Antiferromagnetic bosonic $t$-$J$ models and their quantum simulation in tweezer arrays

Abstract

The combination of optical tweezer arrays with strong interactions -- via dipole-exchange of molecules and van-der-Waals interactions of Rydberg atoms -- has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants: This will enable to simulate the physics believed to underlie many strongly correlated quantum materials. Here we propose an experimental scheme to realize bosonic t-J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-$T_c$ cuprates can be realized. Since the ground states of the 2D bosonic AFM t-J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants -- the simplest instance in which their bosonic statistics plays a role, and contrast our results to the fermionic case. We perform large-scale density matrix renormalization group (DMRG) calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t-J models may contain similar physics as the collective phases in strongly correlated electrons.

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• Dichotomy of heavy and light pairs of holes in the $t-J$ model
• Spin-1 Haldane phase in a chain of Rydberg atoms
• Time-reversal in a dipolar quantum many-body spin system
• Feshbach hypothesis of high-Tc superconductivity in cuprates
• Supersolidity in Rydberg tweezer arrays
• Long-lived multilevel coherences and spin-1 dynamics encoded in the rotational states of ultracold molecules
• Two-dopant origin of competing stripe and pair formation in Hubbard and $t$-$J$ models
• Emergent spinon-holon Feshbach resonance in a doped Majumdar-Ghosh model
• Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion
• Generalized pulse design in Floquet engineering: Application to interacting spin systems
• Double Supersolid Phase in a Bosonic t-J-V Model with Rydberg Atoms