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

D. Yan; F. Yang; J. N. Bai; Weibin Li; X. Q. Shao

REVIEW 2 major objections 4 minor 127 references

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

T0 review · 2 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A Rydberg-atom chain with engineered loss reduces to a non-Hermitian SSH model that shows a robust non-Hermitian skin effect.

desk verdict A credible Rydberg-array proposal for the non-Hermitian SSH model with skin effect, held back by an unvalidated strong-drive dissipation step and a dropped coupling term, but worth refereeing. read the letter →

arxiv 2601.20114 v3 pith:V6IOTNCE submitted 2026-01-27 quant-ph

J. N. Bai , F. Yang , D. Yan , Weibin Li , X. Q. Shao This is my paper · ORCID

classification quant-ph MSC 81Q1281V80 PACS 03.65.Vz32.80.Ee42.50.-p

keywords non-HermitianSSHmodelRydbergatomarraysskineffectsyntheticgaugefieldadiabaticeliminationnon-reciprocalhoppingtopologicalinvariantsdisorderrobustness

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a concrete experimental scheme to realize a non-Hermitian version of the Su-Schrieffer-Heeger (SSH) model using a chain of Rydberg atoms. Each unit cell has two data atoms and one auxiliary atom; multicolor laser dressing creates a synthetic gauge flux, and the auxiliary atoms are given a fast engineered decay. After adiabatically eliminating the auxiliary atoms, the system reduces to a tight-binding Hamiltonian with non-reciprocal hopping both within and between cells. The paper argues that this Hamiltonian exhibits the non-Hermitian skin effect—all bulk eigenstates pile up at one boundary—and that both the skin-effect order parameter and a real-space winding number remain robust to phase and position disorder. If correct, this gives a scalable, programmable neutral-atom platform for studying non-Hermitian topology in real space.

What carries the argument

The key machinery is the combination of (i) multicolor laser dressing that imprints Peierls phases and produces a synthetic magnetic flux of ±π/2 per triangular plaquette, and (ii) engineered dissipation on the auxiliary atom through a short-lived intermediate state, driven in the strong-driving regime so the Rydberg state acquires an effective decay rate Γ/2. This fast loss justifies adiabatic elimination of the auxiliary atoms, which converts the two-path interference (direct and loss-mediated) into non-reciprocal hoppings. The non-reciprocity is parameterized by the ratio r1 = sqrt(J_+/J_-) and r2 = sqrt(A_+/A_-), and a similarity transformation maps the OBC Hamiltonian to a Hermitian one

What would settle it

A full master-equation (or experimental) time evolution of the three-atom unit cell without adiabatic elimination, using the actual drive strength Omega_d: if the population of the auxiliary Rydberg state does not decay exponentially at rate Gamma/2 (e.g., decays slower or oscillates), then the effective non-reciprocal couplings in Eq. (11) are not realized and the skin effect will not appear.

Watch

Extended reading notes

Core claim

The central discovery is that fast engineered dissipation on one auxiliary atom per unit cell turns a Hermitian Rydberg lattice into an effective non-reciprocal SSH chain. In the strong-driving regime (Omega_d >= Gamma/2), the Liouvillian gap saturates at Gamma/2, meaning the auxiliary atom decays exponentially at that rate; adiabatic elimination then produces directional hoppings J_± = J_ab ± J_1 (intra-cell) and A_± = J_inter ∓ J_2 (inter-cell), so the effective Hamiltonian (Eq. 11) is non-Hermitian and non-reciprocal. Under open boundary conditions all eigenstates localize at one edge (the non-Hermitian skin effect), and the real-space winding number remains quantized near one for disorde

Load-bearing premise

The entire non-reciprocal Hamiltonian rests on the assumption that the strong drive makes the auxiliary atom's Rydberg state decay exponentially at rate Gamma/2, but the paper never specifies the actual drive strength nor simulates the full three-level system to confirm that the effective decay rate is reached on the timescale of the coherent couplings.

Editorial extensions

If this is right

The scheme yields a real-space implementation of the non-Hermitian SSH model in a neutral-atom array, with no need for synthetic dimensions.
Both open and periodic boundary conditions can be realized by closing the chain into a ring, allowing direct study of the non-Hermitian bulk-boundary correspondence.
The skin-effect order parameter and real-space winding number remain robust to disorder, implying the topological phase can be probed in current experiments.
The same three-atom unit-cell building block could be extended to 2D or interacting versions to study non-Hermitian many-body physics.
The parameter regime leaves room to tune between topologically trivial and nontrivial phases by changing interatomic distances or Rabi frequencies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The saturation of the decay rate at Gamma/2 in the strong-driving regime is effectively a Liouvillian exceptional point effect; the paper does not analyze the sensitivity of the skin effect to operating slightly below this condition, where the effective decay rate drops dramatically.
The disorder-robustness results are computed in the single-excitation subspace; adding multiple excitations would introduce Rydberg interactions that could modify the skin effect in ways the current model does not capture.
The real-space winding number formula relies on chiral symmetry; an experimental test could probe how strongly symmetry-breaking terms (e.g., residual Stark shifts) affect the quantization, which the paper assumes away.
The most direct experimental signature would be site-resolved detection after an initial single excitation: if the excitation moves unidirectionally and accumulates at one boundary, that is the non-Hermitian skin effect in action.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a plausible and reasonably concrete proposal for realizing the non-Hermitian SSH model in a real-space Rydberg atom array, and the disorder robustness study is useful. The main thing to know is that the central adiabatic-elimination step is not fully proven as printed: the fast dissipative channel is modeled as a simple sqrt(Gamma/2) jump on the auxiliary Rydberg state, and the paper never specifies Omega_d or checks the reduction against the full three-level Liouvillian.

What is new: the mapping from a three-atom unit cell with multicolor dressing and engineered loss to the non-reciprocal SSH Hamiltonian (Eq. 11) is not in the literature. Previous Rydberg synthetic-dimension SSH work is Hermitian, and previous NHSE proposals in cold atoms use different loss mechanisms. The real-space formulation and the direct OBC/PBC implementation are genuinely useful; the ring closure geometry is handled. The paper is also honest about what it does: it validates the truncated six-atom model against the full Hamiltonian (Fig. 2), compares the effective non-Hermitian model to the master equation with the assumed jump (Fig. 3), and provides deposited data.

Soft spots: the strong-drive argument in Sec. III.A establishes a Liouvillian gap of Gamma/2 but does not by itself justify a Markovian Gamma/2 loss on the auxiliary Rydberg amplitude on the timescale of the engineered hopping. For Omega_d >= Gamma/2 the intermediate state cannot be adiabatically eliminated in the usual Omega<

Who it is for: people working on Rydberg quantum simulation of non-Hermitian topology, and anyone interested in dissipation-engineered non-reciprocal hopping. It deserves a serious referee. I would send it out, asking for the Omega_d value, a full three-level simulation of the elimination step, and a sentence quantifying the dropped couplings.

Referee Report

2 major / 4 minor

Summary. The paper proposes a concrete Rydberg-atom-array implementation of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Each unit cell contains two data atoms and one auxiliary atom; multicolor laser dressing generates a synthetic magnetic flux, and a fast dissipative channel on the auxiliary atom is introduced through a three-level driving scheme. After adiabatic elimination, the model reduces to the non-reciprocal SSH Hamiltonian in Eq. (11), with intra-cell couplings J_± and inter-cell couplings A_±. The authors study the resulting non-Hermitian skin effect under open boundary conditions, characterize it via a signed inverse participation ratio and a real-space winding number, and show robustness against modeled phase disorder and position disorder. They also generalize the construction to periodic boundary conditions.

Significance. If the effective reduction is valid, the proposal would provide a useful neutral-atom platform for non-Hermitian topological physics, complementing synthetic-dimension approaches by working directly in real space and allowing scalable, addressable arrays. The manuscript has several strengths: a concrete experimental geometry with explicit detunings and Rabi frequencies, agreement between the six-atom model and the effective six-site dynamics in Fig. 2, a real-space topological invariant that is well suited to disordered systems, disorder-averaged numerical results, and an open-data statement. However, the central claim depends on an adiabatic-elimination step whose dissipative input is not fully validated; this is the main load-bearing gap.

major comments (2)

[Sec. III A, Eq. (7)]
[Sec. III B, Eqs. (8)–(10)]

minor comments (4)

[Sec. III A, Eq. (6)]
[Sec. V B, Fig. 5]
[Sec. V]
[Sec. III A]

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the NHSE is derived from an explicit microscopic-to-effective Hamiltonian chain, not fitted or assumed.

full rationale

The derivation chain is not circular. The microscopic Hamiltonian (Eq. 1) and the truncated six-atom effective model (Eq. 2) are independent inputs, with dressed-exchange amplitudes computed by second-order perturbation theory and benchmarked against Eq. 1 in Fig. 2. The non-reciprocal couplings in Eq. 11 are obtained by adiabatic elimination (Eqs. 8-10) with no parameter fitted to the target NHSE; the skin effect and the winding numbers are then mathematical consequences of the resulting H_NH under OBC/PBC (Eqs. 12-14). The disorder-robustness results (Figs. 5-7 and 9) are predictions from the same effective Hamiltonian with injected phase/position fluctuations, not fits renamed as predictions. Self-citations ([20], [72], [111], [113]) do not carry the argument: the key spectral-gap result is derived in Eqs. (3)-(5), and the multicolor-dressing formula is standard perturbation theory from an external published paper. The main vulnerability is a validation gap, not circularity: the reduction from the three-level Liouvillian to the sqrt(Gamma/2) jump in Eq. (7) is not benchmarked against the full three-level dynamics, and Omega_d is never specified; this affects whether the engineered loss is truly Markovian, but it is an approximation/correctness concern, not an equivalence-by-construction of inputs and outputs.

Assumptions & free parameters 5 free parameters · 8 assumptions · 0 invented entities

The central result depends on hand-chosen laser parameters, an unspecified strong drive Omega_d, and three approximations: large-detuning perturbation theory, short-range truncation, and adiabatic elimination. One additional hidden approximation drops same-sublattice couplings. No new physical entities are introduced.

free parameters (5)

Laser detunings (Delta_I, Delta_II, Delta_III) = 2 pi x (51.3, 59.8, 68.4) MHz
Chosen by hand to satisfy the large-detuning condition while keeping effective couplings; the quantitative NHSE and its robustness depend on them.
Laser Rabi frequencies (Omega_I, Omega_II, Omega_III) = 2 pi x (4.3, 4.65, 5) MHz
Chosen to realize the effective hopping parameters; not fitted to external data.
Dissipation drive Rabi frequency Omega_d = not specified; requires Omega_d >= Gamma/2 ~ 4.23 MHz
The engineered Gamma/2 loss requires strong driving, but the paper never gives Omega_d or validates the three-level dynamics.
Laser phase phi_c^III = pi/2 (all other phases zero)
Chosen to set the synthetic flux to pi/2; controls the direction of non-reciprocal transport.
Disorder amplitudes = epsilon = 0.1 pi/2 for phase; delta R in [-0.1, 0.1] microns
Noise levels chosen to represent experimental imperfections; the 'robust' conclusion is tied to these scales.

assumptions (8)

domain assumption Second-order perturbation theory in the large-detuning regime |Omega| << |Delta| yields the effective Rydberg-mediated hopping J_jk (Eq. 2).
Used to derive the effective Hamiltonian; standard but requires the stated large-detuning condition.
domain assumption Interactions beyond distance d3 can be neglected; the six-atom model captures the full dynamics.
Validated numerically in Fig. 2 for one parameter set; relied on for the 40-atom OBC and PBC models.
ad hoc to paper The auxiliary atom's dissipation is a Markovian loss at rate Gamma/2 on its Rydberg state (Eq. 7).
Derived from the Liouvillian gap in the strong-driving limit; no explicit Omega_d or full three-level simulation is provided.
domain assumption Adiabatic elimination of auxiliary atoms is valid since Gamma/2 >> {gamma_a, gamma_b, J}.
Used to set the auxiliary amplitude derivatives to zero; necessary for the non-reciprocal hopping result.
domain assumption The dynamics is restricted to the single-excitation subspace.
The SSH model is single-particle; multiple Rydberg excitations are excluded from the derivation.
ad hoc to paper The neglected same-sublattice couplings 2 J_ca h1 / Gamma vanish or are negligible.
Needed for Eq. (10) to follow from Eqs. (8)-(9); not stated or quantified in the paper.
domain assumption Disorder is uniformly distributed: delta phi in [-0.1 pi/2, 0.1 pi/2] and delta R in [-0.1, 0.1] microns.
Defines the robustness test; the results are specific to these distributions.
standard math The effective Hamiltonian has chiral symmetry {C1, H} = 0 so the real-space winding number is quantized.
Needed for the topological invariant; holds for the idealized SSH form but may be broken by the omitted couplings.

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Cite this review

Pith. "Pith review of Engineering the non-Hermitian Su-Schrieffer-Heeger model with skin effects in Rydberg atom arrays." pith.science (2026). https://pith.science/paper/V6IOTNCE

@misc{pith2026260120114,
  author       = {Pith},
  title        = {Pith review of: Engineering the non-Hermitian Su-Schrieffer-Heeger model with skin effects in Rydberg atom arrays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6IOTNCE}},
  note         = {Machine review of arXiv:2601.20114}
}

read the original abstract

We propose and systematically analyze a practical scheme for implementing a one-dimensional non-Hermitian (NH) 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 multicolor laser fields. By engineering fast dissipative channels for one auxiliary atom in each unit cell, adiabatic elimination effectively gives rise to a NH skin effect. We examine how fluctuations in the experimental parameters influence both the skin effect and the topological invariant 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 NH topological phenomena.

Figures

Figures reproduced from arXiv: 2601.20114 by the authors.

**Figure 2.** FIG. 2. (a) Illustration of the six-atom model. (b) Popula [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Populations of the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4. (a1) and (a2) represent the complex energy spectra of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. (a) After introducing Mean-distributed phase noise [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. (a) The [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7. Evolution of the complex eigenenergies of the NH SSH c [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 9.** Figure 9: FIG. 9. The deviation 1 [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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The detunings are ( ΔI, ΔII, ΔIII ) = 2/u1D70B× (51.3, 59.8, 68.4) MHz with Rabi frequencies ( ΩI, ΩII, ΩIII ) = 2/u1D70B× (4.3, 4.65, 5) MHz

(hollow circle) and (2) (solid line), respectively. The detunings are ( ΔI, ΔII, ΔIII ) = 2/u1D70B× (51.3, 59.8, 68.4) MHz with Rabi frequencies ( ΩI, ΩII, ΩIII ) = 2/u1D70B× (4.3, 4.65, 5) MHz. Other parameters are taken as the same as Fig. 1. from the Rydberg state /barex /barex/u1D45F/u1D450⟩ to the target ground state /barex /barex/u1D454/u1D450⟩ via ...

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merely induce on-site energy oﬀsets and do not aﬀect the oﬀ-diagonal couplings; they, therefore, have no inﬂuence on the system dy- namics of interest and can be safely neglected in the followi ng analysis. We now use /u1D462/u1D466 /u1D465 to denote the probability amplitude of atom /u1D465in the /u1D466-th unit cell being in the Rydberg state. In the Ha...

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