Engineering the non-Hermitian SSH model with skin effects in Rydberg atom arrays

TL;DR

This work presents a practical scheme to realize a one-dimensional non-Hermitian SSH model in a Rydberg-atom array with three-atom unit cells. By engineering fast dissipation on an auxiliary atom and adiabatically eliminating it, the authors generate non-reciprocal hopping inside and between unit cells, yielding a NHSE-supported SSH topology observable under open and periodic boundary conditions. The topological phase is characterized using real-space winding numbers and localization measures (IPR/dIPR/dMIPR), and shown to be robust against phase and position disorder within realistic experimental ranges. A periodic-boundary generalization to a ring confirms that the bulk topology under PBC aligns with the real-space NHSE, highlighting the scheme's potential as a programmable open-system quantum simulator for non-Hermitian topological phenomena. The approach offers a scalable, controllable platform for exploring NH topology in neutral-atom systems, with potential extensions to interacting topological chains.

Abstract

We propose and systematically analyze a practical scheme for implementing a one-dimensional non-Hermitian Su-Schrieffer-Heeger model using individually addressable Rydberg atom arrays. Our setup consists of an atomic chain with three-atom unit cells, in which a synthetic gauge field is generated by applying multi-color laser fields. By engineering fast dissipative channels for one auxiliary atom in each unit cell, the adiabatic elimination effectively gives rise to a non-Hermitian skin effect. We examine how fluctuations in the experimental parameters influence both the skin effect and the topological invariant under open and periodic boundary conditions in real space and find that both features remain highly robust. This work establishes a versatile, controllable, and programmable open-system quantum simulator with neutral atoms, providing a clear route for exploring rich non-Hermitian topological phenomena.

Figures (9)

• Figure 1: (a) The schematic of a chain structure consisting of $N$ three-atom unit cells. Each unit cell contains two data atoms (yellow) and one auxiliary atom (red), with the distances between atoms inside the unit cell labeled as $R_1=6~\mu$m and the adjacent unit cells denoted by $R_2=3.46~\mu$m and $R_3=8.29~\mu$m. (b) The laser driving process acting on both the data and auxiliary atoms, where neighboring atoms share the same laser, and each atom is driven by two distinct lasers. (c) A fast dissipative channel is constructed by introducing an intermediate state of the auxiliary atoms.
• Figure 2: (a) Illustration of the six-atom model. (b) Populations of the $\sigma_{n-1,c}^+\sigma_{n-1,c}^-$ (purple), $\sigma_{n,a}^+\sigma_{n,a}^-$ (green), $\sigma_{n,b}^+\sigma_{n,b}^-$ (red), $\sigma_{n,c}^+\sigma_{n,c}^-$ (yellow), $\sigma_{n+1,a}^+\sigma_{n+1,a}^-$ (black) and $\sigma_{n+1,c}^+\sigma_{n+1,c}^-$ (blue) governed by the equation of Eqs. (\ref{['eq1']}) (hollow circle) and (\ref{['eq2']}) (solid line), respectively. The detunings are $(\Delta_{\rm I},~\Delta_{\rm II},~\Delta_{\rm III})=2\pi\times(51.3,~59.8,~68.4)~\mathrm{MHz}$ with Rabi frequencies $(\Omega_{\rm I},~\Omega_{\rm II},~\Omega_{\rm III})=2\pi\times(4.3,~4.65,~5)~\mathrm{MHz}$. Other parameters are taken as the same as Fig. \ref{['fig1']}.
• Figure 3: Populations of the $\sigma_{n,a}^+\sigma_{n,a}^-$ (green), $\sigma_{n,b}^+\sigma_{n,b}^-$ (red), $\sigma_{n+1,a}^+\sigma_{n+1,a}^-$ (yellow), and $\sigma_{n,j}^-\sigma_{n,j}^+$ (black) governed by the Eq. (\ref{['eq6']}) (solid line) and $\sigma_{2n-1}^+\sigma_{2n-1}^-$ (green), $\sigma_{2n}^+\sigma_{2n}^-$ (red), $\sigma_{2n+1}^+\sigma_{2n+1}^-$ (yellow) governed by the Eq. (\ref{['10']}) (hollow circle), respectively. Other parameters are taken as the same as Figs. \ref{['fig1']} and \ref{['fig2']}.
• Figure 4: (a1) and (a2) represent the complex energy spectra of Eq. (\ref{['eq12']}) under different parameter regimes, corresponding to $\phi_{ca}=\pi/2$ and $-\pi/2$, respectively. The red circles (left axis) denote the real part of the eigenvalues ${\rm Re}(E_n)$ and the green diamonds (right axis) represent the imaginary part ${\rm Im}(E_n)$. (b1) and (b2) display the spatial probability distributions $|\psi_n|^2$ of the eigenstates associated with the spectra in (a). The red line highlights the topologically protected edge states localized at the boundary, whereas the green lines depict the extended bulk states. Other parameters are taken as the same as Figs. \ref{['fig1']} and \ref{['fig2']}.
• Figure 5: (a) After introducing Mean-distributed phase noise to the $\phi_{ca}$ phase of each link in a $20$ unit-cell chain, the $\rm |dMIPR|$ is calculated according to Eq. (\ref{['eq20']}) for $N_s=100$ independent realizations of random $\delta\phi$. The green bars represent the value for each individual disordered realization, while the red bar indicates the average value. (b) The deviation of the winding number $1-\nu$ as a function of uniform disorder strength. Other parameters are taken as the same as Figs. \ref{['fig1']} and \ref{['fig2']}.