Realization of a doped quantum antiferromagnet with dipolar tunnelings in a Rydberg tweezer array

Abstract: Doping an antiferromagnetic Mott insulator is central to our understanding of a variety of phenomena in strongly-correlated electrons, including high-temperature superconductors. To describe the competition between tunneling $t$ of hole dopants and antiferromagnetic (AFM) spin interactions $J$, theoretical and numerical studies often focus on the paradigmatic $t$-$J$ model, and the direct analog quantum simulation of this model in the relevant regime of high-particle density has long been sought. Here, we realize a doped quantum antiferromagnet with next-nearest neighbour (NNN) tunnelings $t'$ and hard-core bosonic holes using a Rydberg tweezer platform. We utilize coherent dynamics between three Rydberg levels, encoding spins and holes, to implement a tunable bosonic $t$-$J$-$V$ model allowing us to study previously inaccessible parameter regimes. We observe dynamical phase separation between hole and spin domains for $|t/J|\ll 1$, and demonstrate the formation of repulsively bound hole pairs in a variety of spin backgrounds. The interference between NNN tunnelings $t'$ and perturbative pair tunneling gives rise to light and heavy pairs depending on the sign of $t$. Using the single-site control allows us to study the dynamics of a single hole in 2D square lattice (anti)ferromagnets. The model we implement extends the toolbox of Rydberg tweezer experiments beyond spin-1/2 models to a larger class of $t$-$J$ and spin-$1$ models.

• The paper introduces a Rydberg tweezer array platform used to simulate doped quantum antiferromagnets and study their complex many-body dynamics.
• The research demonstrates key phenomena like dynamical phase separation and the formation of repulsively bound hole pairs in simulated 1D and 2D systems.
• This experimental approach provides crucial groundwork for exploring emergent condensed matter phenomena, with implications for understanding high-temperature superconductivity.

Realization of a Doped Quantum Antiferromagnet with Dipolar Tunnelings in a Rydberg Tweezer Array

The paper presents an ambitious study that investigates the dynamics of doped quantum antiferromagnets using a Rydberg tweezer array. This setup allows for the simulation of the bosonic $t$-$J$-$V$ model, a variant of the classical $t$-$J$ model, overcoming notable challenges in observing many-body phase interactions within highly-dense quantum systems.

Overview and Methodology

The research utilizes a Rydberg platform, specifically a tweezer array, to model strongly-correlated electron systems—offering newfound insights into low-energy behaviors and out-of-equilibrium properties of doped Mott insulators. By encoding spin and hole states within distinct Rydberg levels, the study simulates interactions encapsulated by the $t$-$J$-$V$ Hamiltonian, characterized by tunneling (t) and spin interactions (J), supplemented by hole-hole interactions (V). This model equips researchers with a method to examine key phenomena that contribute to high-temperature superconductivity.

An integral novelty lies in the experimental method, allowing manipulation of Rydberg states to model single and paired hole dynamics effectively. These experiments observe hole tunneling dynamics by tuning the relative strengths of interactions through angle adjustments relative to a magnetic field within the tweezer array, enabling access to parameter regimes typically inaccessible to traditional ultracold atomic setups.

Key Findings and Results

1. Phase Separation: By initiating a 12-atom chain in a Néel-order antiferromagnetic alignment interspersed with four holes, researchers successfully demonstrate dynamical phase separation. For small $t/J_\perp$ ratios, observed dynamics indicate a clear boundary between hole-rich and spin-rich domains, with robustness to time evolution corroborated by theoretical simulation.
2. Repulsively Bound Hole Pairs: The study illuminates conditions under which holes pair and remain bound. The dynamics of pair formation and movement reveal subclasses of light and heavy pairs, showcasing dependence on next-nearest neighbor tunneling. This insight reveals new facets regarding interaction interference in doped quantum magnets.
3. Background Dependence: Experiments examining the dynamic evolution of hole pairs in different magnetic spin environments further clarify how spin backgrounds dictate pair-binding and mobility. For instance, holes propagate more rapidly across an antiferromagnetic ($x$-AFM) background compared to a ferromagnetic ($x$-FM) one due to differences in effective binding energies and coupling strengths.
4. Two-Dimensional Magnet Dynamics: The extension of this study to two-dimensional systems captures the dynamics of a single hole within both ferromagnetic and antiferromagnetic spin backgrounds. In FM, interference patterns emerge, emphasizing the impact of dipolar tunneling. Conversely, AFM settings underscore unique spin-hole dynamics critical in the understanding of doped Mott insulators.

Implications and Future Directions

The results provide critical groundwork in exploring emergent phenomena in condensed matter physics, particularly in relation to high-temperature superconductivity. These demonstrated configurations and manipulations of Rydberg states significantly enrich the array of experimental tools available for quantum simulators, allowing a move beyond spin-1/2 models to access other complex many-body systems.

Future research can build upon this foundational work by exploring wider parameter spaces of the $t$-$J$-$V$-$W$ models and leveraging the high fidelity of Rydberg systems to simulate even more intricate interactions, such as those contributing to frustrated magnets or spin liquids. Further refinements in controlling initial conditions and mitigating noise in quantum states will allow for deeper analyses of phase transitions and potential superconductive properties.

Overall, this work exemplifies advancement in simulating and understanding interacting quantum systems, posing significant implications for theoretical models of superconductivity and other related strongly-interacting phenomena.