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arXiv:2607.27107

Engineering SU($N$)-Symmetric Hubbard Models with Microwave-Shielded Dipolar Molecules

Jing-Lun Li, Ragheed Alhyder, Andreas Schindewolf, Kaden R. A. Hazzard, Mikhail Lemeshko, Georgios M. Koutentakis

Published Jul 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Ultracold polar molecules provide strong, long-range interactions that microwave shielding makes tunable and nearly nuclear-spin independent, giving an emergent SU($N$) 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($N$)-symmetric extended Hubbard models with controllable doublon fluctuations, providing access to quantum-simulation in the strongly dipolar regime.

DOI
10.48550/arxiv.2607.27107

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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 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.
We propose encoding a pseudo-spin-1/21/21/2 system in the ground (v=0v=0v=0) and first excited (v=1v=1v=1) vibrational states of polar molecules. Double microwave shielding simultaneously shields molecules in both states, suppressing two-body losses by orders of magnitude while strictly avoiding three-body recombination. The microwave dressing is state-dependent and results in highly tunable, long-range dipolar Ising exchange (JzJ_zJz​), density-density (VVV), and spin-density (WWW) interactions. These interaction length scales readily exceed the typical interparticle spacing, pushing the molecules deep into the strongly interacting regime. In bulk gases, this enables the exploration of itinerant quantum magnetism and quantum droplets with novel anisotropic spin textures; in optical lattices, it naturally realizes extended Hubbard and ttt-JzJ_zJz​ models, opening new directions in quantum simulation.
We show that dipolar interactions between ultracold polar alkali-metal dimers in optical lattices can be used to realize a highly tunable generalization of the ttt-JJJ model, which we refer to as the ttt-JJJ-VVV-WWW model. The model features long-range spin-spin interactions Jz{J}_{z}Jz​ and ${J}_{\ensuremath{\perp}}$ of XXZXXZXXZ type, long-range density-density interaction VVV, and long-range density-spin interaction WWW, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling ttt. The ``spin'' is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed-matter systems. Realistic experimental imperfections are discussed.
Long-range anisotropic dipole-dipole interactions between ultracold polar molecules are predicted to drive exotic quantum phases, yet direct many-body signatures of these interactions in degenerate Fermi gases have remained elusive. Here, we report the observation of an interaction-induced controlled deformation of the Fermi surface, providing a clear many-body signature in a deeply degenerate Fermi gas of 23Na40K^{23}\text{Na}^{40}\text{K}23Na40K molecules. Using double microwave (MW) shielding, we prepare 8×1038 \times 10^38×103 molecules at 0.23(1)0.23(1)0.23(1) times the Fermi temperature, achieving a three-fold suppression of inelastic losses compared to single MW shielding while preserving strong elastic dipolar scattering. We observe Fermi surface deformations of up to 7 %7\,\%7%, more than two times larger than those observed in magnetic atoms, despite operating at two orders of magnitude lower densities. Crucially, we demonstrate continuous tuning of the interaction potential from axial U(1) to biaxial C2_{2}2​ symmetry, directly imprinting this geometry onto the Fermi surface. We find excellent agreement between our experimental results and parameter-free Hartree-Fock theory. These results establish MW-shielded polar molecules as a highly tunable platform for exploring strongly correlated dipolar Fermi matter and offer a promising path towards topological superfluidity.
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.