{"id":"bc63865e-9be1-4156-94bd-be276658106f","arxiv_id":"2411.13841","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A driven nonlinear circuit with only local Kerr nonlinearity displays a switchable non-Hermitian skin effect in its Bogoliubov sideband modes above a drive threshold.","lead":"This paper builds a nonlinear electrical circuit whose small voltage fluctuations behave like Bogoliubov quasiparticles, and shows that raising the drive voltage past a threshold makes these modes suddenly pile up at one edge. It demonstrates a switchable non-Hermitian skin effect using only local Kerr nonlinearity, without engineered asymmetric hopping or p-wave pairing.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The switchable-NHSE claim rests on treating the measured sideband as a linear BdG response, but the paper reports no probe-linearity check or kp-reversal control, leaving a nonlinearity or instrumental-asymmetry alternative open.","rationale":"Agree with the reader that the weakest assumption is the BdG linearization. The theory section is internally consistent and the toy model is standard, but the experimental section does not establish the linear-response regime of the probe. The measured sideband is a forced response at the probe frequency, not a directly measured eigenmode, so its spatial profile is a valid NHSE diagnostic only if the Green's function is dominated by a BdG eigenmode in the linear regime. The fixed 50 mV probe amplitude and absence of a probe-power sweep leave this open. A probe-linearity check would settle it: in the BdG picture the normalized profile is independent of V'pp, while an intermodulation or harmonic-generation artifact would show a dependence. A kp-reversal control would further corroborate the topological direction, but the probe-linearity check is the more direct test of the load-bearing assumption. This does not change the reader's CONDITIONAL verdict; it identifies the specific condition that should be attached.","tokens_in":9532,"tokens_out":8068,"duration_ms":87068,"concrete_test":"Fix Vpp=500 mV and Ω=0.018, and measure the normalized sideband profile Vs_n/∥Vs∥ and IPR for auxiliary-drive amplitudes V'pp = 10, 25, 50, 100, and 200 mV. In the BdG linear regime these normalized quantities should be independent of V'pp; if the IPR increases with probe power or the profile broadens or shifts, the response is nonlinear and the switch cannot be assigned to BdG topology.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the abrupt localization at Vpp≈240 mV is a topological NHSE of Bogoliubov modes. This requires the measured sideband voltage at the auxiliary-drive frequency to be a linear probe of the BdG eigenmodes obtained from ansatz (8)–(9). The main text does not verify that the response is in this linear regime: V'pp is fixed at 50 mV, and no data show that the normalized spatial profile and IPR are independent of V'pp. If the varactor nonlinearity generates intermodulation or harmonic products that grow as Vpp approaches 240 mV, the same abrupt IPR increase could appear without any point-gap winding. The prose distinguishes Bogoliubov sidebands from higher-harmonic generation, but a distinction asserted in words is not a measurement. Additionally, no control reverses the drive phase pattern kp→−kp to show that the localization direction flips, as the winding argument predicts; without this control, a fixed right-localized response could be an instrumental asymmetry.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experimental realization of a non-Hermitian skin effect (NHSE) in Bogoliubov quasiparticles of a nonlinear driven-dissipative circuit. The circuit is an RLC transmission line with varactor nonlinearity, driven by a fundamental tone with a phase gradient kp=2π/3 and probed by a weak auxiliary drive at a sideband frequency. The authors show theoretically that the Bogoliubov-de Gennes (BdG) Hamiltonian has a point-gap winding under periodic boundary conditions when pseudo-Hermiticity spontaneously breaks above a drive amplitude near Vpp≈240 mV, and that open-boundary modes localize to one edge. Experimentally, they observe a sideband whose spatial profile is right-localized in a frequency window consistent with the non-real part of the BdG spectrum, and an abrupt increase of the inverse participation ratio as Vpp crosses the predicted threshold. The central claim is that this is a switchable NHSE of Bogoliubov modes, distinct from both linear-circuit NHSE realizations and from the bosonic Kitaev chain experiments that require nonlocal pairing interactions.","tokens_in":9744,"tokens_out":3741,"duration_ms":35937,"significance":"If the claims hold, this is a valuable experimental demonstration of a nonlinearity-induced, actively switchable NHSE in a simple classical circuit. The threshold voltage is not fitted to the localization data but is computed from independently characterized circuit parameters, which is a genuine strength. The system also differs from earlier optomechanical and superconducting-circuit realizations of the bosonic Kitaev chain in using only a local Kerr-type nonlinearity, making the result potentially accessible to a broad range of synthetic metamaterial platforms. The paper ships a clear toy model and a plausible mapping from circuit equations to a BdG Hamiltonian, though the latter is partly deferred to the supplement. The main weaknesses are the absence of a direct linearity check of the auxiliary-drive probe and the absence of a kp-reversal control; these leave plausible alternative explanations for the observed localization.","major_comments":[{"comment":"The derivation of the effective BdG Hamiltonian from the circuit equation of motion is entirely relegated to the Supplemental Materials [57]. The sentence \"It can then be shown [57]\" is the foundation for the central theoretical interpretation: the measured sideband is identified with a BdG eigenmode, the threshold at 240 mV is computed from this Hamiltonian, and the winding and skin-mode properties follow from it. The main text should reproduce the essential steps of this derivation, or the supplement must be clearly available for review, because the experimental claims inherit all of their meaning from this mapping.","section":"Nonlinear circuit, Eqs. (7)-(9)"},{"comment":"No auxiliary-drive linearity check is reported. All sideband measurements use V'_pp = 50 mV, and the paper does not show that the normalized spatial profile and IPR are independent of V'_pp. If varactor nonlinearity generates intermodulation or harmonic products whose spatial distribution sharpens as Vpp increases, the same abrupt IPR increase could appear without any point-gap winding. The authors should test this by varying V'_pp across the drive range and showing either that the sideband amplitude scales linearly with V'_pp or that the normalized profile and IPR are unchanged; this is a direct test of the BdG linearization assumption that underlies the whole claim.","section":"Results, Figs. 3(b)-3(f)"},{"comment":"The predicted dependence of the localization direction on the drive phase pattern is not tested. The model states that the winding number, and hence the skin-mode direction, is set by kp, but the experiment only demonstrates right-localized modes for kp = 2π/3. Reversing the drive phase gradient to kp = -2π/3 should flip the localization to the left if the mechanism is the predicted NHSE. Without this control, a fixed right-localized response could be an instrumental asymmetry, and the claim that the edge direction is tied to the drive phase is not directly supported.","section":"Results, Fig. 3(c) and Fig. 3(f)"},{"comment":"The experimental IPR and sideband ratio are measured at a single sideband frequency Ω = 0.018, while the theoretical curves in the lower panel are averaged over all BdG modes. The authors note that the averaged curves are smoothed because not all modes break pseudo-Hermiticity simultaneously, but this makes the comparison of the sharpness of the transition indirect. The manuscript should show the theoretical IPR for the specific probed mode (or a narrow frequency window around Ω = 0.018) so that the abruptness of the experimental transition is compared with the same quantity that is measured.","section":"Results, Fig. 3(f)"},{"comment":"The statement that \"the lossier set of skin modes is not observable in our present experiment [57]\" is a selection rule that is essential for interpreting the observed one-sided localization, and it is not justified in the main text. Since the model predicts a double-sided skin effect, the paper should specify in the main text why only the less-lossy set is expected to appear in the measured sidebands, rather than only citing the supplement.","section":"Results, paragraph after Fig. 2(c)"}],"minor_comments":[{"comment":"The abstract says the system \"does not contain unconventional asymmetric hopping nonlinearities,\" while the introduction says it \"does not rely on p-wave-like pairing interactions.\" These are different statements; the wording should be harmonized to avoid confusion about what is being contrasted with the bosonic Kitaev chain.","section":"Abstract and Introduction"},{"comment":"No error bars or repeated measurements are shown for the IPR and sideband-ratio data, making it difficult to assess whether the transition near 240 mV is statistically significant and abrupt.","section":"Fig. 3(f)"},{"comment":"The normalized sideband frequency Ω = (ω' - ωp)/ωp is introduced only in the caption of Fig. 3; it should be defined in the main text when the auxiliary drive is first described.","section":"Fig. 3 caption"},{"comment":"Reference [44] and reference [51] are the same paper (Y. Wang et al., Nature Communications 10, 1102 (2019)) and should be merged or cross-referenced once.","section":"References"},{"comment":"The slowly-varying envelope approximation is invoked without stating the required separation of time scales or the condition that g|ψ|^2 in the toy model is small. A brief statement of these validity conditions would help the reader judge when the BdG description is expected to hold.","section":"Eqs. (8)-(9)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of a physics journal and the central idea is attractive, but the review process should require the supplemental derivation to be available and should request the two missing controls (probe linearity and kp reversal) before publication. The duplicate reference [44]/[51] is a minor editorial issue that should be fixed. I would not reject the paper on the current evidence, but the load-bearing assumptions need to be tested."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper you asked about reports a switchable non-Hermitian skin effect in Bogoliubov sideband modes of a nonlinear transmission line. The new part is experimental: they build a 30-site RLC lattice with varactors, drive it with a fundamental tone at kp=2π/3, add a weak auxiliary probe, and see a sideband localize to one edge abruptly once the drive amplitude passes about 240 mV. The threshold is predicted from independently characterized circuit elements, not fit to the localization data, and the frequency window of strong localization matches the range where the BdG spectrum goes complex. That is a genuinely useful demonstration: switchable skin effect using only a local Kerr nonlinearity, without asymmetric hoppings or p-wave pairing.\n\nThe theoretical framework is not new—the two-site BdG toy model and the interaction-induced double-sided skin effect are in Refs. 17 and 18. The novelty is the circuit implementation and the drive-amplitude switching. For that, the experiment is clean and the main observations line up with theory.\n\nThe soft spots are real but addressable. The central claim depends on treating the measured sideband as a linear probe of BdG eigenmodes, but there is no data showing the spatial profile or IPR is independent of the auxiliary probe amplitude V'pp. If the varactor nonlinearity generates intermodulation products that grow near the threshold, the same abrupt IPR rise could occur without point-gap winding. Also, they never reverse the drive phase gradient kp → -kp. The theory predicts the localization direction should flip; without that control, a fixed right-localized response could in principle be an instrumental asymmetry. The existing data partly mitigate this: localization is absent below threshold and absent at Ω=0.058 above threshold, so a purely static asymmetry would need to be frequency- and drive-dependent. But the two controls are cheap and would close the gap.\n\nA further concern is that they only observe the lossier set of skin modes; the double-sided effect predicted by theory is not directly seen, and the observability selection is explained only in the supplement. Also, no error bars, no public data/code, and key derivations live in the supplement.\n\nOverall, this is a solid, worthwhile experiment with a load-bearing but plausible claim. It deserves serious peer review; a referee should ask for the probe-linearity check, a kp reversal, and the supplement details before acceptance. I would not desk-reject it.\n\nRecommendation: send to review, conditional on those additions.","headline":"A clean circuit demonstration of switchable NHSE in Bogoliubov sidebands with a predicted threshold that matches, though missing probe-linearity and kp-reversal controls that should be added in review.","tokens_in":10283,"tokens_out":4632,"would_cite":true,"duration_ms":38822,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A nonlinear driven-dissipative circuit shows an abruptly switchable non-Hermitian skin effect in Bogoliubov sideband modes above a drive-voltage threshold.","keywords":["non-Hermitian skin effect","Bogoliubov quasiparticles","nonlinear transmission line","pseudo-Hermiticity","point-gap topology","driving threshold","sideband modes","topological metamaterial"],"falsifier":"Measure the complex Bogoliubov band structure under periodic boundary conditions and check that the open-boundary localized modes are encircled by point-gap loops with winding ±1; absence of this winding would falsify the skin-effect interpretation.","tokens_in":9317,"feed_emoji":"⚡","tokens_out":6674,"duration_ms":55977,"temperature":0.7,"pith_summary":"The paper claims to show, in a nonlinear transmission-line circuit of 30 unit cells, that Bogoliubov sideband modes undergo a non-Hmitian skin effect that switches on abruptly when the fundamental driving voltage rises past about 240 mV. Below the threshold the sideband modes are extended; above it they localize to one edge of the lattice. The authors interpret the switch as spontaneous breaking of a pseudo-Hermitian symmetry in the Bogoliubov–de Gennes (BdG) Hamiltonian, which opens a point gap in the complex spectrum and produces winding-protected skin modes. They identify this as the first experimental switchable NHSE in Bogoliubov modes that requires only a local Kerr-type nonlinearity, without asymmetric hoppings or p-wave pairing interactions. If correct, the result makes the NHSE actively controllable by an external drive rather than a fixed property of a lattice.","feed_headline":"Bogoliubov sidebands localize once drive tops 240 mV","feed_subtitle":"A nonlinear transmission line abruptly switches from extended to edge-localized sideband modes near 240 mV.","key_machinery":"The central object is the Bogoliubov–de Gennes (BdG) Hamiltonian that governs fluctuations on a coherently driven fundamental mode. For an envelope ansatz consisting of a pump plus small sideband components, the equations of motion close into a non-Hermitian eigenproblem of the form $H(u,v)^T = \\omega_f (u,v)^T$, with $H$ written in terms of a driven-lattice Hamiltonian $H_u$ and a pairing block $H_v$ that is diagonal in the present circuit. $H$ obeys pseudo-Hermiticity ($\\Gamma_3 H \\Gamma_3 = H^\\dagger$) and, under open boundary conditions, non-Hermitian particle–hole symmetry; these symmetries force a quadruplet structure of eigenvalues and give a 'non-Hermitian particle/hole pinning' property ($\\|u\\|^2 = \\|v\\|^2$) for pseudo-Hermiticity-broken eigenstates. The load-bearing mechanism is the spontaneous breaking of pseudo-Hermiticity as the drive amplitude $V_\\mathrm{pp}$ crosses the threshold: below it all eigenvalues are real and there is no point gap; above it, complex eigenvalue quadruplets appear in a finite window of quasimomentum, the periodic-boundary spectrum forms point-gapped loops with winding $\\pm 1$, and the open-boundary modes become one-sided skin modes. The drive wavenumber $k_p = 2\\pi/3$ is what makes the effective hoppings nonreciprocal in the BdG description.","core_discovery":"On its own terms, the paper's central discovery is that a one-dimensional chain of driven nonlinear RLC resonators, with back-to-back varactors providing a local Kerr nonlinearity, hosts Bogoliubov quasiparticles described by a non-Hermitian BdG Hamiltonian, and that these quasiparticles exhibit the non-Hermitian skin effect (NHSE). The NHSE is switchable: for drive amplitudes below roughly 240 mV the BdG eigenfrequencies are almost all real and the sideband modes are delocalized; above that threshold pseudo-Hermiticity spontaneously breaks, the complex spectrum develops point-gap winding under periodic boundary conditions, and the open-boundary eigenmodes become exponentially localized to one side. Experimentally, the authors observe a sideband at the auxiliary probe frequency and its mirror peak, measure the spatial sideband profile, and show that the inverse participation ratio and the left-to-right sideband amplitude ratio jump sharply at the same threshold predicted by the model. They further show that the localized modes occur only in the frequency window where the BdG eigenvalues are complex, consistent with the theoretical spectrum. The mechanism does not rely on asymmetric inter-site hopping or p-wave pairing; the fundamental drive itself imparts the left–right asymmetry to the BdG Hamiltonian.","pith_inferences":["If the BdG linearization remains valid, the switchable skin effect could be exploited as a voltage-controlled topological switch, for routing or sensing in microwave circuits, with the threshold tunable by component parameters.","The requirement of only a local Kerr nonlinearity suggests that the same mechanism could be transferred to photonic or optomechanical platforms with Kerr nonlinearity and a phase-structured pump, potentially enabling dynamically reconfigurable non-Hermitian topological states.","A quantitative test that would distinguish the BdG mechanism from generic nonlinear response is to check the linear-response scaling of the localized sideband amplitude with the auxiliary probe amplitude; a true BdG eigenmode should show a region of linear scaling, while higher-harmonic generation would deviate.","The paper's claim implies that the complex point-gap winding, not the static lattice geometry, controls the localization direction; one could verify this by reversing the sign of $k_p$ (drive phase gradient) and observing the skin modes move to the opposite edge, which the paper does not report explicitly."],"forward_implications":["Raising the fundamental drive amplitude across the threshold switches the Bogoliubov sideband response from delocalized to edge-localized, giving an all-electrical on/off control of the skin effect.","The localization is frequency-selective: only sideband frequencies in the range $\\mathrm{Re}(\\Omega_f)$ where the BdG eigenvalues are non-real (about $\\Omega < 0.03$ in the experiment) show strong edge localization; other frequencies remain extended.","The same circuit can be used to probe pseudo-Hermiticity breaking directly through the sideband spectrum and the left–right sideband amplitude ratio, which acts as an experimental signature of the symmetry breaking.","Because the mechanism uses only a local Kerr nonlinearity and the phase pattern of the drive, similar switchable NHSEs should be realizable in other nonlinear lattices and metamaterials with local nonlinearities.","The lossier set of skin modes predicted by the double-sided skin effect is not observed in this experiment; since the model says these modes exist but are too lossy, they could be accessed in future setups with lower loss or gain."],"supporting_citations":[{"why":"Prior model of interaction-induced double-sided skin effect in an exciton-polariton Bogoliubov system, which this experiment extends to a circuit platform.","marker":"[18]"},{"why":"Provides the pseudo-Hermiticity and PT-symmetry framework used to explain the reality of the spectrum and its spontaneous breaking.","marker":"[20]"},{"why":"Defines point-gap topology and the non-Hermitian skin effect, the central topological signature identified in the experiment.","marker":"[25]"},{"why":"Supplies the connection between the non-Hermitian skin effect and topological invariants under open boundary conditions.","marker":"[30]"},{"why":"Earlier experimental realization of a bosonic Kitaev chain in optomechanics, a contrast showing the present work needs no nonlocal pairing.","marker":"[32]"},{"why":"Earlier superconducting-circuit realization of bosonic Kitaev chain, another contrast for the minimal local-nonlinearity mechanism.","marker":"[33]"},{"why":"Establishes generalized bulk–boundary correspondence in topolectrical circuits, the circuit-level foundation this experiment builds on.","marker":"[40]"},{"why":"Provides the quantitative correspondence between winding numbers and skin-mode localization used to identify the observed edge states.","marker":"[58]"}],"fun_headline_variants":["Drive past 240 mV flips Bogoliubov waves to edge states","Non-Hermitian skin effect switches on in Bogoliubov modes","Circuit's Bogoliubov modes localize above voltage threshold","Kerr nonlinearity enables switchable skin effect in sidebands"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the measured sideband signals are governed by the linearized Bogoliubov–de Gennes eigenproblem with the slowly-varying envelope ansatz, so that the abrupt localization above 240 mV is the predicted topological skin effect rather than a generic higher-harmonic or nonlinear response.","fun_headline_variants_meta":{"raw":{"variants":["Drive past 240 mV flips Bogoliubov waves to edge states","Non-Hermitian skin effect switches on in Bogoliubov modes","Circuit's Bogoliubov modes localize above voltage threshold","Kerr nonlinearity enables switchable skin effect in sidebands"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000507,"raw_usage":{"total_tokens":2487,"prompt_tokens":979,"completion_tokens":1508,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":595,"completion_tokens_details":{"reasoning_tokens":1441}},"tokens_in":595,"tokens_out":1508,"duration_ms":48229,"temperature":1.0,"reasoning_tokens":1441,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:49:29.889752+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the complex Bogoliubov band structure under periodic boundary conditions and check that the open-boundary localized modes are encircled by point-gap loops with winding ±1; absence of this winding would falsify the skin-effect interpretation.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior model of interaction-induced double-sided skin effect in an exciton-polariton Bogoliubov system, which this experiment extends to a circuit platform."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier experimental realization of a bosonic Kitaev chain in optomechanics, a contrast showing the present work needs no nonlocal pairing."},{"cited_title":"Helbig, T","cited_arxiv_id":null,"evidence_quote":"Establishes generalized bulk–boundary correspondence in topolectrical circuits, the circuit-level foundation this experiment builds on."}],"review_version":1}