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arXiv:2607.28533

Hubbard physics with ultracold polar molecules: on-site interaction energies for shielded molecules

Carlin Stewart-Wiese, Joy Dutta, Jeremy M. Hutson

Published Jul 30, 2026• 0 citations
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Abstract

We explore on-site interaction energies $U$ for pairs of shielded ultracold molecules on the same lattice site. We use 2-dimensional effective potentials appropriate for microwave shielding, which have dipole-dipole character at long range but feature a very large repulsive core when the two molecules come close together. This causes very strong correlation between the motions of two molecules on the same site. We find behavior very different from that for ultracold atoms: in particular, there are states for which $U$ is negative for weak lattices but crosses zero to positive values as the lattice strength increases. This behavior is found for both unbound pairs and 2-body bound states. The latter will give access to previously unexplored types of strongly dipolar Hubbard physics with multiple site occupancy.

DOI
10.48550/arxiv.2607.28533

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We explore on-site interaction energies UUU for pairs of shielded ultracold molecules on the same lattice site. We use 2-dimensional effective potentials appropriate for microwave shielding, which have dipole-dipole character at long range but feature a very large repulsive core when the two molecules come close together. This causes very strong correlation between the motions of two molecules on the same site. We find behavior very different from that for ultracold atoms: in particular, there are states for which UUU is negative for weak lattices but crosses zero to positive values as the lattice strength increases. This behavior is found for both unbound pairs and 2-body bound states. The latter will give access to previously unexplored types of strongly dipolar Hubbard physics with multiple site occupancy.
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.
Engineering SU(NNN)-Symmetric Hubbard Models with Microwave-Shielded Dipolar Molecules
Ultracold polar molecules provide strong, long-range interactions that microwave shielding makes tunable and nearly nuclear-spin independent, giving an emergent SU(NNN) symmetry. However, extended Hubbard models of polar molecules in optical lattices lack, so far, controllable finite on-site interactions, a key ingredient of strong correlated physics. We show that tuning the Rabi frequency of the microwave coupling can bring two individual molecules (monomers) on neighboring lattice sites into resonance with a field-linked dimer (doublon) on one of the sites, enabling coherent doublon--monomer-pair conversion. In this model, we characterize the key Hubbard parameters and the dimer lifetime, demonstrating that the on-site and off-site interactions can be tuned nearly independently through the microwave amplitude and orientation, respectively. Our results provide a roadmap for implementing SU(NNN)-symmetric extended Hubbard models with controllable doublon fluctuations, providing access to quantum-simulation in the strongly dipolar regime.
We show that, in appropriate regimes, ultracold collisionally shielded molecules in an optical lattice realize a controlled extended Hubbard model, despite their large-radius hard-core repulsion. We compute the Hubbard parameters and show lattice depth and microwave-induced dipolar interactions provide flexible, independent control of on- and off-site interactions. This makes shielded molecules a powerful platform for extended Hubbard models and enables an interaction microscope that can distinguish inter-hole interactions in doped Mott insulators - crucial to superconductivity and strange metallicity - that are indistinguishable with quantum gas microscopy alone.
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.
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 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.