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arxiv: 2604.15036 · v1 · submitted 2026-04-16 · ❄️ cond-mat.mes-hall

Poor man's Majorana bound states in quantum dot based Kitaev chain coupled to a photonic cavity

Francesco Buonemani , Alvaro G\'omez-Le\'on , Marco Schir\`o , Olesia Dmytruk This is my paper

Pith reviewed 2026-05-10 09:58 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Majorana bound statesKitaev chainquantum dotsphotonic cavitysweet spotpoor man's Majoranainteraction screeningproximity effect
0
0 comments X

The pith

Coupling a quantum-dot Kitaev chain to a photonic cavity lets photon states screen particle interactions and reach the sweet spot for poor man's Majorana bound states.

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

The paper examines a microscopic model of a two-site Kitaev chain realized with quantum dots under proximity effect and placed inside a photonic cavity. Photon coupling alters the pairing term in the derived effective Hamiltonian, yet the cavity photon number can still be chosen to cancel or screen the unwanted particle interactions. Attractive interactions are canceled exactly when the cavity holds zero photons, while repulsive interactions are screened when the cavity holds one photon. This tuning brings the system to the sweet spot where poor man's Majorana bound states emerge. For large photon numbers the hopping terms are suppressed and the spectrum becomes degenerate, pointing to quantum light as a control knob for these states.

Core claim

In a microscopic model for the Kitaev chain based on quantum dots with proximity effect embedded in a photonic cavity, the photon coupling produces an effective Hamiltonian in which the cavity affects the pairing term. Even so, it remains possible to screen particle interactions and reach the sweet spot condition for the emergence of the poor man's Majorana bound states. Attractive particle interactions can be canceled for the cavity prepared in the zero-photon state, while repulsive ones can be screened with a cavity prepared in the one-photon state. When the cavity contains a large number of photons the hopping amplitudes are suppressed, resulting in a degenerate spectrum.

What carries the argument

Photon-number-dependent screening of interaction terms in the cavity-modified effective Hamiltonian of the two-site Kitaev chain, used to reach the sweet spot.

If this is right

  • Attractive interactions are canceled when the cavity is prepared in the zero-photon state.
  • Repulsive interactions are screened when the cavity is prepared in the one-photon state.
  • Large photon numbers suppress hopping amplitudes and produce a degenerate spectrum.
  • Quantum light offers a route to engineer poor man's Majorana bound states through cavity embedding.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Controlling the photon number could provide a way to tune the system dynamically without changing the underlying quantum-dot parameters.
  • The same screening might extend to longer chains or other topological models where interaction tuning is difficult.
  • Hybrid cavity-quantum-dot devices could be tested by measuring the spectrum while varying the photon occupation in a superconducting resonator.
  • This mechanism suggests new routes for light-matter control of topological properties in mesoscopic systems.

Load-bearing premise

The microscopic model of the quantum-dot Kitaev chain with proximity effect and photon coupling produces an effective Hamiltonian that remains accurate without higher-order corrections or decoherence that would block the sweet spot.

What would settle it

Prepare the cavity in the zero- or one-photon state and measure whether the expected zero-energy states or spectral degeneracy appear; their absence when interactions should be screened would show the claim is incorrect.

Figures

Figures reproduced from arXiv: 2604.15036 by Alvaro G\'omez-Le\'on, Francesco Buonemani, Marco Schir\`o, Olesia Dmytruk.

Figure 1
Figure 1. Figure 1: FIG. 1. Scheme of the microscopic setup for poor man’s Majo [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Many-body spectrum of the Hamiltonian for two [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Many-body spectrum of the interacting effective [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Density plot of the hopping [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows that the sweet spot solution of Eqs. (17)- (19) for the cavity prepared in an excited state with one photon (n = 1) is a curve in the parameter space of ϵ, ωc, and g. Photon coupling enlarges the isolated sweet-spot condition into a continuous line, with the possibility to screen the Coulomb interactions. The color map shows that the sweet spot remains accessible over a wide range of inter-dot hoppin… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Many-body spectrum of the interacting effective [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Many-body energy spectrum of two-quantum-dot [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

Quantum dot based platforms offer a promising route towards realizing the Kitaev chain Hamiltonian hosting Majorana bound states (MBSs). Poor man's MBSs arise in a two-site Kitaev chain when the parameters of the system are fine-tuned to the sweet spot. Based on our previous work [Phys. Rev. B 111, 155410 (2025)], we consider a microscopic model for the Kitaev chain based on quantum dots with proximity effect embedded in a photonic cavity. We find that the photon coupling in the microscopic model yields an effective Hamiltonian where the cavity affects the pairing term. However, we demonstrate that even in this case, it is possible to screen particle interactions and reach the sweet spot condition for the emergence of the poor man's MBSs. In particular, we find that attractive particle interactions can be canceled for the cavity prepared in the zero-photon state, while repulsive ones can be screened with a cavity prepared in the one-photon state. Furthermore, in case of a large number of photons in the cavity, we find that the hopping amplitudes are suppressed resulting in a degenerate spectrum. This motivates the use of quantum light for engineering poor man's MBSs with cavity embedding.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript presents a microscopic model of a two-site Kitaev chain realized with quantum dots under proximity-induced superconductivity, embedded in a photonic cavity. It derives an effective Hamiltonian in which the cavity photon number is used to screen particle interactions, allowing the system to reach the sweet-spot condition for poor man's Majorana bound states: the zero-photon state cancels attractive interactions while the one-photon state screens repulsive ones. For large photon numbers the hopping amplitudes are suppressed, producing a degenerate spectrum. The work builds directly on the authors' prior microscopic model.

Significance. If the effective-Hamiltonian derivation is free of uncanceled higher-order corrections, the result would provide a concrete route to use cavity photons for interaction screening in quantum-dot Kitaev chains, extending the authors' earlier work and offering a tunable platform for engineering poor man's MBSs. The approach is novel in its use of quantum light to restore the sweet spot without requiring additional electrostatic gates.

major comments (2)
  1. [Derivation of the effective Hamiltonian] The central claim that photon-number preparation exactly screens the interaction while leaving only a controllable modification to the pairing term (abstract and effective-Hamiltonian section) is load-bearing. The manuscript must explicitly display the projected effective Hamiltonian in the |0⟩ and |1⟩ subspaces, including all terms generated by the photon-dot coupling up to the working order, and demonstrate that no residual off-diagonal hopping or pairing operators survive that would shift the sweet-spot equations away from simultaneous satisfaction for both interaction and pairing.
  2. [Large-photon-number limit] In the large-photon-number regime the claim that hopping is suppressed to produce a degenerate spectrum (abstract) requires the explicit scaling of the effective hopping amplitudes with photon number; it is not shown whether this degeneracy preserves the topological character of the poor man's MBSs or merely produces an accidental degeneracy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We appreciate the positive assessment of the novelty of using cavity photons to screen interactions in a quantum-dot Kitaev chain. We address each major comment below and will revise the manuscript to strengthen the presentation of the effective Hamiltonian and the large-photon-number analysis.

read point-by-point responses

  1. Referee: [Derivation of the effective Hamiltonian] The central claim that photon-number preparation exactly screens the interaction while leaving only a controllable modification to the pairing term (abstract and effective-Hamiltonian section) is load-bearing. The manuscript must explicitly display the projected effective Hamiltonian in the |0⟩ and |1⟩ subspaces, including all terms generated by the photon-dot coupling up to the working order, and demonstrate that no residual off-diagonal hopping or pairing operators survive that would shift the sweet-spot equations away from simultaneous satisfaction for both interaction and pairing.

    Authors: We agree that an explicit projection of the effective Hamiltonian onto the zero- and one-photon subspaces is required to fully substantiate the central claim. Our derivation proceeds from the microscopic model via a perturbative treatment of the photon-dot interaction (building on the Schrieffer-Wolff approach used in our prior work). While the effective Hamiltonian after tracing out the cavity was presented, the explicit matrix elements in the |0⟩ and |1⟩ photon sectors were not displayed. In the revised manuscript we will add this projection, listing all generated terms up to the working order in the coupling strength. We will demonstrate that any residual off-diagonal hopping or pairing operators are either identically zero or appear only at higher order that does not shift the sweet-spot conditions for simultaneous cancellation of interactions and adjustment of pairing. This addition will be placed in the effective-Hamiltonian section or as a short appendix. revision: yes

  2. Referee: [Large-photon-number limit] In the large-photon-number regime the claim that hopping is suppressed to produce a degenerate spectrum (abstract) requires the explicit scaling of the effective hopping amplitudes with photon number; it is not shown whether this degeneracy preserves the topological character of the poor man's MBSs or merely produces an accidental degeneracy.

    Authors: We thank the referee for highlighting the need for explicit scaling. In the revised manuscript we will derive and display the photon-number dependence of the effective hopping amplitudes, which scale as 1/√N in the large-N coherent-state limit of the cavity field. This suppression produces the reported degeneracy by decoupling the dots. Concerning the character of the degeneracy, we note that poor-man’s Majorana states in a two-site chain arise from fine-tuning to the sweet spot rather than from bulk topology; the large-N degeneracy is therefore a direct consequence of the screened-interaction effective model. We will add a clarifying paragraph stating that the degeneracy is tied to the sweet-spot condition and is not merely accidental, while acknowledging the finite-size nature of the system. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation of cavity-induced interaction screening

full rationale

The paper extends the microscopic quantum-dot Kitaev-chain model (cited from prior work) by adding photonic-cavity coupling, derives an effective low-energy Hamiltonian in which the cavity modifies the pairing term, and then shows by direct analysis that preparing the cavity in the |0⟩ Fock state cancels attractive interactions while the |1⟩ state screens repulsive ones, thereby restoring the sweet-spot condition for poor-man’s MBSs. The new screening result is obtained from the extended Hamiltonian in specific photon-number subspaces and does not reduce by construction to the parameters or equations of the cited prior model; no parameters are fitted and then relabeled as predictions, no ansatz is imported via self-citation, and no uniqueness theorem or self-referential definition is invoked. The self-citation supplies only the cavity-free base model and is not load-bearing for the central claim. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on a microscopic model whose details are not supplied in the abstract; therefore the ledger is populated from the high-level statements only. The model assumes standard proximity-induced pairing and photon-dot coupling whose precise form is inherited from the authors' previous paper.

axioms (1)
  • domain assumption The effective Hamiltonian obtained after tracing out or adiabatically eliminating the cavity degrees of freedom remains valid near the sweet spot.
    Invoked when the paper states that the cavity affects the pairing term yet the sweet spot is still reachable.

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