{"id":"893337e8-dc58-4b3d-8227-db5e3322aa5c","arxiv_id":"2412.05215","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A trapped asymmetric dipolar Bose mixture in the double supersolid phase should show a doublet of compressional breathing modes, one per component, giving an experimental fingerprint of two coexisting superfluids.","lead":"Dipolar Bose mixtures can form a double supersolid where two superfluids share a crystal-like density modulation. This paper predicts that the double supersolid has two separate compressional breathing modes, one dominated by each component, which experiments can directly observe.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The predicted breathing doublet is demonstrated for one two-droplet parameter set, so the paper's general 'directly reveals two-fluid character' claim lacks support.","rationale":"I considered whether the two-component LHY term (Eqs. 3-4) is the most load-bearing weak point. It is a real quantitative uncertainty, but it would mainly shift frequencies, the doublet splitting, and the location of the incoherent transition. The qualitative three-mode structure and the doubling of the superfluid breathing modes follow from the U(1) x U(1) x translational symmetry breaking, so they are more robust than the precise numerical values. The 'directly reveals' claim is more fragile: it depends on the specific mode-composition result that each superfluid breathing mode is almost fully dominated by one component, and on the doublet being resolvable in an experimentally accessible response. That result is demonstrated for one two-droplet parameter set only. The reader's weakest assumption already noted the single-parameter coverage, but emphasized the LHY approximation more strongly; I would put the emphasis on the unestablished generality, because that is what converts a numerical observation into a universal experimental marker. The conditional verdict already captures the needed restriction, so I would leave it unchanged. No claim is made here about author behavior; the concern is entirely about the evidence supporting the generality claim.","tokens_in":61359,"tokens_out":14844,"duration_ms":167341,"concrete_test":"Repeat the BdG and compressional-response analysis for additional asymmetric configurations at the same trap: (i) µ2 = 9.5 µB, (ii) µ2 = 8 µB, and (iii) N1/N = 0.4, plus a three-droplet case obtained by adjusting a12 or the trap aspect ratio; in each case extract the two softened superfluid modes and their P values, and check whether each mode still has |P| > 0.9 and whether the two peaks remain separately resolved in the S̄(ω) spectrum for both components.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central experimental prediction is that in a double supersolid the compressional response shows two superfluid modes, each almost fully dominated by one component, and that this 'would generally be a clear proof' of the two-fluid character. The support for this is Fig. 3, which is computed for a single configuration: equal populations of two 162Dy components with µ1 = 10 µB, µ2 = 9 µB, a11 = a22 = 100 a0, a two-droplet ground state, and one trap geometry. The text asserts that the results are 'to a large extend representative of other asymmetric mixtures,' but no second asymmetry, population imbalance, droplet number, or trap geometry is shown. This matters because the mode labels P and Q are strong functions of a12 near the transition, and because in the symmetric limit the x2 perturbation is exactly orthogonal to the spin superfluid mode, so the doublet is not generic by symmetry: it emerges from the particular degree of spin-density hybridization. If the near-single-component dominance (|P| near 1) is specific to this parameter set, the proposed protocol does not 'directly reveal' two-fluid behavior in other asymmetric dipolar mixtures.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the low-lying excitation spectrum of a trapped miscible dipolar Bose mixture using the two-component extended Gross-Pitaevskii equations with a Lee-Huang-Yang correction and the associated Bogoliubov-de Gennes equations. It focuses on an asymmetric mixture of two 162Dy components with different dipole moments (µ1=10µB, µ2=9µB), equal intra-species scattering lengths, equal populations, and a fixed three-dimensional harmonic trap. The authors introduce diagnostics P, Q, ησ, and λσ to characterize the component weight, density/spin character, and phase-fluctuation strength of each mode. Their central results are that the asymmetric double supersolid displays a three-mode low-lying structure (in-phase dipole, out-of-phase spin dipole, and a supersolid Goldstone mode), and that axial compressional excitations produce a doublet of superfluid breathing modes, each almost fully dominated by one component. The paper also identifies spectral signatures of the transition in which one component becomes an incoherent droplet array while the other remains superfluid.","tokens_in":61592,"tokens_out":8355,"duration_ms":84235,"significance":"If the numerical results are correct, the paper offers an experimentally accessible signature of the double-supersolid phase and of component-dependent superfluid fractions in dipolar mixtures: the compressional-response doublet shown in Fig. 6. The study uses physical input parameters (scattering lengths, dipole moments, trap frequencies, and particle number) with no parameters fitted to the output, and the predicted three-mode structure is falsifiable with existing experimental techniques. The mode-character diagnostics P, Q, ησ, and λσ are a useful extension of tools developed for single-component dipolar supersolids. The main limitations are the reliance on the approximate two-component LHY functional and the fact that the central prediction is demonstrated for a single two-droplet parameter set; neither limitation is internally inconsistent, but together they bound the strength of the paper's generality claims.","major_comments":[{"comment":"The central claim that the compressional doublet 'would generally be a clear proof' of the two-fluid character of the double supersolid is supported by exactly one parameter set: µ1=10µB, µ2=9µB, a11=a22=100a0, N1=N2=N/2, and one fixed trap geometry with a two-droplet ground state. The text in Sec. VI states that the results 'are to a large extend representative of other asymmetric mixtures,' and Sec. VII repeats the generality claim while acknowledging the restriction to two-droplet supersolids 'due to numerical complexity.' This generality is not demonstrated. Section V shows that in the symmetric limit the x2 perturbation is exactly orthogonal to the spin superfluid mode, so the appearance of two compressional superfluid modes is not symmetry-enforced; it depends on the degree of spin-density hybridization, which is parameter dependent, as the strong variation of P with a12 in Fig. 3 indicates. Please either add calculations for at least one additional asymmetry, population imbalance, droplet number, or trap geometry, or explicitly restrict the central prediction to the demonstrated regime.","section":"Sec. VI, Figs. 3 and 6; Sec. VII"},{"comment":"The quantitative predictions, including the breathing-doublet frequencies, the mode-softening locations, and the value a12≈65–70a0 for the onset of the incoherent-droplet transition, are presented without any numerical methods or convergence checks. The manuscript does not specify the computational grid or box size, the imaginary-time or relaxation scheme used to obtain the ground states, the basis or eigensolver used for the BdG matrix in Eqs. (6)–(8), the number of retained modes, or tests showing that the frequencies and the diagnostics P, Q, ησ, and λσ are converged with respect to these choices. No code or data are provided. Without this information the numbers in Figs. 3, 6, and 7 cannot be independently assessed, and the claimed agreement at the transition cannot be verified.","section":"Secs. IV and VI"},{"comment":"The phase diagram is constructed using ad hoc density-contrast thresholds, C1=0.99 and C2=0.1 and 0.99, and no sensitivity analysis is reported. The later assignment of the double-supersolid to ID-supersolid transition at a12≈65–70a0 (Sec. VI.D, Fig. 7) is described as being in 'very good agreement' with the contrast-based phase boundary, but that comparison is only meaningful if the boundary does not shift appreciably with the chosen thresholds. Please quantify the threshold dependence or provide an independent phase criterion for the spectral identification.","section":"Sec. III, Fig. 1; Sec. VI.D"}],"minor_comments":[{"comment":"The submitted manuscript text contains extensive extraneous material on 'Topological hole localization in binary Bose mixtures in spin-dependent ladders' interleaved with the main text, together with repeated garbled equations and figure captions. This must be removed and all figures reproduced cleanly; as submitted, it prevents a reliable check of the displayed results.","section":"Throughout, especially Secs. V–VI and Figs. 2–5"},{"comment":"The notation ̃μσ is introduced for the chemical potential obtained from the ground-state calculation, but the tilde is not used consistently elsewhere in the paper; please unify the notation.","section":"Eq. (7)"},{"comment":"In the discussion of Fig. 6, it would be helpful to state explicitly how the separate response spectra for the two components are normalized and whether the relative heights in the two panels can be compared quantitatively, given the description that each S̄(ω) is normalized to the maximum value in either component.","section":"Sec. VI.C"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the submitted manuscript appears to contain substantial unrelated material ('Topological hole localization in binary Bose mixtures in spin-dependent ladders') and repeated corrupted passages, particularly around Secs. V–VI and the figures. I reviewed the legible scientific content, but the authors should be asked to provide a clean manuscript. There is also no code/data deposit or numerical convergence documentation; if the journal encourages reproducibility, this should be requested. The central physics is plausible and the paper is potentially suitable after a revision that addresses the generality and numerical-detail concerns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The paper is a competent numerical study of the trapped excitation spectrum of a miscible dipolar double supersolid, and it delivers a genuinely testable prediction: in an asymmetric mixture, the two superfluid breathing modes become almost single-component, so a simple axial compression should reveal a doublet and, with it, the disparate superfluid fractions. The second thing: the generality claim is wider than the evidence. Everything in the asymmetric analysis comes from one parameter set—equal populations of two 162Dy components with mu1=10 muB, mu2=9 muB, a11=a22=100 a0, one trap, two droplets—so the 'clear proof' sentence in the conclusions is not established.\n\nWhat is actually new: the trapped discrete spectrum of a miscible double supersolid, including the spin-hybridized rotons, the component-dominated breathing doublet, and the lowest-mode marker for the one-component incoherent transition. The methods are standard eGPE plus BdG plus compressional response, but the observables are new and the parameters are stated physical inputs, not fitted. The circularity burden is low; the doublet is a falsifiable consequence of the model. The symmetric-limit decoupling is handled cleanly, and connecting the lower-frequency component-1-dominated mode to lower superfluid fraction via Leggett's bound is a sensible interpretation.\n\nSoft spots, in order. First and largest: the central 'representative of other asymmetric mixtures' claim is backed by one two-droplet configuration. In the symmetric limit the x2 perturbation is orthogonal to the spin superfluid mode, so the doublet is not symmetry-protected; it emerges from the particular degree of spin-density hybridization. A second parameter set—say a population imbalance or a different trap aspect ratio—would go a long way. This is a limitation, not a fatal flaw; the prediction still stands for the case shown. Second: no code, data, or convergence checks, and the two-component LHY term is itself the main quantitative uncertainty; frequencies and the a12 around 65-70 a0 transition could shift. Minor but present. Third: the arXiv text is corrupted—an unrelated appended paper, repeated blocks, equation typos. That should be fixed before publication.\n\nWho it's for: the dipolar quantum-gas community, especially experimental groups doing compression spectroscopy on mixtures. It deserves a serious referee; the predictions are concrete and the framework is established. I would send it to review with a request for one more parameter scan and a clean manuscript. I'd cite it if I were writing on dipolar mixture spectra.","headline":"A testable prediction—the compressional doublet—in a solid numerical study, but the generality claim rests on one parameter set and the manuscript needs cleanup.","tokens_in":62072,"tokens_out":2519,"would_cite":true,"duration_ms":27048,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.75.Kk","03.75.Mn","67.85.-d"],"model":"deepseek-v4-flash","headline":"In the double-supersolid phase of a trapped dipolar Bose mixture, axial compression should split the superfluid breathing response into two single-component peaks, directly revealing two coexisting superfluids with different superfluid…","keywords":["dipolar Bose mixtures","double supersolid","Bogoliubov-de Gennes equations","collective excitations","breathing modes","superfluid fraction","incoherent droplet regime"],"falsifier":"Measure the component-resolved axial compressional response of an asymmetric dipolar mixture in the double-supersolid regime: the claim requires two distinct superfluid breathing peaks with $P\\simeq\\pm1$ (each carried by one component) and the lower-frequency peak belonging to the more contrasted component. Observing comparable component weights in both peaks, a single unsplit peak, or the lower-frequency peak belonging to the less contrasted component would contradict the central prediction. The predicted location of the single-component incoherent transition ($a_{12}\\simeq65$–$70\\,a_0$ from $\\lambda_1/\\eta_1\\to0$) can likewise be checked against the measured phase coherence between the two central droplets.","tokens_in":61165,"feed_emoji":"🧲","tokens_out":10940,"duration_ms":102460,"temperature":0.7,"pith_summary":"The paper predicts a distinctive fingerprint for the double-supersolid phase of a trapped, miscible dipolar Bose mixture: the low-lying excitation spectrum rearranges into a three-mode structure in which the compressional (breathing) response splits into two superfluid modes, each carried almost entirely by one of the two components. Because a simple axial compression excites both modes, measuring that response would directly reveal that two interacting superfluids coexist and that their superfluid fractions differ markedly. The same spectra also show the roton, Higgs, and Goldstone modes acquiring a strong density-spin hybridization in an asymmetric mixture, and they let one watch a single component cross into the incoherent droplet regime while the other remains superfluid.","feed_headline":"Compression splits breathing modes into two superfluid peaks","feed_subtitle":"Each peak belongs to one component, so a single measurement reads both superfluid fractions.","key_machinery":"The argument is carried by the extended Gross-Pitaevskii equations for the two components, which include the two-component Lee-Huang-Yang energy density from quantum fluctuations, together with their linearization into Bogoliubov-de Gennes equations. Each eigenmode is then classified by two observables: $Q$, the relative weight of total-density versus spin (relative-density) modulation, and $P$, the relative contribution of each component, with $P=1$ ($P=-1$) marking a mode of only component 1 (2). The phase-fluctuation strengths $\\eta_\\sigma$ and $\\lambda_\\sigma$ further detect the supersolid-to-droplet crossover, since a component entering the incoherent droplet regime develops phase variations confined between droplets, so $\\lambda_\\sigma/\\eta_\\sigma$ approaches zero. The doublet claim follows from applying an equal $x^2$ compression to both components and computing the normalized response $\\bar S(\\omega)$ separately for each component; the interpretation of the lower-energy peak as the lower superfluid fraction relies on a cited upper bound on superfluid fraction.","core_discovery":"On its own terms, the paper establishes that for a miscible mixture of two dipolar condensates with unequal dipole moments (illustrated by $^{162}\\mathrm{Dy}$ components with $\\mu_1 = 10\\,\\mu_B$ and $\\mu_2 = 9\\,\\mu_B$), reducing the interspecies scattering length $a_{12}$ drives the system into a two-droplet double supersolid. In that phase the two gapless Goldstone modes of the unmodulated mixture plus the softened roton reorganize into a triplet: an in-phase dipole mode at $\\omega_x$, an out-of-phase dipole mode, and a supersolid Goldstone mode with strong spin-density hybridization and a dominant weight in the more dipolar component. The axial breathing response doubles: the hardening crystal mode is roughly equally shared, while the two softer superfluid modes become almost pure single-component modes, with the lower-energy mode dominated by the more contrasted component, which has the lower superfluid fraction. The paper further shows that the lowest mode's phase-fluctuation ratio $\\lambda_1/\\eta_1$ collapsing toward zero marks the transition of only component 1 into the incoherent droplet regime, leaving component 2 superfluid.","pith_inferences":["Beyond the paper, if the doublet splitting scales monotonically with the asymmetry between components (dipole moments, populations, or intraspecies scattering lengths), the same compressional measurement could serve as a quantitative two-fluid probe of superfluid-fraction differences well beyond the specific $10\\mu_B/9\\mu_B$ case studied here.","Beyond the paper, the near-single-component character of each superfluid breathing mode suggests a sum-rule picture in which the compressional response decomposes into two nearly independent one-component oscillator strengths; checking the measured peak weights against the relative particle numbers would test whether the single-component dominance is exact or only approximate.","Beyond the paper, the same $Q$, $P$, $\\eta_\\sigma$, $\\lambda_\\sigma$ classification could be exported to immiscible double supersolids or dipolar-non-dipolar mixtures, where spin-density hybridization is expected to be even stronger and where the three-mode structure may leave a different experimental signature.","Beyond the paper, since the halo decoupling appears as an abrupt hardening and disappearance of one breathing peak from $\\bar S(\\omega)$, time-resolved measurements after a quench of $a_{12}$ could reveal the dynamics of the incoherent transition rather than only its static signature."],"forward_implications":["In the double-supersolid regime, an axial compression applied equally to both components should produce two distinct superfluid breathing peaks in $\\bar S(\\omega)$, one dominated by component 1 and one by component 2.","Comparing the two peak energies gives a direct, component-resolved ordering of superfluid fractions: the more contrasted (more dipolar) component carries the lower-energy mode and the lower superfluid fraction.","Tracking the lowest mode's phase-fluctuation ratio $\\lambda_1/\\eta_1$ should reveal the onset of the incoherent droplet regime for only one component, with halo decoupling near $a_{12}\\simeq70\\,a_0$ and droplet decoherence near $a_{12}\\simeq65\\,a_0$.","A symmetric mixture hides this physics because the compressional perturbation couples only to density modes; the doublet is therefore a probe specific to asymmetric mixtures.","In the ID-supersolid regime the low-lying spectrum reduces to a two-mode structure, mirroring the two Goldstone modes expected when only one component remains superfluid."],"supporting_citations":[{"why":"It supplies the extended Gross-Pitaevskii equations with the two-component Lee-Huang-Yang energy density used for all ground states and excitation spectra.","marker":"[23, 31]"},{"why":"It provides the miscible-mixture ground-state phases and the catalyzation effect used to explain why the rotons are dominated by the more dipolar component.","marker":"[30]"},{"why":"It gives the general counting of gapless Goldstone modes for spontaneously broken symmetries, yielding three modes for the double supersolid.","marker":"[19]"},{"why":"It computes the excitation spectrum of an infinite-tube dipolar mixture, the idealized three-mode structure against which the trapped spectrum is interpreted.","marker":"[29]"},{"why":"It reports the experimental axial compressional excitation method in a dipolar supersolid that the paper adapts to probe the breathing response.","marker":"[16]"},{"why":"It demonstrates the two-frequency compressional response at the single-component supersolid transition, the experimental baseline for the predicted doublet.","marker":"[17]"},{"why":"It shows the roton-Higgs-Goldstone mode evolution across the single-component supersolid transition used to interpret the mixture modes.","marker":"[18]"},{"why":"It supplies the upper bound on the superfluid fraction used to associate the lower-energy breathing mode with the lower superfluid fraction.","marker":"[33]"}],"fun_headline_variants":["Breathing modes reveal two superfluid fractions in dipolar mixture","Double supersolid: single probe reads both components' superfluid","Dipolar supersolid splits breathing mode by component","Two compressional modes expose disparate superfluid characters"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central prediction stands on the extended Gross-Pitaevskii equations with the two-component Lee-Huang-Yang quantum-fluctuation term being quantitatively accurate at the droplet densities of this strongly dipolar mixture, including the coherence of the droplet halo near the incoherent transition.","fun_headline_variants_meta":{"raw":{"variants":["Breathing modes reveal two superfluid fractions in dipolar mixture","Double supersolid: single probe reads both components' superfluid","Dipolar supersolid splits breathing mode by component","Two compressional modes expose disparate superfluid characters"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000629,"raw_usage":{"total_tokens":2913,"prompt_tokens":954,"completion_tokens":1959,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":570,"completion_tokens_details":{"reasoning_tokens":1894}},"tokens_in":570,"tokens_out":1959,"duration_ms":13505,"temperature":1.0,"reasoning_tokens":1894,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:49:42.085718+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the component-resolved axial compressional response of an asymmetric dipolar mixture in the double-supersolid regime: the claim requires two distinct superfluid breathing peaks with $P\\simeq\\pm1$ (each carried by one component) and the lower-frequency peak belonging to the more contrasted component. Observing comparable component weights in both peaks, a single unsplit peak, or the lower-frequency peak belonging to the less contrasted component would contradict the central prediction. The predicted location of the single-component incoherent transition ($a_{12}\\simeq65$–$70\\,a_0$ from $\\lambda_1/\\eta_1\\to0$) can likewise be checked against the measured phase coherence between the two central droplets.","supporting_citations":[{"cited_title":"Scheiermann, L","cited_arxiv_id":null,"evidence_quote":"It provides the miscible-mixture ground-state phases and the catalyzation effect used to explain why the rotons are dominated by the more dipolar component."},{"cited_title":"Watanabe and T","cited_arxiv_id":null,"evidence_quote":"It gives the general counting of gapless Goldstone modes for spontaneously broken symmetries, yielding three modes for the double supersolid."},{"cited_title":"Hertkorn, F","cited_arxiv_id":null,"evidence_quote":"It shows the roton-Higgs-Goldstone mode evolution across the single-component supersolid transition used to interpret the mixture modes."}],"review_version":1}