In-Situ Rewiring of Two-Dimensional Ion Lattice Interactions Using Metastable State Shelving

TL;DR

The paper demonstrates in-situ rewiring of trapped-ion spin-spin interactions by shelving selected ions into the long-lived $^2F_{7/2}$ metastable state, effectively removing them from dynamics under a global Mølmer-Sørensen Ising drive. Using a triangular $^{171}$Yb$^{+}$ ion crystal, the authors show that shelved ions decouple while unshelved ions retain the original couplings, enabling rapid reconfiguration of interaction graphs without physically moving ions. Quantitative results on 2- and 3-ion systems verify that measured $J_{ij}$ values match predictions and that shelving can suppress all interactions when necessary; shelved ions remain decoupled for timescales many orders of magnitude longer than the interaction times, with deshelving rates scaling roughly as $1/\Omega^2$. This approach opens pathways to programmable lattice geometries and open-system simulations in larger trapped-ion arrays, with potential extensions to deterministic shelving and lifetime engineering for scalable quantum simulations.

Abstract

Trapped-ion lattice geometries, which determine the interactions between trapped-ion qubits, are typically governed by the balance of Coulomb repulsion forces with the external trapping potential. Here we demonstrate how the effective ion lattice geometry and resulting qubit-qubit interactions may be reconfigured in-situ, by shelving specific ions in metastable states outside the qubit subspace. Using a triangular lattice of three $^{171}$Yb$^{+}$ ions, we optically pump selected ions into the long-lived $^2F_{7/2}$ state. We then apply a global Ising-like Hamiltonian to the system and verify that the shelved qubits are fully removed from participation in the quantum dynamics. We characterize the metastable state lifetime in the presence of laser-driven ion-ion interactions, finding a deshelving rate that is orders of magnitude slower than the spin-spin interaction rate and scales quadratically with applied laser intensity.

Figures (6)

• Figure 1: Concept of lattice rewiring via selective ion shelving. (a) Near the center of a large 2D Coulomb crystal, ions self-assemble into a triangular lattice geometry. Each lattice site encodes an effective spin-1/2 system (blue circles). (b)--(c) When an ion is shelved outside the spin-1/2 subspace (gray circles), it no longer interacts with the remaining effective spins. Shelving specific ions within a triangular array provides access to (b) honeycomb and (c) Kagomé lattice geometries, among others.
• Figure 2: Experimental setup geometry for a three-ion triangular crystal. All beams propagate in and are linearly polarized along the $xy$-plane (no $\pi$ component). The ion crystal lies on the $xz$-plane. Non-copropagating Raman beams have a wavevector difference $\Delta\vec{k}$ along the $\hat{x}$ direction and couple to the axial crystal modes.
• Figure 3: (a) Partial energy level diagram of $^{171}$Yb$^{+}$, showing transitions relevant for optical pumping into the $^2F_{7/2}$ state. The 356 nm transition is relevant to deshelving out of the $^2F_{7/2}$ state and is discussed separately in Sec. \ref{['sec:deshelving']}. (b) Spectroscopy of the 411 nm $^2S_{1/2}\rightarrow^2D_{5/2}$ transitions in a background magnetic field of 3.6 G. We optically pump to the $^2F_{7/2}$ state by driving our strongest observed resonance, corresponding to $\Delta m_F=-1$ transitions between the $^2S_{1/2}~{| {F=1} \rangle}$ and $^2D_{5/2}~{| {F=3} \rangle}$ manifolds (red dashed line).
• Figure 4: Depopulation of the $^2S_{1/2}$ manifold during optical pumping to the $^2F_{7/2}$ state. The characteristic shelving time is approximately $55~$ms.
• Figure 5: (a) Pulse sequence used for preparing different configurations of shelved ions and measuring their resulting dynamics. The first detection block is used to verify the initial shelving configuration before driving quantum state evolution. (b)--(c) Dynamics of two trapped ions under an applied Ising interaction, without (b) and with (c) metastable state shelving. The gray line in (c) shows the unshelved data for reference. (d)--(g) Dynamics of three trapped ions under an applied Ising interaction. The coherent oscillations differ depending on which ions are shelved. In panel (d), we show the predicted dynamics based on trap parameters (black, solid) as well as the individual $J_{ij}$ couplings extracted from shelving measurements (orange, dashed).