{"id":"c0d91dff-c077-427a-b483-f73d356533f1","arxiv_id":"2608.04082","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For a few bosons in a ring with two weak links, strong interactions make the many-body quantum Fisher information at zero rotation nonzero and large, improving slow-rotation sensing beyond the Bose-Hubbard prediction.","lead":"A numerical study of a few strongly interacting atoms in a ring trap shows that the sensitivity to slow rotation is not degraded, but enhanced, by strong interactions, contrary to the standard two-mode model. The many-body quantum Fisher information at zero rotation stays finite, which could make miniaturized atom-based gyroscopes more practical.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract's 'maximal for large interaction couplings' is contradicted by the paper's own Fig. 4(b) for N=4 and N=6, where QFI peaks at intermediate coupling and then falls.","rationale":"The reader's weakest assumption (basis convergence for N=4,6) is real and worth testing, but the more direct threat to the paper's central claim is that the abstract's headline sentence is not what the reported data show. The manuscript's own text and End Matter describe an intermediate maximum followed by a steep decrease for N=4 and N=6, so the claim 'maximal for large interaction couplings' is internally inconsistent with the presented results. I therefore focus the stress test on that contradiction, while noting that the missing M-scan compounds it: the QFI depends on orbital derivatives through Eq. (15), so basis truncation affects exactly the peak region. The N=2 M=2 vs M=24 comparison provides independent support that the qualitative effect is not a small-basis artifact for two particles, but it does not cover the small-N cases that the abstract generalizes to. In good faith, I do not see reason to accuse the authors of using the uncorrected QFI formula from Ref. [68]; footnote [83] acknowledges the omitted term and Eq. (15) includes it, so the remaining issue is that implementation of the corrected formula is not explicitly confirmed for the reported data. If the authors qualify the abstract to 'intermediate, N-dependent optimal coupling' and supply the M-scan, the remaining scientific content—self-consistent many-body treatment yields nonzero, interaction-enhanced QFI at Ω=0, unlike fixed-orbital Bose-Hubbard—remains plausible and interesting. Hence the verdict stays CONDITIONAL, unchanged from the reader.","tokens_in":13342,"tokens_out":7691,"duration_ms":77090,"concrete_test":"Recompute F_Q(Ω=0) for N=4 at V0/Er=8 and N=6 at V0/Er=11.2 for λ = 0.01, 0.1, 1, 10 using M=12 and M=24. Determine λ_max and compare F_Q(λ_max) with F_Q(10); if F_Q(10) < F_Q(λ_max), the abstract's 'maximal for large interaction couplings' is false. The same run provides the missing M-scan: if the peak height or position shifts by more than about 5% between M=12 and M=24, the reported curves are not converged.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim as stated in the abstract—'the many-body quantum Fisher information becomes maximal for large interaction couplings'—is contradicted by the paper's own numerical results for N=4 and N=6. In the main text (Section 'Criticality-enhanced QFI', Fig. 4(b)) the authors write that 'for both N=4 and N=6, the maximal QFI is obtained at an intermediate interaction strength (close to the fermionization crossover), which is larger for deeper lattices V0/Er'; End Matter B adds that when the occupation entropy saturates to ln4/ln6 in the fermionized limit, the QFI shows a 'steep decrease'. Thus the QFI-vs-λ curves for the small-N cases in Fig. 4(b) are non-monotonic: they rise to a peak at intermediate coupling and decline at large coupling. Only the N=2 case (Fig. 4(a)) saturates at large λ. The abstract's 'both small rotation velocities and small particle numbers' and 'maximal for large interaction couplings' therefore overstates the paper's own finding. This is an internal inconsistency in the headline claim, not a disagreement with external consensus. The peak location is also precisely where the QFI is most sensitive to the orbital-derivative terms in Eq. (15), and the paper provides no M-convergence scan for N=4,6 (M=12,18 are asserted 'to reach convergence' in the Fig. 4 caption), so the quantitative support for the corrected claim is not yet fully established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the quantum Fisher information (QFI) for estimating the rotation rate Ω of a few strongly interacting bosons (N=2, 4, 6) in a quasi-one-dimensional ring trap with two weak links. The authors derive the two-site Bose-Hubbard limit analytically, showing that the QFI there decays as λ1D^{-2}, then compute the full many-body QFI with the multiconfigurational time-dependent Hartree method (MCTDH), including orbital-derivative contributions to the QFI. The central reported results are that the self-consistent many-body treatment yields a finite QFI at zero rotation, that for N=2 the QFI at Ω=0 grows and saturates with interaction strength, and that for N=4 and N=6 the QFI at Ω=0 reaches a maximum at an intermediate interaction strength near the fermionization crossover and then decreases. The paper concludes that strong interactions can enhance rotation sensitivity at small rotation rates, contrary to the Bose-Hubbard two-mode prediction.","tokens_in":13579,"tokens_out":6715,"duration_ms":71421,"significance":"If the corrected version of the claim holds, the paper is significant: it challenges the usual expectation that interactions always degrade interferometric rotation sensitivity, provides a concrete few-atom parameter regime where the opposite occurs, and demonstrates that self-consistently determined orbital shapes materially change the metrological prediction. The manuscript has clear strengths: an exact analytical Bose-Hubbard limit, a variational many-body method that explicitly includes orbital-derivative terms in the QFI, a convergence check for N=2 with M=2 versus M=24 orbitals, and a falsifiable prediction of an optimal intermediate coupling for N=4 and N=6. The main weakness is that the abstract and conclusion overstate the result for N>2, and the numerical convergence for N=4 and N=6 is asserted rather than demonstrated.","major_comments":[{"comment":"The abstract states that 'For both small rotation velocities and small particle numbers, the many-body quantum Fisher information becomes maximal for large interaction couplings.' This is contradicted by the paper's own Fig. 4(b) and by End Matter B: for N=4 and N=6, F_Q(Ω=0) peaks at an intermediate λ1D close to the fermionization crossover and then decreases steeply as the occupation entropy saturates to ln4 or ln6, while only the N=2 case saturates at large λ. The conclusion's sentence that 'increasing the interaction coupling enhances for small rotation rates the ultimate quantum sensitivity' is therefore also only valid up to the coupling optimum for N>2. Please revise the abstract and conclusion to state the N-dependent behavior explicitly: monotonic increase for N=2, non-monotonic with an optimal intermediate coupling for N=4 and N=6.","section":"Abstract; Conclusion; Fig. 4(b)"},{"comment":"The caption of Fig. 4(b) states that M=12 (N=4) and M=18 (N=6) orbitals were used 'to reach convergence,' but no systematic M-scan or numerical error estimate is presented. The central claim that the optimal interaction strength is intermediate, and that the QFI decreases in the fermionized limit, depends on the location and height of the QFI peak and on the magnitude of the large-λ decrease. These quantities are particularly sensitive to the orbital-derivative terms in Eq. (15), which are the terms most affected by the truncation of the orbital space. The manuscript should provide, at minimum, M-scans for one representative N=4 curve and one representative N=6 curve, including the peak region and the largest λ1D shown, with convergence indicators for F_Q, S_occ, and |g^(1)_LR|.","section":"Fig. 4 caption; Section A of the End Matter"},{"comment":"The sentence 'When γ is increased, the QFI peak height increases and is shifted towards shallower lattice depths' is difficult to verify from Fig. 4(b), where the horizontal axis is λ1D for fixed values of V0/Er. From the displayed data, the peak shifts to larger λ1D as the lattice depth increases, which is a different statement. Please clarify whether this sentence refers to the QFI as a function of V0/Er at fixed γ (as in Fig. 4(a)) or to the λ1D-axis of Fig. 4(b), and adjust the wording to match the figure.","section":"Criticality-enhanced QFI; Fig. 4(b)"}],"minor_comments":[{"comment":"The notation 'F_Q(Ω→0)=O(Ω0^2)' appears dimensionally inconsistent with Eq. (6), where the prefactor is (2π/Ω0)^2, and with the QFI having dimensions of 1/Ω^2 if Ω0 is an angular frequency unit. This is likely a typo for O(Ω0^{-2}); please correct or explain the intended scaling.","section":"Conclusion"},{"comment":"The vertical axis label in Fig. 2 is rendered as 'FQ­2 0', which is ambiguous. It should read F_Q/Ω0^2 or F_Q Ω0^2, depending on the normalization convention, and the same convention should be used consistently in Figs. 2, 3, and 4.","section":"Fig. 2 axis label"},{"comment":"The statement that the QFI shows a 'steep decrease' as S_occ saturates to ln4/ln6 should be quantified, since only a few data points are visible in Fig. 4(b) at the largest couplings; a brief numerical value or a fitted trend would make the claimed decrease more transparent.","section":"End Matter B"},{"comment":"The sentence 'This work was still supported by the NRF of Korea...' contains an unusual use of 'still'; consider rephrasing to 'This work was supported by...'.","section":"Funding statement"}],"recommendation":"major_revision","confidential_remarks":"The paper's main issue is an overbroad abstract and conclusion, not a flawed central calculation; the correction is feasible within the manuscript's scope. The convergence evidence for N=4 and N=6 needs to be made quantitative, but the qualitative claim of a non-monotonic QFI with an optimal intermediate coupling is already supported by the structure shown in Fig. 4(b) and End Matter B. I would not recommend rejection, but the headline claim must be revised before the paper can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a real result worth reading, but the abstract overstates it. The core finding is that for N=2 bosons in a ring with two weak links, the many-body QFI at zero rotation is nonzero and grows with interaction strength, saturating at large coupling, which directly contradicts the fixed-orbital Bose-Hubbard prediction of zero. That contrast is the genuinely new piece, and the N=2 case is backed by an explicit M=2 vs M=24 convergence check plus an analytic BH limit that checks out.\n\nWhat the paper does well: it frames rotation sensing as Hamiltonian parameter estimation, computes the QFI from self-consistent MCTDH orbitals rather than assuming fixed Wannier functions, and shows the orbital response matters. The demonstration that the BH model underestimates the QFI and misses the Omega=0 response is convincing. The finite-size precursor of the superfluid-to-Mott transition as a QFI-enhancement mechanism is a nice observation, and the connection to occupation entropy for fermionization is suggestive.\n\nSoft spots: the abstract says 'for both small rotation velocities and small particle numbers, the many-body QFI becomes maximal for large interaction couplings.' That is accurate for N=2 but not for N=4 and N=6: Fig. 4(b) shows QFI peaking at intermediate coupling and then decreasing as the system fermionizes. The main text and End Matter B actually say this, so the abstract overgeneralizes and should be qualified. Second, the N=4 and N=6 results rest on M=12 and M=18 orbitals, but the paper gives no systematic M-scan or error estimates. For a quantity as sensitive as QFI, especially near the peak, this is a meaningful gap; the assertion that these values 'reach convergence' is not backed by data. Third, footnote [83] notes a correction to the QFI formula used in the authors' prior work; they do not quantify how much that changes the present curves. That is a transparency issue, not necessarily a fatal one.\n\nThe citation pattern is fine; heavy self-citation is justified because the MCTDH-QFI framework is theirs and the prior work is directly relevant. No code or data is shipped, which limits reproducibility.\n\nBottom line: this deserves a serious referee. It is a new numerical prediction with a clear physical message, and the N=2 result appears solid. But I would not let the abstract stand as is. Ask for a qualified abstract, a convergence study for N=4,6, and a statement on the QFI correction. If those come back, this could be a solid paper.","headline":"The N=2 result is solid and new, but the abstract overgeneralizes it to N=4 and N=6, and the convergence evidence for those cases is missing.","tokens_in":14176,"tokens_out":3086,"would_cite":true,"duration_ms":28359,"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":"For a few strongly interacting bosons in a ring, the quantum Fisher information for rotation stays finite at zero rotation and grows with interaction strength, a self-consistent many-body calculation shows.","keywords":["quantum Fisher information","rotation sensing","ultracold bosons","ring trap","strong interactions","MCTDH","superfluid-Mott transition","quantum metrology"],"falsifier":"Recompute the QFI at $\\Omega=0$ for $N=4$ and $N=6$ with successively larger orbital numbers (for example $M=16,24,32$ for $N=4$ and $M=24,32,48$ for $N=6$) at the interaction strengths where the peaks appear in Fig. 4(b), and check whether the peak height and location remain unchanged; alternatively, diagonalize the few-body problem exactly for $N=4$ in the same trap and compare the resulting QFI at $\\Omega=0$ with the MCTDH value.","tokens_in":13069,"feed_emoji":"🌀","tokens_out":10636,"duration_ms":98696,"temperature":0.7,"pith_summary":"This paper proposes that strong repulsive interactions, usually considered a nuisance for atom interferometers, can be turned into a resource for rotation sensing. The authors consider a few bosons trapped on a quasi-one-dimensional ring with two weak links and estimate the rotation rate from the ground state, using the quantum Fisher information as the ultimate precision bound. Their self-consistent many-body calculation shows that the quantum Fisher information at zero rotation rate stays finite and even grows with interaction strength, contradicting the fixed-orbital two-mode and mean-field models in which it vanishes. If the result holds, miniaturized few-atom gyroscopes could detect slow rotations with high spatial resolution, and the optimal operating point is near the superfluid-to-Mott-insulator transition.","feed_headline":"Interactions boost ultimate precision of a few-atom gyroscope","feed_subtitle":"Self-consistent many-body calculation finds rotation information survives at rest, contrary to mean-field models.","key_machinery":"The central object is the self-consistently determined many-body wavefunction of the multi-configurational time-dependent Hartree (MCTDH) method, in which both the orbitals and their Fock-space occupation coefficients are varied together. The argument is carried by a decomposition of the quantum Fisher information into coefficient, cross, and orbital contributions, given in Eqs. (14) and (15). The orbital term, which describes how the single-particle orbitals themselves depend on $\\Omega$, is absent in fixed-orbital two-mode Bose-Hubbard treatments and is exactly what produces the finite QFI at $\\Omega=0$ as well as its enhancement with interaction strength. A superimposed two-site lattice potential $V_0\\cos^2\\theta$ creates the two weak links, and tuning $V_0$ sweeps the system across the superfluid-to-Mott-insulator transition, where the QFI at $\\Omega=0$ peaks.","core_discovery":"The central claim is that the many-body quantum Fisher information $F_Q$ for estimating the rotation rate $\\Omega$ of a few strongly interacting bosons in a ring trap with two weak links is not degraded by interactions, but instead becomes maximal for large interaction couplings when rotation velocities and particle numbers are small. In particular, the quantum Fisher information at vanishing rotation rate remains finite, $F_Q(\\Omega\\to 0)=O(\\Omega_0^2)$, a genuine many-body effect that arises because the single-particle orbitals of the self-consistent MCTDH solution respond to $\\Omega$ even where the occupation statistics do not change. The authors find that $F_Q(\\Omega=0)$ rises with the coupling $\\lambda_{1D}$ and saturates for $N=2$, while for $N=4$ and $N=6$ it peaks near the fermionization crossover before decreasing; the peak height is larger for deeper lattices. They further show that for large enough coupling the sensitivity is higher for smaller particle numbers, and that the maximum QFI is reached near the superfluid-to-Mott-insulator transition in lattice depth.","pith_inferences":["If the orbital-response mechanism is generic, then for any Hamiltonian parameter that deforms the trap or the orbitals—such as a gravity tilt, a lattice-depth change, or a field gradient—the QFI at zero parameter value should remain finite; this could extend the approach beyond rotation to other single-parameter estimation tasks.","The non-monotonic behavior of the QFI with $\\lambda_{1D}$ for $N=4$ and $N=6$ suggests the fermionization crossover itself is a resource: an experiment could tune the interaction to the peak and use the occupation entropy as a proxy for the optimal operating point.","Following the paper's cited comparison between classical and quantum Fisher information for particle-distribution readout, a quantum gas microscope measurement of the two-site occupation statistics should nearly saturate the predicted QFI for rotation, giving a practical readout for few-atom sensors.","An immediate test of the predicted small-$N$ advantage would compare $N=2$, $4$, and $6$ sensors at fixed lattice depth and strong coupling; if the trend reverses for larger $N$, the benefit is confined to the few-atom regime studied here."],"forward_implications":["If the central claim holds, ultracold boson rotation sensors should be operated at strong coupling: increasing $\\lambda_{1D}$ improves the ultimate sensitivity to slow rotations instead of degrading it through phase diffusion.","The finite QFI at $\\Omega=0$ means the ground state at rest already carries rotation information, so slow rotations can be estimated without first engineering an entangled or interferometric input state.","Because the sensitivity at large coupling is higher for smaller $N$, few-atom rings become viable metrological devices, and arrays of such rings could map inhomogeneous rotation fields with high spatial resolution.","The QFI maximum sits near the superfluid-to-Mott-insulator crossover, so tuning the lattice depth $V_0$ to this transition provides an operational recipe for optimal sensitivity.","Models with fixed orbitals, such as the Bose-Hubbard and mean-field descriptions, systematically underestimate the QFI and incorrectly predict zero sensitivity at $\\Omega=0$; including the orbital response is necessary for correct predictions."],"supporting_citations":[{"why":"Supplies the framework for computing the many-body QFI self-consistently from MCTDH orbitals and Fock-space coefficients; the present paper corrects a term in its QFI expression.","marker":"[68]"},{"why":"Provides the multiconfigurational time-dependent Hartree method for bosons that yields the self-consistent orbitals used throughout.","marker":"[62]"},{"why":"Gives the computational implementation of the MCTDH method used for the numerical results.","marker":"[66]"},{"why":"Establishes the mean-field Fisher-information treatment of matter-wave interferometry that the authors contrast with, where the QFI vanishes at zero rotation.","marker":"[19]"},{"why":"Introduces the two-mode double-well model with rotation-dependent Peierls phase, the fixed-orbital baseline that the self-consistent result is compared against.","marker":"[53]"},{"why":"Reports the experimental Tonks-Girardeau gas that sets the strong-coupling regime accessible with the chosen parameters.","marker":"[49]"},{"why":"Describes the condensation-to-fermionization crossover used to interpret the interaction-strength dependence of the QFI for N>2.","marker":"[75]"},{"why":"Benchmarks the MCTDH method against the exact two-boson wavefunction, supporting the accuracy of the numerical approach in the strongly correlated regime.","marker":"[67]"}],"fun_headline_variants":["Strong interactions boost few-atom gyroscope precision","Many-body ring gyroscope sharpens with interaction strength","Zero-rotation sensitivity peaks at strong many-body coupling","Strongly interacting bosons sense slow rotations better"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported peak positions and heights of the QFI for $N=4$ and $N=6$ depend on the $M=12$ and $M=18$ orbital truncations being converged, an assertion the paper supports only by statement, not by a systematic orbital-number scan.","fun_headline_variants_meta":{"raw":{"variants":["Strong interactions boost few-atom gyroscope precision","Many-body ring gyroscope sharpens with interaction strength","Zero-rotation sensitivity peaks at strong many-body coupling","Strongly interacting bosons sense slow rotations better"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000806,"raw_usage":{"total_tokens":3491,"prompt_tokens":848,"completion_tokens":2643,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":464,"completion_tokens_details":{"reasoning_tokens":2580}},"tokens_in":464,"tokens_out":2643,"duration_ms":22826,"temperature":1.0,"reasoning_tokens":2580,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T00:34:05.710993+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the QFI at $\\Omega=0$ for $N=4$ and $N=6$ with successively larger orbital numbers (for example $M=16,24,32$ for $N=4$ and $M=24,32,48$ for $N=6$) at the interaction strengths where the peaks appear in Fig. 4(b), and check whether the peak height and location remain unchanged; alternatively, diagonalize the few-body problem exactly for $N=4$ in the same trap and compare the resulting QFI at $\\Omega=0$ with the MCTDH value.","supporting_citations":[{"cited_title":"Baak and U","cited_arxiv_id":null,"evidence_quote":"Supplies the framework for computing the many-body QFI self-consistently from MCTDH orbitals and Fock-space coefficients; the present paper corrects a term in its QFI expression."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the multiconfigurational time-dependent Hartree method for bosons that yields the self-consistent orbitals used throughout."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the mean-field Fisher-information treatment of matter-wave interferometry that the authors contrast with, where the QFI vanishes at zero rotation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the two-mode double-well model with rotation-dependent Peierls phase, the fixed-orbital baseline that the self-consistent result is compared against."},{"cited_title":"Paredes, A","cited_arxiv_id":null,"evidence_quote":"Reports the experimental Tonks-Girardeau gas that sets the strong-coupling regime accessible with the chosen parameters."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the condensation-to-fermionization crossover used to interpret the interaction-strength dependence of the QFI for N>2."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Benchmarks the MCTDH method against the exact two-boson wavefunction, supporting the accuracy of the numerical approach in the strongly correlated regime."}],"review_version":1}