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:2505.22122 · Physical Review A

Effective potential and scattering length of shielded polar molecules

Peng Xu, Gang Chen

Published Sep 18, 2025• 3 citations
arXivHTMLPDF

Abstract

We investigate the effective potential and scattering length of ultracold polar molecules under different shielding techniques. First, we derive the effective potential for two polar molecules in the presence of (i) an elliptical polarization field alone, (ii) combined elliptical and linear polarization fields, and (iii) combined elliptical polarization and static fields. The effective potential is then expressed as a sum of a zero-range contact interaction and a long-range dipolar interaction under the Born approximation. We find that the methods (i) and (ii) only partially suppress attractive interactions, while the method (ii) allows for the construction of bound states with different polarization shapes. The last shielding method (iii) can achieve complete cancellation of residual attractive forces [Micheli et al., Phys. Rev. A 76, 043604 (2007); Gorshkov et al., Phys. Rev. Lett. 101, 073201 (2008)], which is particularly significant for maintaining quantum degeneracy in ultracold dipolar systems. Our results provide a comprehensive understanding of the effective potential and scattering length of shielding polar molecules, which is crucial for studying many-body physics in ultracold dipolar systems.

DOI
10.1103/dw1b-g5cs

Related papers

Effective anisotropic interaction potentials for pairs of ultracold molecules shielded by a static electric field

Bijit Mukherjee, Luis Santos, Jeremy M. Hutson

Abstract Quantum gases of ultracold polar molecules have novel properties because of the strong dipolar forces between molecules. Current experiments shield the molecules from destructive collisions by engineering long-range repulsive interactions using microwave or static electric fields. These shielding methods produce interaction potentials with large repulsive cores that are not well described with contact potentials. In this paper we explore the anisotropic interaction potentials that arise for pairs of polar molecules shielded with static electric fields. We derive computationally inexpensive approximations for the potentials that are suitable for use in calculations of many-body properties. The interaction potentials for molecules shielded with static fields are substantially different from those that arise from microwave shielding and will produce quite different many-body physics.

arXiv:2507.03164•New Journal of Physics•Sep 1, 2025•4 citations

Controlling collisional loss and scattering lengths of ultracold dipolar molecules with static electric fields

Bijit Mukherjee, Jeremy M. Hutson

Trapped samples of ultracold molecules are often short-lived because close collisions between them result in trap loss. We investigate the use of shielding with static electric fields to create repulsive barriers between polar molecules to prevent such loss. Shielding is very effective even for RbCs, with a relatively low dipole moment, and even more effective for molecules such as NaK, NaRb, and NaCs, with progressively larger dipoles. Varying the electric field allows substantial control over the scattering length, which will be crucial for the stability or collapse of molecular Bose-Einstein condensates. This arises because the dipole-dipole interaction creates a long-range attraction that is tunable with electric field. For RbCs, the scattering length is positive across the range where shielding is effective because the repulsion responsible for shielding dominates. For NaK, the scattering length can be tuned across zero to negative values. For NaRb and NaCs, the attraction is strong enough to support tetra-atomic bound states, and the scattering length passes through resonant poles where these states cross threshold. For KAg and CsAg, there are multiple bound states and multiple poles. For each molecule, we calculate the variation of the scattering length with field and comment on the possibilities for exploring new physics. Published by the American Physical Society 2024

arXiv:2311.08301•Physical Review Research•Feb 6, 2024•12 citations

Microwave Shielding of Ultracold Polar Molecules

Tijs Karman, Jeremy M. Hutson

We use microwaves to engineer repulsive long-range interactions between ultracold polar molecules. The resulting shielding suppresses various loss mechanisms and provides large elastic cross sections. Hyperfine interactions limit the shielding under realistic conditions, but a magnetic field allows suppression of the losses to below 10^{-14} cm^{3} s^{-1}. The mechanism and optimum conditions for shielding differ substantially from those proposed by Gorshkov et al. [Phys. Rev. Lett. 101, 073201 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.073201], and do not require cancellation of the long-range dipole-dipole interaction that is vital to many applications.

arXiv:1806.03608•Physical Review Letters•Oct 16, 2018•138 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

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

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
We investigate the effective potential and scattering length of ultracold polar molecules under different shielding techniques. First, we derive the effective potential for two polar molecules in the presence of (i) an elliptical polarization field alone, (ii) combined elliptical and linear polarization fields, and (iii) combined elliptical polarization and static fields. The effective potential is then expressed as a sum of a zero-range contact interaction and a long-range dipolar interaction under the Born approximation. We find that the methods (i) and (ii) only partially suppress attractive interactions, while the method (ii) allows for the construction of bound states with different polarization shapes. The last shielding method (iii) can achieve complete cancellation of residual attractive forces [Micheli et al., Phys. Rev. A 76, 043604 (2007); Gorshkov et al., Phys. Rev. Lett. 101, 073201 (2008)], which is particularly significant for maintaining quantum degeneracy in ultracold dipolar systems. Our results provide a comprehensive understanding of the effective potential and scattering length of shielding polar molecules, which is crucial for studying many-body physics in ultracold dipolar systems.
Abstract Quantum gases of ultracold polar molecules have novel properties because of the strong dipolar forces between molecules. Current experiments shield the molecules from destructive collisions by engineering long-range repulsive interactions using microwave or static electric fields. These shielding methods produce interaction potentials with large repulsive cores that are not well described with contact potentials. In this paper we explore the anisotropic interaction potentials that arise for pairs of polar molecules shielded with static electric fields. We derive computationally inexpensive approximations for the potentials that are suitable for use in calculations of many-body properties. The interaction potentials for molecules shielded with static fields are substantially different from those that arise from microwave shielding and will produce quite different many-body physics.
Trapped samples of ultracold molecules are often short-lived because close collisions between them result in trap loss. We investigate the use of shielding with static electric fields to create repulsive barriers between polar molecules to prevent such loss. Shielding is very effective even for RbCs, with a relatively low dipole moment, and even more effective for molecules such as NaK, NaRb, and NaCs, with progressively larger dipoles. Varying the electric field allows substantial control over the scattering length, which will be crucial for the stability or collapse of molecular Bose-Einstein condensates. This arises because the dipole-dipole interaction creates a long-range attraction that is tunable with electric field. For RbCs, the scattering length is positive across the range where shielding is effective because the repulsion responsible for shielding dominates. For NaK, the scattering length can be tuned across zero to negative values. For NaRb and NaCs, the attraction is strong enough to support tetra-atomic bound states, and the scattering length passes through resonant poles where these states cross threshold. For KAg and CsAg, there are multiple bound states and multiple poles. For each molecule, we calculate the variation of the scattering length with field and comment on the possibilities for exploring new physics. Published by the American Physical Society 2024
We use microwaves to engineer repulsive long-range interactions between ultracold polar molecules. The resulting shielding suppresses various loss mechanisms and provides large elastic cross sections. Hyperfine interactions limit the shielding under realistic conditions, but a magnetic field allows suppression of the losses to below 10^{-14} cm^{3} s^{-1}. The mechanism and optimum conditions for shielding differ substantially from those proposed by Gorshkov et al. [Phys. Rev. Lett. 101, 073201 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.073201], and do not require cancellation of the long-range dipole-dipole interaction that is vital to many applications.
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.
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.
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.