Robust topological quantum state transfer with long-range interactions in Rydberg arrays

Abstract

We develop a theoretical framework for fast, robust and high-fidelity topological quantum state transfer in one-dimensional systems with long-range couplings, motivated by chains of Rydberg atoms with dipole-dipole interactions. Such long-range interactions naturally give rise to extended Su-Schrieffer-Heeger and Rice-Mele models supporting topologically protected edge states. We show that these edge states enable high-fidelity edge-to-edge excitation transfer using both time-independent protocols, based on coherent edge state dynamics, and time-dependent protocols, based on adiabatic modulation of system parameters. Long-range couplings play a central role by enhancing the relevant energy gaps, leading to a substantial improvement in transfer efficiency compared to nearest neighbour models. The resulting transfer is robust against positional disorder, reflecting its topological origin and highlighting the potential of long-range interacting platforms for reliable quantum state transfer.

Figures (8)

• Figure 1: Single-sided topological edge states. a) SSH model with even number of sites. The energy spectrum (right) depicted as a function of the ratio $J_1'/J_1$ shows that in the topologically trivial regime ($J_1'/J_1>1$) the mid-gap states occupy the bulk (3), while for the specific case $J_1'/J_1=0$, two single-sided edge states appear, (2) and (1). b) SSH model with odd number of sites. Here, single-sided edge states exist in both the topological (1) and trivial (3) regimes. At the transition point, where $J_1'=J_1$, the mid-gap state is an equal superposition of all sites on sublattice $B$ (2). c) Rice-Mele model. The mid-gap states are split due to the energy shift $\hbar\Delta$, and single-sided edge states (1) and (2) are found in the regime where $J_1'/J_1<1$, while again for $J_1'/J_1>1$ the mid-gap states occupy the bulk (3).
• Figure 2: Realization of topological models with Rydberg atoms. a) Each Rydberg atom is modeled as a two-level system with transition energy $\hbar\omega_a$. A staggered detuning realizes an alternating on-site potential, with atoms on sublattice $A$ (blue) and $B$ (red) experiencing a detuning $\hbar\Delta$ and $-\hbar\Delta$, respectively. b) One-dimensional chain of Rydberg atoms arranged in a bipartite lattice composed of two sublattices, $A$ and $B$. A single Rydberg excitation can hop between sites via dipole–dipole interactions, indicated by solid, dashed, and dotted lines corresponding to different coupling ranges. Sublattice $B$ is displaced relative to sublattice $A$ by a distance $b$ along the $x$-direction and $h$ along the $y$-direction. The transition dipole moments are aligned by an external field and form an angle $\theta=\theta_m$ with the $x$-axis. c) Angular dependence of the dipole–dipole interaction strength. At the angle $\theta_m=\arccos(1/\sqrt{3})$, the dipole–dipole coupling vanishes.
• Figure 3: QST in the even extended SSH model. a) Ratio of effective hoppings $\bar{J}'/\bar{J}$ as a function of the geometric parameters $b$ and $h$. b) Time $T_{\mathrm{osc}}$ required for a single Rabi flop between the two edges evaluated along the red line indicated in panel a). The grey shaded region marks parameter values for which the target fidelity $F(T_\mathrm{osc})>99.9\%$ is achieved. c) Dynamics of the excitation density $|\braket{\psi(t)|\uparrow_n}|^2$ of site $n$. This shows Rabi flopping dynamics for the chain configuration $b=0.78a$ and $h=-0.145a$, showing coherent oscillations between the two boundaries as a function of time $t$. d) Same dynamics as in panel c), but with a sublattice energy quench $\hbar\Delta$ applied at time $t_Q=2.635 \,\mathrm{ms}$, when the excitation reaches maximal localization on the opposite edge, suppressing further oscillations and stabilizing the transfer.
• Figure 4: QST in the odd extended SSH model. a) Overlap $F_L$ ($F_R$) between the zero-energy eigenstate $\ket{\psi_0}$ and a perfectly localized left (right) edge state as a function of the geometrical parameters $b$ and $h$. White regions indicate forbidden configurations where two tweezers are closer than $2.5\, \mathrm{\mu m}$. Black dots mark the selected initial and final chain configurations; the corresponding eigenstates $\ket{\psi_i}$ and $\ket{\psi_f}$ and associated lattice geometries for a chain of $N=9$ atoms are shown below. Dotted circles denote empty lattice sites, while filled circles indicate the presence of an excitation ($\ket{\uparrow}$). b) Transfer fidelity $F$ as a function of the total transfer time $T$ for a linear path in parameter space (dashed) and the optimized one (solid), see main text. Dotted vertical lines indicate the transfer times needed to reach the target fidelity for the optimized smooth path ($T_{\text{transfer}}^{o} = 19.5\, \mu\text{s}$) and the linear path ($T_{\text{transfer}}^{l}=43\, \mu\text{s}$). The inset shows the energy gap $\Delta E$ between the mid-gap state and the bulk states in parameter space, together with the corresponding transfer paths. The optimized path follows Eq. \ref{['SmoothOptimizedPath']} with $h_m=-0.3026a$ and $p=0.2194$.
• Figure 5: Long-range enhancement of transfer efficiency in the odd extended SSH model. Transfer fidelity $F$ obtained using the optimized smooth parameter path in the odd SSH model for nearest neighbour couplings only (blue) and for the full long-range Rydberg couplings (red) for a chain of $N=9$ atoms. The inset shows the transfer velocity $v$ as a function of chain length, highlighting the enhancement induced by long-range interactions.