Dynamics of antiferromagnetic Dimers in Rydberg Atom Chains

TL;DR

This work derives an effective PXQ model for a strongly interacting one-dimensional Rydberg atom chain in the anti-blockade regime ($Δ = V_0$, $V_0 \gg Ω$), revealing a conserved antiferromagnetic dimer number $N_{cl}$ and a block-diagonal Hilbert-space structure. Through analytical mapping to the Heisenberg XX model and construction of coupling graphs, the authors classify subspaces and identify their internal connectivity, showing that the full dynamics in the PXQ limit conserve dimers and become integrable in the thermodynamic limit. Numerical comparisons with the full Rydberg Hamiltonian show that increased NN interaction suppresses leakage from the dimer-conserving subspace and aligns dynamics with PXQ predictions, while long-range tails introduce deviations that grow with $V_0$ but do not destroy dimer conservation. The results highlight the potential to study antiferromagnetic dimer dynamics and related constrained dynamics on Rydberg-atom quantum simulators, with implications for engineered quantum transport and quantum information applications.

Abstract

We investigate the dynamics of antiferromagnetic dimers within a Rydberg atom chain in the regime where laser detuning compensates for nearest-neighbor (NN) interactions. Using an effective PXQ model, we demonstrate that the associated Hilbert space decomposes into disconnected, dimer-conserving subspaces. The classification of these subspaces is provided, and the computational basis states spanning them are identified. Through a combination of analytical mapping and numerical simulations, we compare the dynamics of the PXQ model with those of the full Rydberg atom chain. The deviations are attributed to two factors, laser-induced leakage from the constrained Hilbert subspace and the influence of long-range interactions beyond the NN limit. Our results indicate that subspace leakage can be mitigated by increasing the NN interaction strength. While this simultaneously amplifies the effects of long-range interactions, the conservation of the dimer number remains. Our study opens up possibilities for exploring the dynamics of antiferromagnetic dimers using the Rydberg atom quantum simulator.

Figures (10)

• Figure 1: One-dimensional Rydberg atom chain. The neighboring atoms are separated by a distance $r_0$. Atoms are excited from the ground state $\ket{\downarrow}$ to the Rydberg state $\ket{\uparrow}$ with Rabi frequency $\Omega$ and detuning $\Delta$. In the Rydberg state, atoms interact via van der Waals interactions. $V_0$ is the nearest-neighbor interaction term.
• Figure 2: Dimer configurations and boundaries of the chain. We illustrate dimers with $N_{\text{cl}}=1$ and $L=6$. Beyond the boundaries, the atoms are in the ground state (grey sites). This ensures that the number of $\ket{\downarrow\uparrow}$ and $\ket{\uparrow\downarrow}$ dimers is equal. Any two neighboring dimers must be separated by a continuous block of excited atoms.
• Figure 3: Schematic illustration of the block-diagonal structure of the Hamiltonian. Under the conditions $\Delta = V_0$ and $V_0 \gg \Omega \gg V_{\text{NNN}}$, the Hamiltonian $\hat{H}_0$ is effectively described by the PXQ Hamiltonian. Due to the conservation of the antiferromagnetic dimers, the PXQ Hamiltonian becomes block-diagonal.
• Figure 4: Coupling graphs in subspace $N_{\text{cl}} = 1$ for $L=4$(a) and $L=5$(b), and $N_{\text{cl}} = 2$ for $L=5$(c). In the graph, each basis forms a vertex, whereas the coupling that links the neighboring basis states gives the edge.
• Figure 5: Coupling graph of basis states. For a given $L$, the maximal value of $N_{\text{cl}}$ is $= [(L+1)/2]$. For $L=4$(a), $5$(b), and $6$(c), the corresponding ones are $2$, $3$ and $3$.