⚛️ quantum physics

Engineering the non-Hermitian Su-Schrieffer-Heeger model with skin effects in Rydberg atom arrays

This paper proposes and analyzes a robust, programmable scheme for realizing a non-Hermitian Su-Schrieffer-Heeger model with skin effects in Rydberg atom arrays, demonstrating that the system's topological features remain stable against experimental fluctuations.

Original authors: J. N. Bai, F. Yang, D. Yan, Weibin Li, X. Q. Shao

Published 2026-07-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: J. N. Bai, F. Yang, D. Yan, Weibin Li, X. Q. Shao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: A Quantum "One-Way Street"

Imagine you have a long line of people (atoms) standing in a row. In the world of normal physics, if someone passes a ball to their neighbor, that neighbor can easily pass it back. It's a two-way street.

However, this paper proposes a way to build a special quantum system where the ball only moves in one direction. If you pass it to the right, it can't come back to the left. This is called a "non-Hermitian" system, and it creates a strange phenomenon called the "Skin Effect."

Think of the Skin Effect like a crowd of people at a concert who, for some reason, all decide to huddle tightly against the left wall. Even though there is plenty of space in the middle of the room, everyone piles up at the edge. In this quantum system, the "energy" or "excitation" of the atoms piles up at the ends of the chain instead of spreading out evenly.

How They Built It: The "Three-Person Team"

The scientists propose building this system using Rydberg atoms. These are normal atoms (like Rubidium) that have been excited to a very high energy state, making them huge and very sensitive to each other.

To create the one-way traffic, they arrange the atoms in groups of three, like a small triangle:

Two "Data" Atoms: These are the main characters that hold the information.
One "Helper" (Auxiliary) Atom: This is the trickster.

The Analogy: Imagine a relay race.

The two data atoms are the runners.
The helper atom is a coach standing in the middle.
The scientists use lasers (like flashlights) to talk to the atoms.
By carefully tuning the lasers and making the "coach" atom very unstable (so it quickly loses its energy and resets), they force the runners to only pass the baton in one direction.

The "unstable coach" is the key. Because the coach is constantly losing energy (dissipation), it acts like a one-way valve. It lets the energy flow from Runner A to Runner B, but blocks it from going back. This creates the "Skin Effect" where the energy gets stuck at the ends of the line.

The "Magic Triangle"

The atoms are arranged in a triangle shape within each group. The scientists shine three different colored lasers on them. By adjusting the timing (phase) of these lasers, they create a "synthetic magnetic field."

The Analogy: Imagine a roundabout. Usually, cars can go clockwise or counter-clockwise. But by setting up a specific traffic light system (the lasers), they force all cars to go only clockwise. This creates a "chiral" or one-way flow of energy around the triangle, which is essential for the Skin Effect to happen.

Is It Robust? (The "Messy Room" Test)

In the real world, things are never perfect. Lasers flicker, atoms wiggle, and temperatures change. The paper asks: If we make a mess of the experiment, does the one-way traffic still work?

The authors tested three types of "mess":

Laser Phase Noise: The lasers aren't perfectly steady; they wobble a little.
Laser Intensity Noise: The brightness of the lasers fluctuates.
Position Disorder: The atoms aren't standing in perfect spots; they wiggle around a tiny bit.

The Result: The system is incredibly tough. Even with these imperfections, the atoms still pile up at the edges (the Skin Effect), and the special "topological" properties (the rules that make the one-way traffic work) remain intact. It's like a house of cards that keeps its shape even if you blow on it gently.

Why This Matters (According to the Paper)

This paper doesn't claim to cure diseases or build faster computers right now. Instead, it claims to have designed a blueprint for a new kind of simulator.

A Programmable Lab: They show that we can build this "one-way street" using neutral atoms that we can pick up and move with tweezers.
Real Space vs. Math: Usually, scientists study these effects using complex math in "momentum space" (a theoretical world). This paper shows how to do it in "real space" (physically arranging atoms in a line), which makes it easier to see and measure directly.
Exploring the Unknown: This setup allows scientists to study how "topology" (the shape of the system) and "dissipation" (energy loss) work together, something that is hard to do in other systems.

Summary

The authors have designed a recipe to build a quantum chain of atoms where energy gets trapped at the ends due to a one-way traffic rule created by a "helper" atom and some lasers. They proved that this setup is very stable and won't break even if the experiment isn't perfect. This provides a new, controllable way to study strange quantum phenomena that don't exist in our everyday world.

Technical Summary: Engineering the Non-Hermitian Su-Schrieffer-Heeger Model with Skin Effects in Rydberg Atom Arrays

Problem Statement
The paper addresses the challenge of experimentally realizing non-Hermitian (NH) topological phases, specifically the non-Hermitian Su-Schrieffer-Heeger (SSH) model exhibiting the non-Hermitian skin effect (NHSE), using neutral atom platforms. While NH physics has been explored in photonic and circuit systems, the authors argue that Rydberg atom arrays offer distinct advantages: scalable real-space geometries, single-site addressability, and the ability to actively engineer dissipation through laser-driven transitions. The specific problem tackled is how to construct a controllable, non-reciprocal SSH chain with tunable intra- and inter-cell couplings and how to robustly observe the NHSE and topological edge states in the presence of realistic experimental disorder (laser phase noise, Rabi amplitude fluctuations, and atomic position disorder).

Methodology
The authors propose a scheme utilizing a one-dimensional array of individually addressable $^{87}$ Rb atoms arranged in three-atom unit cells (two data atoms, $a$ and $b$ , and one auxiliary atom, $c$ ).

Hamiltonian Engineering:
- Synthetic Gauge Fields: Atoms are driven by multi-color laser fields to couple ground states to Rydberg states. Through laser-assisted dipolar exchange in the large-detuning regime, effective hopping amplitudes are generated. By controlling the optical phases of the lasers, a synthetic magnetic flux ( $\Phi = \pm \pi/2$ ) is threaded through the triangular plaquette of each unit cell, inducing chiral excitation transport.
- Dissipation-Induced Non-Reciprocity: To generate the non-Hermitian skin effect, the authors engineer a fast dissipative channel for the auxiliary atom ( $c$ ). This is achieved by coupling the Rydberg state of the auxiliary atom to a short-lived intermediate state ( $|p\rangle$ ) via a strong Rabi drive, followed by spontaneous emission to the ground state.
- Adiabatic Elimination: In the regime where the decay rate of the auxiliary atom ( $\Gamma$ ) is much larger than the coherent coupling strengths, the auxiliary degrees of freedom are adiabatically eliminated. This process effectively transforms the system into a two-sublattice SSH model with asymmetric (non-reciprocal) hopping amplitudes ( $J_L \neq J_R$ and $G_L \neq G_R$ ) both within and between unit cells.
Theoretical Framework:
- The system is analyzed under both Open Boundary Conditions (OBC) and Periodic Boundary Conditions (PBC).
- Under OBC, the authors utilize a similarity transformation to map the NH Hamiltonian to an equivalent Hermitian form, demonstrating that the eigenstates of the NH system acquire an exponential envelope, leading to the accumulation of states at the boundaries (NHSE).
- Under PBC, where boundary accumulation is absent, the authors define a real-space topological invariant based on the Bott index and biorthogonal projectors to characterize bulk topology without relying on momentum space.
Disorder Analysis:
- The robustness of the system is tested against three types of experimentally relevant noise:
  - Laser Phase Disorder: Random perturbations to the Peierls phases.
  - Rabi-Amplitude Disorder: Fluctuations in laser intensities.
  - Position Disorder: Stochastic displacements of atoms affecting van der Waals interactions.
- The authors evaluate the stability of the skin effect using the signed directional inverse participation ratio (dIPR) and the stability of the topology using a real-space winding number.

Key Contributions and Results

Realization of NHSSH: The paper provides a concrete, scalable protocol to implement a non-reciprocal SSH model in Rydberg arrays, where non-reciprocity arises from the interplay of synthetic gauge fields and engineered dissipation.
Observation of NHSE: Numerical simulations confirm that under OBC, the system exhibits the non-Hermitian skin effect, where a macroscopic number of eigenstates localize at the boundaries, even in the PT-symmetric phase (where eigenvalues remain real).
Topological Edge States: In the non-trivial topological regime ( $G_L G_R > J_L J_R$ ), in-gap edge states are identified. These states remain pinned near zero energy and are spatially localized at the boundaries.
Robustness to Disorder:
- The skin effect (quantified by $|dMIPR|$) and the topological invariant (winding number $\nu$ ) remain robust against phase noise, Rabi amplitude fluctuations (up to 1%), and position disorder (up to 0.1 $\mu$ m).
- The real-space winding number remains quantized ( $\nu \approx 1$ ) across all disorder types, confirming the stability of the topological phase.
- The imaginary parts of the eigenenergies remain near zero for Rabi and position disorder, indicating the system stays in the PT-symmetric phase under these perturbations.
Real-Space Topological Characterization: The authors successfully extend the analysis to PBC by defining a real-space NH winding number, demonstrating that bulk topology can be characterized in the absence of translational symmetry.

Significance and Claims
The paper claims to establish a "versatile, controllable, and programmable open-system quantum simulator" using neutral atoms. Its primary significance lies in:

Direct Real-Space Implementation: Unlike approaches relying on synthetic dimensions or momentum-space constructions, this scheme realizes the NHSSH model directly in real space, allowing for the direct resolution of boundary accumulation and local disorder effects.
Active Dissipation Engineering: It demonstrates a method to actively engineer non-reciprocal hopping and dissipation using laser-driven transitions, offering dynamical tunability not easily achievable in static photonic systems.
Experimental Feasibility: The work provides a clear route for exploring rich non-Hermitian topological phenomena, asserting that the proposed features (skin effect, edge states, and topological invariants) are robust enough to be observed with current Rydberg atom experimental parameters.
Foundation for Future Studies: The authors suggest this platform can be extended to interacting topological chains, higher-dimensional NH lattices, and dissipative many-body systems to study the interplay of topology, nonreciprocity, disorder, and interactions.

The paper maintains a modest tone regarding its claims, emphasizing that the proposed scheme provides a "clear route" for exploration rather than claiming the immediate realization of complex many-body NH phases, and explicitly notes that the observed deviations in topological invariants in pristine systems are finite-size artifacts.