{"id":"85a13c7a-319c-4e8b-87bf-0895617c5718","arxiv_id":"2601.05846","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Rotation alone can drive a dipolar Bose condensate into a supersolid and, as persistent currents enter, periodically melt it back into a superfluid, creating re-entrant supersolid pockets.","lead":"Spinning an ultracold dipolar gas is predicted to switch it between a smooth superfluid and a crystal-like supersolid—and back again—without changing the interactions between atoms. Because rotation speed is easy to tune in existing dysprosium experiments, this offers a practical new control knob for studying supersolids and how vortices interact with crystalline order.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (2) is applied to the SS phase although it is derived for a uniform superfluid; in a density-modulated state the Doppler shift is anomalous (f_s<1), so the predicted Ω_R^(1) boundary and re-entrant sequence may not be quantitatively robust.","rationale":"The reader's weakest assumption identifies the same load-bearing premise: Eq. (2) is a uniform-superfluid result and its use inside the supersolid is not rigorously justified. I agree with that assessment and sharpen it by noting that the Doppler shift in a supersolid is not simply the Galilean boost; the superfluid fraction f_s<1 suppresses or modifies the shift (Ref. [90]). This makes the mode-swapping picture doubly fragile: not only are the angular-momentum labels approximate, but even the frequency shift that drives the de-softening is suspect. The manuscript's own Appendix B concedes the non-perfect tight confinement and energy discontinuity, further weakening the analytical foundation.\n\nStill, the eGPE ground-state phase diagram in Fig. 2(b) and the real-time dynamics in Fig. 4 provide independent numerical evidence for a rotation-induced supersolid. The re-entrant pockets are extracted from density contrast of the actual ground states, not solely from Eq. (2). If the full BdG calculation inside the q=1 SS indeed confirms the mode assignment, the central claim survives. Because that confirmation is promised but not shown, a conditional acceptance with a request for the missing BdG spectra is the appropriate outcome. The first-order-transition heuristic and missing error bars are secondary issues that do not change this verdict.","tokens_in":15315,"tokens_out":19167,"duration_ms":212398,"concrete_test":"Using the authors' parameters (toroidal trap, N=32400, as=92.8a0), compute the full non-decoupled BdG spectrum of the q=1 SS ground state (n_d=6 density peaks, phase winding q=1) at Ω/2π = 3.5, 4.0, and 4.4 Hz without assuming angular-momentum eigenstates. Identify the lowest mode whose density fluctuation δn has a dominant m=6 (or, in the reduced zone, equivalent) component, i.e., the would-be Goldstone phason. With the q=1 chemical potential fixed, test whether its frequency obeys ω_6(Ω) = ω̃_6 − 6(Ω − ℏ/(MR²)) with constant ω̃_6. If the slope deviates (e.g., is suppressed by the superfluid fraction f_s), Eq. (2) is invalid in the SS and the Ω_R^(1) boundary and re-entrant prediction must be recomputed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central re-entrant scenario rests on Eq. (2), ω_M = ω̃_M − MΩ_eff, being valid in the SS phase. Appendix B derives Eq. (2) for a uniform SF in a tight ring, where m (and hence M=m−q) is a good quantum number. Once the roton+ condenses (m_R=6), the state has only C_6 symmetry, L_z is not conserved, and BdG modes are Bloch states with κ = m mod 6. The manuscript nevertheless uses the same Doppler shift to claim that at Ω_PC^(1) the q=1 persistent current 'swaps' the Higgs− and Goldstone modes, de-softens the Goldstone mode, and restores SF. This is precisely the step that produces the re-entrant SF→SS→SF sequence and the Ω_R^(1) boundary in Fig. 2. Independent work on supersolids (Ref. [90], 'Anomalous Doppler effect in superfluid and supersolid atomic gases') shows that the excitation spectrum of a moving supersolid is not obtained by a bare Galilean boost; the shift is governed by the superfluid fraction f_s<1. The paper cites Ref. [90] but does not apply it. If Eq. (2) fails in the SS, the quantitative location of the re-entrant pockets (and possibly their existence) is not established. Appendix B's caveat that the tight-confinement condition is 'not perfectly satisfied' and that ω̃_M^(q) must be introduced ad hoc underscores that the SS extension of Eq. (2) is assumed, not derived. The full-BdG cross-check mentioned in Appendix B would settle this, but the necessary spectra (eigenvectors and frequencies inside the q=1 SS, decomposed by δn angular momentum) are not shown.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This Letter studies rotating dipolar Bose-Einstein condensates in toroidal and oblate harmonic traps. Using the extended Gross-Pitaevskii equation with LHY corrections and the associated Bogoliubov-de Gennes (BdG) spectra, the authors show that increasing the rotation frequency can soften a roton mode and drive a superfluid-to-supersolid transition even when the scattering length is held near (but below) the quantum critical point. They further propose that the entry of a quantized persistent current or vortex reverses the effective Doppler shift, converting the Goldstone mode back into a finite-energy roton and restoring the superfluid. This produces a sequence of re-entrant supersolid pockets as a function of rotation frequency. The main text presents excitation spectra, phase diagrams in the (Omega, a_s) plane, a Ginzburg-Landau argument for a first-order transition, and real-time simulations showing dynamical emergence of density modulation.","tokens_in":15793,"tokens_out":7332,"duration_ms":85091,"significance":"If the central scenario is correct, the paper introduces a qualitatively new control parameter for supersolidity: instead of tuning interactions, one can use rotation to generate and destroy crystalline order through the nucleation of topological charge. The proposed vortex/persistent-current-driven de-softening of the Goldstone mode is an original mechanism, and the re-entrant phase diagram is a crisp, falsifiable prediction. The numerical work is substantial: full 3D eGPE plus BdG calculations, a phase diagram in two parameters, and dynamical quenches with phenomenological damping. The analytic mode-splitting formula (Eq. (2)) is derived from the BdG equations in the uniform superfluid limit and provides a useful design principle. However, the manuscript applies this formula to the density-modulated supersolid phase, where the derivation does not strictly apply; this is the main weakness and is discussed in the major comments. The paper should also be credited for citing, but not yet incorporating, the relevant anomalous-Doppler literature, which indicates the authors are aware of the subtlety.","major_comments":[{"comment":"The central re-entrant scenario rests on applying Eq. (2) to the density-modulated supersolid. In a uniform superfluid, m is a good quantum number and Eq. (2) follows from the BdG equations (Appendix B). In the supersolid, continuous rotational symmetry is spontaneously broken to C_{n_d}; BdG modes are Bloch states indexed by kappa = m mod n_d, and the Doppler shift is known to be anomalous, controlled by the superfluid fraction f_s < 1 (Ref. [90]). The manuscript cites Ref. [90] but does not use it. The 'mode-swapping' step—by which the q=1 persistent current turns the Higgs- mode into a roton+ and lifts the Goldstone mode—is asserted, not derived. The claimed full-BdG cross-check in Appendix B is not shown for the q=1 supersolid: no eigenfrequencies or eigenvectors of the modulated state near Omega_R^(1), decomposed by the angular momentum of delta n, are presented. This is load-bearin","section":"Appendix B, Eq. (12); Fig. 2(a)"},{"comment":"Appendix B concedes that the tight-confinement condition is 'not perfectly satisfied', that the energies are not continuous at Omega_PC, and that the intrinsic frequency must be replaced by a q-dependent tilde_omega_M^(q). This means the quantitative predictions in the supersolid are not actually derived from the Galilean formula; they rely on an ad hoc patch. Moreover, it is unclear whether the branches in Fig. 2(a) are the full-BdG results or the patched analytic expression. The text states that 'all results presented in the main text are cross-verified by solving the full, non-decoupled BdG problem', but no such comparison is shown. Please state, for each curve in Fig. 2(a), which calculation is being plotted, and include the full-BdG spectra in the q=1 supersolid used to locate Omega_R^(1). Without this, a reader cannot verify the key de-softening mechanism.","section":"Appendix B, Eq. (12); Fig. 2(a)"},{"comment":"The claim that TRS breaking makes the SF-SS transition first-order rests on the estimate L_z ~ I Omega (1 - f_s), which is introduced without derivation. In a density-modulated state, L_z, the moment of inertia, and the superfluid fraction have nontrivial spatial dependences, and the sign and magnitude of the resulting linear-in-f_s term are not demonstrated. A linear term alone does not guarantee a discontinuous jump unless its coefficient is sufficiently large relative to the quadratic terms. This point is secondary to the re-entrance mechanism, but it is presented as a central result ('fundamentally shifts the transition to first-order') and should be substantiated or softened.","section":"Roton instability and re-entrant SS state; Ginzburg-Landau argument"}],"minor_comments":[{"comment":"The abstract uses 'vortex-driven de-softening', but in the toroidal geometry the relevant topological objects are persistent currents, not vortices. Please adjust the wording to cover both cases.","section":"Abstract"},{"comment":"The color scale in the phase diagram is not described and the contour defining the SF/SS boundary is not specified. Please add a caption description of C and a marker for the maximum at Omega_PC^(1).","section":"Fig. 2(b)"},{"comment":"The labels roton+ and roton- are used before the sign convention with respect to M is explained. A brief definition tied to Eq. (2) would improve readability.","section":"Page 3, roton+ / roton- definitions"},{"comment":"It would help to state explicitly that the damping term gamma is used only in the real-time simulations and not in the ground-state imaginary-time propagation, and to comment on the dependence of the final density contrast on the chosen gamma values.","section":"Appendix A, Eq. (6)"},{"comment":"Reference [78] is formatted with full author names while others use surname initials; unify the style. Also check that Ref. [77] (supplementary video) is available to the reader.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is timely and the numerical infrastructure is solid, but the main physical mechanism is currently under-verified at exactly the point where it is most novel: the behavior inside the q=1 supersolid. The authors' own Appendix B caveats and their citation of the anomalous-Doppler effect (Ref. [90]) suggest they know the issue. I believe the manuscript can be made acceptable by adding the missing full-BdG spectra inside the supersolid or by deriving the corrected dispersion with the superfluid fraction and showing that the re-entrant pockets persist. I do not see a circularity problem: Eq. (2) is derived from the BdG equations in the uniform limit and the phase diagram is obtained numerically. The GL argument for first-order behavior is more of a sketch than a proof and should be labeled as such or supported. The topic fits the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing worth knowing about this paper is that it reports a new control knob for supersolidity in dipolar BECs: rotation frequency, rather than interaction strength. The central numerical result is a sequence of SF→SS→SF transitions as Ω increases, with discrete persistent-current entry reversing the effective Doppler shift and de-softening the Goldstone mode. If the numerics hold up, that is a genuinely new and testable prediction for existing experiments.\n\nThe paper does a lot right. The phase diagrams are computed in two geometries (toroidal and oblate harmonic), the spectra come from full BdG linearization of the eGPE, and the analytic model in Appendix B is a clean derivation of the Doppler-shifted spectrum in a uniform ring. The dynamical simulations with damping and noise show the SS emerging after a quench, which is a nice experimental bridge. I don't see any fitting of constants to the target phase diagram; the re-entrant sequence is an output, not an input. That counts.\n\nThe soft spots are real but not fatal. The main one is exactly what the reader flagged: Eq. (2) is derived for a uniform superfluid with well-defined angular momentum m, and the paper then uses it in the SS phase where the density modulation breaks continuous rotational symmetry and m is only defined modulo 6. The manuscript acknowledges the tight-confinement condition is not perfectly satisfied and that energies are discontinuous at the persistent-current transition, and it patches the analytic formula with a q-dependent tilde{omega}. That is a legitimate concern. The paper cites the anomalous Doppler result for supersolids (Ref. [90]) but does not apply it; if the effective Doppler shift in the SS is governed by the superfluid fraction f_s < 1, the quantitative locations of the re-entrant pockets could shift. The paper claims full BdG cross-checks, but the relevant spectra inside the q=1 SS, resolved by angular momentum, are not shown. This is the one figure that would settle the question, and it is missing.\n\nThe first-order transition argument is also heuristic—the moment-of-inertia relation L_z ≈ IΩ(1−f_s) is plausible but not derived. And there are no error bars or code/data included, which makes independent verification harder.\n\nBottom line: the central claim is plausible and the new physics is interesting enough to warrant a serious referee. I would send it to review, asking for the SS-phase spectra and a careful response on the Doppler-shift application. If those check out, this is a solid letter.","headline":"Rotation-controlled re-entrant supersolidity is the genuinely new result here; the analytic mode-swapping inside the supersolid phase is the main soft spot, and one missing spectrum would settle it.","tokens_in":16220,"tokens_out":1969,"would_cite":true,"duration_ms":21703,"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":"Tuning rotation frequency, not interactions, can drive a dipolar condensate between superfluid and supersolid phases, and back, repeatedly.","keywords":["supersolid","dipolar Bose-Einstein condensate","rotation","persistent current","roton","Goldstone mode","Bogoliubov spectrum","re-entrant phase"],"falsifier":"A measurement of the density contrast versus rotation frequency at fixed scattering length: the prediction is that the contrast rises at the roton-instability frequency, falls to zero at the first persistent-current threshold, and rises again at the next threshold. If the contrast stays finite across the persistent-current entry, or if the Goldstone mode remains gapless past the threshold, the de-softening mechanism is falsified. This could be checked by time-of-flight imaging or Bragg spectroscopy in a rotating dipolar gas.","tokens_in":15169,"feed_emoji":"🌀","tokens_out":5775,"duration_ms":58493,"temperature":0.7,"pith_summary":"This paper claims that the rotation frequency of a dipolar Bose-Einstein condensate is a control parameter for supersolidity, independent of the interparticle interactions. At a fixed scattering length near the quantum-critical point, increasing rotation softens a roton mode, condensing the gas into a density-modulated supersolid. Then the entry of a single persistent current reverses the effective flow, lifts the gapless Goldstone mode back to a finite-energy roton, and restores the uniform superfluid. As rotation increases further, each step of winding-number nucleation resets the effective velocity, producing discrete pockets of supersolidity separated by superfluid intervals. If correct, this gives an experimentally accessible knob for switching crystalline order on and off in ultracold gases.","feed_headline":"Rotation alone cycles a dipolar gas between superfluid and supersolid","feed_subtitle":"The same rotation that creates density order can erase it again via quantized currents, yielding re-entrant supersolid pockets.","key_machinery":"The central object is the Galilean-shifted dispersion relation ω_M^(q)(Ω) = ω̃_M − M Ω_eff, which separates the interaction-driven mode frequencies from a Doppler shift set by the effective flow Ω_eff = Ω − ℏq/(M R²). It predicts the splitting of roton branches, sets the threshold for roton softening, and accounts for the mode swapping that de-softens the Goldstone mode when the winding number q changes. The paper uses this formula to construct the re-entrant phase diagram and to identify the conditions under which rotation-induced supersolidity should occur.","core_discovery":"The central discovery is a vortex-driven de-softening mechanism. In a rotating dipolar gas, the roton instability that creates a supersolid is governed by the effective flow velocity Ω_eff = Ω − Ω_GS, where Ω_GS is the angular velocity of the persistent-current ground state. When a persistent current enters, the sign of Ω_eff reverses, swapping the energies of the Goldstone and Higgs modes. The formerly gapless Goldstone mode becomes a gapped roton−, which suppresses the density modulation and restores the superfluid. This cycle repeats for higher winding numbers, yielding re-entrant supersolid phases. The paper demonstrates this with analytical dispersion relations and numerical Bogoliubov","pith_inferences":["If the de-softening mechanism holds, the re-entrant pockets should also appear when the rotation is ramped downward, with hysteresis expected for a first-order transition; the paper does not discuss this.","The same mode-swapping physics might be mimicked by synthetic gauge fields in non-dipolar gases, since only the effective flow velocity matters, not the mechanical rotation.","The paper's three conditions for rotation-induced supersolidity (low-energy angular excitations, concave spectrum, roton below phonon) suggest a search strategy: systems satisfying these could show the effect even with weak dipolar interactions.","At higher winding numbers, where the pockets get broader and closer together, one might expect a crossover to a multiply charged superfluid with re-entrant ordering; whether pockets merge or remain discrete is an unresolved extrapolation."],"forward_implications":["Rotation offers a new experimental handle to induce supersolidity without tuning interparticle interactions, within reach of existing dipolar-gas setups.","The superfluid-to-supersolid transition driven by rotation is predicted to be first-order, with a jump in the superfluid fraction, unlike the second-order transition usually seen in rings.","The re-entrant sequence means that a single sample, at fixed scattering length, can be toggled between superfluid and supersolid multiple times by increasing rotation.","The mechanism is argued to generalize to other platforms with low-energy angular excitations, provided the roton instability is the lowest critical velocity.","The transition's first-order character implies a Higgs-mode gap at the critical point, giving a spectral fingerprint that experiments can look for."],"fun_headline_variants":["Vortices flip supersolid order on and off by rotation","Rotation's vortices erase and restore supersolid order","Re-entrant supersolid phases from rotating dipolar gases","Rotating dipolar gas cycles superfluid and supersolid states","Vortex flow tunes supersolid stability in dipolar gases"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The mode-swapping argument assumes that the excitation spectrum of the density-modulated supersolid can still be described by the same angular-momentum quantum numbers as the uniform superfluid, an approximation that is only exact in a tightly confining ring and is not perfectly satisfied in the numerical geometries.","fun_headline_variants_meta":{"raw":{"variants":["Vortices flip supersolid order on and off by rotation","Rotation's vortices erase and restore supersolid order","Re-entrant supersolid phases from rotating dipolar gases","Rotating dipolar gas cycles superfluid and supersolid states","Vortex flow tunes supersolid stability in dipolar gases"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000139,"raw_usage":{"total_tokens":953,"prompt_tokens":661,"completion_tokens":292,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":405,"completion_tokens_details":{"reasoning_tokens":210}},"tokens_in":405,"tokens_out":292,"duration_ms":3453,"temperature":1.0,"reasoning_tokens":210,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T11:31:50.352934+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A measurement of the density contrast versus rotation frequency at fixed scattering length: the prediction is that the contrast rises at the roton-instability frequency, falls to zero at the first persistent-current threshold, and rises again at the next threshold. If the contrast stays finite across the persistent-current entry, or if the Goldstone mode remains gapless past the threshold, the de-softening mechanism is falsified. This could be checked by time-of-flight imaging or Bragg spectroscopy in a rotating dipolar gas.","supporting_citations":[],"review_version":1}