich

Bose-Einstein condensation of dipolar molecules can be achieved by shielding loss channels with microwave fields. The microwave coupling can be approximated by effective dipole-dipole interactions with a short-range repulsion. We study properties and stability of these molecular Bose gases with a many-body variational method, the hypernetted-chain Euler-Lagrange method for a wide range of densities and repulsion strengths of the microwave shield. We find a homogeneous gas-like phase which, however, is unstable at low density against density waves: at a critical density, which depends on the repulsion strength, the dipolar fluid undergoes a phase transition to a layer phase. Thus, if the molecular condensate is expanded adiabatically by decreasing the confinement strength, it will spontaneously form layers at the critical density. These quasi-two-dimensional layers can be self-bound, hence form two-dimensional liquids. By varying the microwave shield, the predicted equilibrium densities span more than an order of magnitude.

arXiv:2507.18986•Jul 25, 2025•0 citations

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

Nonequilibrium quench dynamics of Bose-Einstein condensates of microwave-shielded polar molecules

Abdelâali Boudjemâa

We theoretically investigate the nonequilibrium dynamics of homogeneous ultracold Bose gases of microwave-shielded polar molecules following a sudden quench of the scattering length at zero temperature. We calculate in particular the quantum depletion, the anomalous density, the condensate fluctuations, and the pair-correlation function using both the time-dependent Bogoliubov approach and the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. During their time evolution, these quantities exhibit slow or fast oscillations depending on the strength of the shielding interactions. We find that at long timescales the molecular condensate is characterized by nonequilibrium steady-state momentum distribution functions, with depletion, anomalous density, and correlations that deviate from their corresponding equilibrium values. We demonstrate that the pair correlations expand diffusively at short times while they spread ballistically at long times.

arXiv:2506.20835•Physical Review A•Jun 11, 2025•5 citations

Effective Potential and Superfluidity of Microwave-Shielded Polar Molecules

Fulin Deng, Xing-Yan Chen, Xinyu Luo +3 more

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.

arXiv:2210.13253•Physical Review Letters•May 3, 2023•33 citations

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
We investigate the ground-state phases of ultracold gases composed of bosonic microwave-shielded polar molecules (MSPMs). Using a translational symmetry-breaking variational ansatz with Jastrow correlations, we characterize the many-body correlations arising from the large shielding core of the two-body potential in a dense gas. We show that the molecular gases are always stabilized by the shielding potential and support a self-bound gas phase and an expanding gas phase. Furthermore, we find that, analogous to liquid ^{4}He, the condensate fraction is significantly reduced when the size of the shielding core of the two-body potential becomes comparable to the intermolecular distance. For experimental detection, we also identify a bimodal feature in the momentum distribution. Our work invalidates the application of the Gross-Pitaevskii equation to molecular gases and establishes a universal framework to reveal the many-body correlations in dense molecular gases.
We investigate the finite-temperature phase diagram of polar molecules shielded by dual microwave fields using the path integral Monte Carlo method combined with the worm algorithm. We determine the critical temperature T c for Bose-Einstein condensations (BECs) and identify two distinct phases below T c : the expanding gas (EG) phase and the self-bound gas (SBG) phase. We further analyze the temperature and interaction-strength dependence of the condensate and superfluid fractions. Notably, in contrast to dilute atomic BECs, the SBG phase displays a low condensate fraction and a high superfluid fraction, resembling the behavior of strongly correlated 4 He superfluids. These significant many-body correlations arise from the interplay between long-range dipole-dipole interactions and the short-range shielding potential. Furthermore, we demonstrate that the aspect ratio of the gas provides a characteristic geometric signature to accurately determine the EG-to-SBG transition, robust against external trapping potentials. Our findings provide unbiased and numerically exact results to guide upcoming experiments with polar molecules.
Bose-Einstein condensation of dipolar molecules can be achieved by shielding loss channels with microwave fields. The microwave coupling can be approximated by effective dipole-dipole interactions with a short-range repulsion. We study properties and stability of these molecular Bose gases with a many-body variational method, the hypernetted-chain Euler-Lagrange method for a wide range of densities and repulsion strengths of the microwave shield. We find a homogeneous gas-like phase which, however, is unstable at low density against density waves: at a critical density, which depends on the repulsion strength, the dipolar fluid undergoes a phase transition to a layer phase. Thus, if the molecular condensate is expanded adiabatically by decreasing the confinement strength, it will spontaneously form layers at the critical density. These quasi-two-dimensional layers can be self-bound, hence form two-dimensional liquids. By varying the microwave shield, the predicted equilibrium densities span more than an order of magnitude.
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.
We theoretically investigate the nonequilibrium dynamics of homogeneous ultracold Bose gases of microwave-shielded polar molecules following a sudden quench of the scattering length at zero temperature. We calculate in particular the quantum depletion, the anomalous density, the condensate fluctuations, and the pair-correlation function using both the time-dependent Bogoliubov approach and the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. During their time evolution, these quantities exhibit slow or fast oscillations depending on the strength of the shielding interactions. We find that at long timescales the molecular condensate is characterized by nonequilibrium steady-state momentum distribution functions, with depletion, anomalous density, and correlations that deviate from their corresponding equilibrium values. We demonstrate that the pair correlations expand diffusively at short times while they spread ballistically at long times.
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.
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.