{"id":"b6b6607f-19ba-4f2a-9445-0cc360d9a1ea","arxiv_id":"2607.28533","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"For microwave-shielded molecules, on-site U is non-monotonic in trap frequency and can cross zero, so two-body bound states allow tunable multi-occupancy Hubbard physics without a hard-core constraint.","lead":"Shielded ultracold polar molecules on one lattice site show on-site interaction energies U that can flip from negative to positive as the lattice is tightened. Bound molecular pairs then let experimenters tune U/t across the full range needed for multi-occupancy dipolar Hubbard physics.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.5","headline":"Bound-state U zero-crossing is computed in a single isotropic harmonic well; pair size vs lattice spacing is unchecked, so the quoted U/t window is unquantified.","rationale":"The reader correctly isolates the harmonic single-well replacement as the weakest assumption and still accepts the paper. That is the right call: the zero-crossing mechanism (U(0)=−Eb<0, initial dU/dω=−3/2ℏ, later rise from core–trap squeezing) does not rely on harmonicity and should survive in a lattice well; coupled-channel methods and the published microwave potentials are standard. The only soft spot is quantitative—where U crosses zero and thus whether U/t really covers −10…+50 under realistic anharmonicity and possible pair delocalization. That softens confidence intervals on Fig. 2, not the existence of tunable double occupancy for shielded bound pairs. No internal inconsistency, no hidden fitting, no stronger flaw found. Verdict remains ACCEPT; a pair-size / anharmonic re-solve would be the natural follow-up, not a reason to downgrade.","tokens_in":10718,"tokens_out":719,"duration_ms":85091,"concrete_test":"At the Fig. 2 zero-crossing (Ω=3.5 MHz, Δ/Ω=1, ω≈8.2 kHz), compute rms pair size ⟨R²⟩^{1/2} from the coupled-channel relative wavefunction. If ⟨R⟩≳a_lat/2, re-diagonalize the two-molecule Hamiltonian in a single (or double) sin² lattice well along one axis with the same V(R,θ), extract the lowest even pair energy relative to two separated sites, and replot U/t vs V0/Er. If the U=0 point leaves the range where |U/t| can still be swept through −10…+50 by modest Ω or V0 changes, the multi-occupancy tuning claim weakens.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central applied claim is that bound shielded pairs let U/t be tuned through ≈−10…+50 by lattice depth (Fig. 2, Ω=3.5 MHz), without a hard-core constraint. That number comes from U=E_rel−(3/2)ℏω with E_rel from an exactly separable isotropic harmonic trap (Methods, Eqs. 2–3). Real lattice wells are anharmonic and multi-site; CM–relative separation fails, and Wannier leakage is omitted. The paper only asserts the approximation is “reasonably accurate for V0≳5Er” with no error bar on U or on the zero-crossing. For the weakly bound branch (binding energies of a few kHz) the free-space pair size can approach the lattice constant (λ/2≈532 nm). If the relative wavefunction at the reported crossing (ω≈8 kHz, V0/Er≈13) already samples neighboring cells, the single-site U and the mapped U/t window shift by an unknown amount, and the simple on-site Hubbard parameter is incomplete (pair hopping / extended terms appear). Qualitative non-monotonicity of U(ω) is robust; the quantitative “experimentally relevant window without hard-core” is the load-bearing, untested step.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper computes on-site interaction energies U for pairs of microwave-shielded ultracold polar molecules on the same optical-lattice site. Using published 2D effective potentials (long-range dipole–dipole plus a large repulsive core) and numerically exact coupled-channel solutions of the relative-motion Schrödinger equation in an isotropic harmonic well, the authors show that U(ω) is strongly non-monotonic. Both unbound pairs and weakly bound two-body states can have U < 0 at weak confinement and cross zero to U > 0 as the trap frequency increases. For the bound branch they argue that U/t can be tuned through the experimentally relevant window ≈ −10 to +50 by lattice depth alone, without imposing a hard-core constraint, thereby opening previously inaccessible regimes of strongly dipolar Hubbard physics with multiple site occupancy.","tokens_in":11004,"tokens_out":926,"duration_ms":36103,"significance":"If the reported tunability of U holds under realistic lattice conditions, the work supplies a concrete, experimentally actionable route to multi-occupancy dipolar Hubbard models with molecules—regimes that have been largely excluded by collisional loss or by hard-core constraints. The calculations rest on established effective potentials and on standard, machine-validated coupled-channel machinery (BOUND/MOLSCAT), with scattering lengths computed independently for comparison. The qualitative contrast with the atomic contact formula (Eq. 1) is clear and physically well motivated by the excluded volume of the shielding core. This is a timely and useful contribution for the growing community working on molecular quantum gases in lattices.","major_comments":[{"comment":"Methods (Eqs. 2–3) and Fig. 2: The quantitative claim that bound-state U/t can be tuned through ≈ −10…+50 (Fig. 2, Ω = 3.5 MHz, zero-crossing near V0/Er ≈ 13, ω ≈ 8 kHz) rests entirely on the single isotropic harmonic well. The manuscript asserts this is “reasonably accurate for V0 ≳ 5 Er” but gives no error estimate on U or on the location of the zero-crossing once lattice anharmonicity and Wannier leakage are restored. For the weakly bound branch (binding energies of a few kHz) the free-space pair size can become comparable to the lattice constant (λ/2 ≈ 532 nm). The authors should estimate the rms pair size at the reported crossing and either (i) show that the relative wave function remains well localized inside one cell or (ii) qualify the mapped U/t window and note the possible appearance of pair-hopping/extended terms. Qualitative non-monotonicity of U(ω) is robust; the load-bearin","section":"Methods, Eqs. 2–3; Fig. 2"}],"minor_comments":[{"comment":"Fig. 1: The dotted curves from Eq. 1 are helpful but are shown only for the two smallest |a|. Adding a brief statement in the caption that the contact formula fails even qualitatively for large |a| would prevent misreading.","section":"Fig. 1"},{"comment":"Universality paragraph (Results): The statement that E_rel and U are universal when scaled by E3 is useful; it would help the reader if the corresponding scaled values of ω at the zero-crossings were quoted once in the text or a table.","section":"Results"},{"comment":"Introduction / Conclusions: A short forward reference to static-field or dual-microwave shielding (already cited) would clarify that the qualitative conclusions are expected to carry over, as asserted in the final paragraph.","section":"Introduction; Conclusions"},{"comment":"Typographical: “Schr¨ odinger” appears with a stray space; “RESUL TS” in the section heading has an embedded space.","section":"Methods; Results heading"}],"recommendation":"minor_revision","confidential_remarks":"The harmonic-well caveat is the only substantive open point; once the authors add a short pair-size estimate or a clearer qualification of the U/t window, the manuscript is suitable for acceptance. I see no novelty or citation-pattern concerns."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The real news here is simple: for microwave-shielded NaCs (and by universality any polar molecule), both unbound pairs and weakly bound dimers have on-site U that starts negative at weak confinement and crosses to positive as ω rises. The bound branch lets you dial U/t from roughly −10 to +50 just by lattice depth, without a hard-core constraint. That is the concrete experimental handle the field has been missing for multi-occupancy dipolar Hubbard physics.\n\nThey do the calculation the right way. Relative and COM separate exactly in a harmonic well; they solve the coupled-channel relative-motion problem with the published 2-d microwave-shielding potentials using BOUND/MOLSCAT. No contact-potential shortcuts, no fitting. Scattering lengths are computed independently only for comparison. The deviation from the atomic Jaksch formula is large and physical—the repulsive core squeezes the wavefunction. Figures 1 and 2 make the zero-crossing and the U/t window obvious. Self-citations are to the methods and potentials, not circular.\n\nThe soft spot is exactly the one the stress-test names: everything is inside a single isotropic harmonic well. Anharmonicity, Wannier leakage, and possible pair size comparable to lattice spacing at the few-kHz binding energies are not quantified. The authors say “reasonably accurate for V0 ≳ 5 Er” and stop. Qualitative non-monotonicity will survive; the precise location of the zero-crossing and the quoted U/t numbers might shift once multi-site effects are restored. That is a real but proportionate limitation for a first mapping paper, not a load-bearing collapse.\n\nThis is for people already working on molecular lattices or dipolar Hubbard models. They will get a clear target and a method they can extend. Math and numerics look clean; citation pattern is normal. I would send it to referees without hesitation and would cite the U(ω) curves if I were designing the next multi-occupancy experiment. Worth a reading-group slot.","headline":"Solid computation showing shielded molecular pairs give a tunable U that crosses zero inside the Hubbard window—new and usable, with the harmonic-trap caveat already flagged.","tokens_in":11620,"tokens_out":509,"would_cite":true,"duration_ms":18156,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Shielded polar molecules on a lattice can have on-site interaction U that flips from attractive to repulsive as the lattice is tightened, opening Hubbard physics with double occupancy.","keywords":["ultracold polar molecules","microwave shielding","Hubbard model","on-site interaction","optical lattices","dipolar interactions","double occupancy"],"falsifier":"Measure the double-occupancy fraction or pair-tunnelling rate for microwave-shielded NaCs (or an equivalent species) while scanning lattice depth across the predicted zero-crossing of U; the sign change in effective interaction should appear as a clear change in the many-body response.","tokens_in":11621,"feed_emoji":"⚛️","tokens_out":822,"duration_ms":22746,"temperature":0.7,"pith_summary":"Ultracold polar molecules usually cannot share a lattice site because they collide and are lost. Microwave shielding puts a large repulsive core around each pair while leaving long-range dipole forces intact. This paper calculates the on-site interaction energy U for two shielded molecules on the same site and finds that U behaves unlike the familiar atomic case. For both unbound pairs and weakly bound molecular dimers, U can be negative in a weak lattice yet cross zero and become positive as the lattice is strengthened. The bound-state branch lets experimentalists tune the ratio U/t through the window needed for pair superfluids, supersolids and other multi-occupancy phases, without imposing a hard-core constraint that forbids double occupancy.","feed_headline":"Shielded molecules flip U from attractive to repulsive","feed_subtitle":"Bound pairs let experimentalists tune double occupancy across the Hubbard window without hard-core loss","key_machinery":"Exact separation of relative and centre-of-mass motion inside a harmonic well, solved by coupled-channel bound-state calculations on the two-dimensional microwave-shielding potential that combines a hard repulsive core with anisotropic dipole–dipole tails.","core_discovery":"For microwave-shielded molecules the on-site interaction U is often non-monotonic in trap frequency: it is negative at weak confinement and crosses zero to positive values as the lattice is tightened. This zero-crossing occurs for both continuum pairs and two-body bound states; the bound states place the crossing inside the experimentally accessible range of lattice depths, so that U/t can be swept continuously from roughly −10 to +50.","pith_inferences":["Because the zero-crossing is controlled by the competition between the repulsive core and the trap, modest changes in microwave Rabi frequency or detuning should move the crossing without rebuilding the lattice.","The strong angular correlations induced by the dipole tail mean that lattice geometry (cubic versus anisotropic) will reshape the effective U even more than for magnetic atoms.","Once double occupancy is allowed, occupation-dependent tunnelling terms already present in molecular Hubbard models will become quantitatively important and should be re-evaluated with the correlated two-body wave-functions computed here."],"forward_implications":["Bound two-molecule states become a practical knob for dialling U across the full range needed for multi-occupancy Hubbard models.","Hard-core constraints that previously excluded double occupancy can be lifted while still retaining strong long-range dipolar interactions.","Pair superfluidity, supersolid order and occupation-dependent tunnelling become experimentally accessible with polar molecules.","The same qualitative U(ω) behaviour is expected for other shielding schemes (static electric, dual-microwave, elliptical) once their effective potentials are inserted."],"fun_headline_variants":["Shielded molecules: U flips from negative to positive with lattice depth","Microwave-shielded pairs show U zero-crossing in accessible lattices","Bound molecular pairs tune U/t from −10 to +50 without hard-core loss","On-site U for shielded molecules crosses zero as confinement tightens","Dipolar Hubbard access via bound states with sign-changing U"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The real optical lattice is replaced by a single isotropic harmonic well, ignoring anharmonicity and leakage of the wave-function into neighbouring sites.","fun_headline_variants_meta":{"raw":{"variants":["Shielded molecules: U flips from negative to positive with lattice depth","Microwave-shielded pairs show U zero-crossing in accessible lattices","Bound molecular pairs tune U/t from −10 to +50 without hard-core loss","On-site U for shielded molecules crosses zero as confinement tightens","Dipolar Hubbard access via bound states with sign-changing U"]},"model":"grok-4.5","effort":"low","cost_usd":0.004268,"raw_usage":{"total_tokens":1207,"prompt_tokens":689,"num_sources_used":0,"completion_tokens":97,"cost_in_usd_ticks":42684000,"prompt_tokens_details":{"text_tokens":689,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":421,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":689,"tokens_out":97,"duration_ms":7666,"temperature":1.0,"reasoning_tokens":421,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T08:33:38.221669+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure the double-occupancy fraction or pair-tunnelling rate for microwave-shielded NaCs (or an equivalent species) while scanning lattice depth across the predicted zero-crossing of U; the sign change in effective interaction should appear as a clear change in the many-body response.","supporting_citations":[],"review_version":2}