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1. A neutral-atom Hubbard quantum simulator in the cryogenic regime

   https://doi.org/10.1038/s41586-025-09112-w  

   Xu, Muqing; Kendrick, Lev Haldar; Kale, Anant; Gang, Youqi; Feng, Chunhan; Zhang, Shiwei; Young, Aaron W; Lebrat, Martin; Greiner, Markus (June 2025, Nature)

   Ultracold fermionic atoms in optical lattices offer pristine realizations of Hubbard models1, which are fundamental to modern condensed-matter physics2,3. Despite notable advancements4–6, the accessible temperatures in these optical lattice material analogues are still too high to address many open problems7–10. Here we demonstrate a several-fold reduction in temperature6,11–13, bringing large-scale quantum simulations of the Hubbard model into an entirely new regime. This is accomplished by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters14,15, which is extremely challenging to simulate classically10. At half-filling, the long-range antiferromagnetic order is close to saturation, leading to a temperature of T /t =0.05−0.05 +0.06 based on comparisons with numerically exact simulations. Doped away from half-filling, it is exceedingly challenging to realize systematically accurate and predictive numerical simulations9. Importantly, we are able to use quantum simulation to identify a new pathway for achieving similarly low temperatures with doping. This is confirmed by comparing short-range spin correlations to state-of-the-art, but approximate, constrainedpath auxiliary-field quantum Monte Carlo simulations16–18. Compared with the cuprates2,19,20, the reported temperatures correspond to a reduction from far above to below room temperature, at which physics such as the pseudogap and stripe phases may be expected3,19,21–24. Our work opens the door to quantum simulations that solve open questions in material science, develop synergies with numerical methods and theoretical studies, and lead to discoveries of new physics8,10. 

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2. Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ ₂ lattice gauge theories

   https://doi.org/10.1126/sciadv.aav7444  

   Barbiero, Luca; Schweizer, Christian; Aidelsburger, Monika; Demler, Eugene; Goldman, Nathan; Grusdt, Fabian (October 2019, Science Advances)

   From the standard model of particle physics to strongly correlated electrons, various physical settings are formulated in terms of matter coupled to gauge fields. Quantum simulations based on ultracold atoms in optical lattices provide a promising avenue to study these complex systems and unravel the underlying many-body physics. Here, we demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices, using a combination of coherent lattice modulation with strong interactions. Specifically, we propose implementation of ℤ 2 lattice gauge theories coupled to matter, reminiscent of theories previously introduced in high-temperature superconductivity. We discuss a range of settings from zero-dimensional toy models to ladders featuring transitions in the gauge sector to extended two-dimensional systems. Mastering lattice gauge theories in optical lattices constitutes a new route toward the realization of strongly correlated systems, with properties dictated by an interplay of dynamical matter and gauge fields. 

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3. Observation of generalized t-J spin dynamics with tunable dipolar interactions

   https://doi.org/10.1126/science.adq0911  

   Carroll, Annette N; Hirzler, Henrik; Miller, Calder; Wellnitz, David; Muleady, Sean R; Lin, Junyu; Zamarski, Krzysztof P; Wang, Reuben_R W; Bohn, John L; Rey, Ana Maria; et al (April 2025, Science)

   Long-range and anisotropic dipolar interactions profoundly modify the dynamics of particles hopping in a periodic lattice potential. We report the realization of a generalizedt-Jmodel with dipolar interactions using a system of ultracold fermionic molecules with spin encoded in the two lowest rotational states. We independently tuned the dipolar Ising and spin-exchange couplings and the molecular motion and studied their interplay on coherent spin dynamics. Using Ramsey spectroscopy, we observed and modeled interaction-driven contrast decay that depends strongly both on the strength of the anisotropy between Ising and spin-exchange couplings and on motion. This study paves the way for future exploration of kinetic spin dynamics and quantum magnetism with highly tunable molecular platforms in regimes that are challenging for existing numerical and analytical methods. 

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4. Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules

   https://doi.org/10.1038/s41567-023-02328-5  

   Gregory, Philip D; Fernley, Luke M; Tao, Albert Li; Bromley, Sarah L; Stepp, Jonathan; Zhang, Zewen; Kotochigova, Svetlana; Hazzard, Kaden_R A; Cornish, Simon L (March 2024, Nature Physics)

   Abstract Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for⁸⁷Rb¹³³Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation. 

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5. Experimental realization of an extended Fermi-Hubbard model using a 2D lattice of dopant-based quantum dots

   https://doi.org/10.1038/s41467-022-34220-w  

   Wang, Xiqiao; Khatami, Ehsan; Fei, Fan; Wyrick, Jonathan; Namboodiri, Pradeep; Kashid, Ranjit; Rigosi, Albert F.; Bryant, Garnett; Silver, Richard (December 2022, Nature Communications)

   Abstract The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models. 

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