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arXiv:2407.12752 · Physical Review A

Supersolidity in Rydberg tweezer arrays

Lukas Homeier, Simon Hollerith, Sebastian Geier, N.-C. Chiu, Antoine Browaeys, Lode Pollet

Published Jan 31, 2025• 10 citations
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Abstract

Rydberg tweezer arrays provide a versatile platform to explore quantum magnets with dipolar XY or van der Waals Ising ZZ interactions. Here, we propose a scheme combining dipolar and van der Waals interactions between two Rydberg states, where the amplitude of the latter can be greater than that of the former, realizing an extended Hubbard model with long-range tunnelings in optical tweezer arrays. On the triangular lattice with repulsive interactions, we predict the existence of a robust supersolid phase with a critical entropy per particle S / N ≈ 0.19 accessible in current Rydberg tweezer experiments supported by large-scale quantum Monte Carlo simulations. We further demonstrate the experimental feasibility by identifying pairs of Rydberg states in Rb 87 realizing the required interactions. Such a lattice supersolid is long lived, found over a wide parameter range in an isotropic and flat two-dimensional geometry, and can be realized for hundreds of particles allowing one to directly probe the defect-induced picture of supersolids. Its thermodynamical and dynamical properties can hence be studied at a far larger scale than hitherto possible.

DOI
10.1103/physreva.111.l011305

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Rydberg tweezer arrays provide a versatile platform to explore quantum magnets with dipolar XY or van der Waals Ising ZZ interactions. Here, we propose a scheme combining dipolar and van der Waals interactions between two Rydberg states, where the amplitude of the latter can be greater than that of the former, realizing an extended Hubbard model with long-range tunnelings in optical tweezer arrays. On the triangular lattice with repulsive interactions, we predict the existence of a robust supersolid phase with a critical entropy per particle S / N ≈ 0.19 accessible in current Rydberg tweezer experiments supported by large-scale quantum Monte Carlo simulations. We further demonstrate the experimental feasibility by identifying pairs of Rydberg states in Rb 87 realizing the required interactions. Such a lattice supersolid is long lived, found over a wide parameter range in an isotropic and flat two-dimensional geometry, and can be realized for hundreds of particles allowing one to directly probe the defect-induced picture of supersolids. Its thermodynamical and dynamical properties can hence be studied at a far larger scale than hitherto possible.
Recent advances in Rydberg tweezer arrays bring novel opportunities for programmable quantum simulations beyond previous capabilities. In this Letter, we investigate a bosonic t-J-V model currently realized with Rydberg atoms. Through large-scale quantum Monte Carlo simulations, we uncover an emergent double supersolid (DSS) phase with the coexistence of two superfluids and crystalline order. Tunable long-range tunneling and repulsive hole-hole interactions enable a rich phase diagram featuring a double superfluid phase, a DSS phase, and an antiferromagnetic insulator. Intriguingly, within the DSS regime we observe an unconventional thermal enhancement of crystalline order. Our results establish the bosonic t-J-V model as a promising and experimentally accessible platform for exploring exotic quantum phases in Rydberg atom arrays.
Neutral atoms become strongly interacting when their electrons are excited to loosely bound Rydberg states. We investigate the strongly correlated quantum phases of matter that emerge in two-dimensional atom arrays where three Rydberg levels are used to encode an effective spin-1 degree of freedom. Dipolar exchange between such spin-1 Rydberg atoms naturally yields two distinct models: (i) a two-species hardcore boson model, and (ii) upon tuning near a Förster resonance, a dipolar spin-1 XY model. Through extensive, large-scale infinite density matrix renormalization group calculations, we provide a broad roadmap predicting the quantum phases that emerge from these models on a variety of lattice geometries: square, triangular, kagome, and ruby. We identify a wealth of correlated states, including lattice supersolids and simplex phases, all of which can be naturally realized in near-term experiments.
Motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [C. Chen et al., Nature (London) 616, 691 (2023)], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U(1)U(1)U(1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle $S/N\ensuremath{\approx}0.5$, close to the one at the critical temperature, Sc/N=0.585(15){S}_{c}/N=0.585(15)Sc​/N=0.585(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.
Recent experiments with ultracold Rydberg-excited atoms have shown that long-range interactions can give rise to spatially ordered structures. Observation of crystalline phases in a system with Rydberg atoms loaded into an optical lattice seems also within reach. Here we investigate a bosonic model on a triangular lattice suitable for description of such experiments. Numerical simulations based on bosonic dynamical mean-field theory reveal a rich phase diagram with different supersolid phases. Comparison with the results obtained for a square lattice geometry shows qualitatively similar results in a wide range of parameters; however, on a triangular lattice we do not observe the checkerboard supersolid. Moreover, unlike on a square lattice, we did not find a phase transition from uniform superfluid to supersolid induced by increase of the hopping amplitude on a triangular lattice. Based on our results, we propose an intuitive interpretation of the nature of different supersolid phases. We also propose parameters for the experimental realization.
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 one 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 compare our results to the fermionic case. We perform large-scale density matrix renormalization group 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.