{"id":"be55454c-aa29-4a7e-a6d8-7c9d9de5d2e1","arxiv_id":"2511.02664","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A Sagnac phonon interferometer in an annular Fermi superfluid directly measures the circulation quantum as h/2m, revealing Cooper-pair superflow across the BEC-BCS crossover.","lead":"This paper reports a new 'Sagnac phonon interferometer' that sends sound waves around a ring-shaped superfluid made of fermionic atoms, and uses the rotation-induced shift between two sound waves to measure the quantum of circulation. The measured circulation quantum is h/2m—half the bosonic value—demonstrating that the superflow is carried by Cooper pairs across the BEC–BCS crossover.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The calibration of ℓ_z and N_s/N rests on the unverified assumption that the normal-fluid velocity is zero after equilibration (Eq. 28 vs Eq. 1); the low-temperature h/2m claim is less exposed than the finite-temperature superfluid fraction.","rationale":"The reader identified the same weakest assumption; I agree. The concern is genuine but does not move the CONDITIONAL verdict. The paper's central h/2m claim is independently supported: the linear-response derivation in Methods (Eqs. 23–28) is model-independent in the k→0 limit if phonons exhaust the sum rules; the measured sound velocity at unitarity gives ξ_B = 0.396(29), consistent with previous experiments; the step-like Δc vs imprinted phase (Fig. 3c,d) ties the signal to the quantized circulating state; and at the lowest temperature used (T/Tc≈0.4) the normal fraction is small, so a residual v_n would need to be implausibly large to convert the measured h/2m into h/m. The finite-temperature superfluid-fraction extraction is more exposed, and the manuscript honestly flags the assumption as validated only indirectly. A direct t_eq scan would settle whether residual normal-fluid velocity contaminates the quantitative results. Thus the appropriate verdict remains CONDITIONAL, unchanged from the reader's assessment.","tokens_in":19981,"tokens_out":12390,"duration_ms":143808,"concrete_test":"At a fixed unitary interaction and w=1, vary the equilibration time t_eq between the phase imprint and the quench of V_pert (e.g., t_eq = 10, 50, 150, 300 ms) and measure the precession rate Ω = Δc/R̄ while also measuring the winding number w by time-of-flight after the interferogram. If the ratio Δc/w is constant within error for t_eq ≥ 50 ms, v_n has already relaxed and the reported values are safe; if Δc/w decreases and then plateaus, the 50 ms value is contaminated by f_n v_n and the reported ℓ_z and N_s/N must be corrected or shifted to the plateau. A companion scan at T/Tc≈0.6, where f_n is several times larger, amplifies any residual normal-flow signal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is stated in the main text: 'any residual incoherent motion of the normal component is damped during the equilibration period preceding the quench of V_pert, effectively yielding f_n v_n ≃ 0.' Through Eq. (28) of Methods, Δc = f_s v_s + f_n v_n, so the conversion Δc → ℓ_z = m R̄ Δc (Eq. 1) and the superfluid fraction N_s/N = 2m R̄ Δc/ℏ are calibrated by this single assumption. If a finite azimuthal normal-flow velocity v_n survives the 50 ms equilibration, every plotted ℓ_z and N_s/N point is offset by m R̄ f_n v_n; the offset is temperature- and interaction-dependent and cannot be absorbed by simply redefining κ. The step-like dependence of Δc on the imprinted phase (Fig. 3c,d) provides evidence that the signal tracks the quantized supercurrent rather than a normal-fluid moment of inertia, and the finite-temperature N_s/N data agree with published results after trap averaging, but neither check directly bounds v_n: the phase step shows quantization of the carrier, not the absence of a normal-fluid contribution; the comparison with previous work is an indirect consistency test that shares the same two-fluid Doppler ansatz. This does not threaten the factor-of-two distinction at the lowest temperatures (T/Tc≈0.4, where f_n is small), but it is the weakest link for the quantitative values and for the temperature-dependent superfluid fraction extraction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a Sagnac-type phonon interferometer implemented in an annular superfluid Fermi gas of 6Li across the BEC–BCS crossover. Two counter-propagating first-sound modes are excited; a quantized persistent current of winding number w Doppler-splits the phonon frequencies, and the resulting precession of the standing-wave density pattern is used to extract the angular momentum per particle l_z and, at finite temperature, the superfluid fraction N_s/N. The central claim is that the circulation quantum is kappa = h/2m, established by l_z/(hbar w) = 1/2 in both the molecular BEC and unitary regimes, in contrast to the bosonic h/m. A temperature-dependent measurement at unitarity gives a decreasing superfluid fraction consistent with previous homogeneous-gas results after trap corrections. The manuscript also reports phonon velocities, damping rates, and a Bertsch parameter xi_B = 0.396(29).","tokens_in":20385,"tokens_out":6421,"duration_ms":64131,"significance":"If correct, this is the first direct, in-situ measurement of the half-quantum circulation in atomic Fermi superfluids and provides a clean demonstration that circulating superflow is carried by fermion pairs across the crossover. The use of phononic Sagnac interferometry is an attractive and minimally destructive probe, and the authors connect the measured Doppler shift to the f-sum rule and the m2^- sum rule rather than assuming the result. The step-like response of the Doppler shift to the imprinted phase is strong evidence for quantized supercurrent, and the trap-corrected finite-temperature superfluid fraction agrees with several independent experiments and theories. The work is therefore significant for quantum-gas physics and for two-fluid hydrodynamics of strongly interacting fermions.","major_comments":[{"comment":"The conversion from Doppler shift to angular momentum and superfluid fraction relies on Eq. (28), Δc = f_s v_s + f_n v_n, combined with the assumption f_n v_n ≃ 0, stated in the main text after Eq. (2). The step-like Δc(Δφ_I) behavior in Figs. 3c,d rules out a normal-fluid moment-of-inertia response that would grow linearly with the imprinted phase, but it does not by itself bound a stationary azimuthal normal-fluid velocity. At T/T_c ≈ 0.4–0.6, and especially at the BCS point 1/k_Fa = −0.55 where T/T_c is closer to unity, f_n is not negligible; a finite v_n would produce a systematic offset mR̄ f_n v_n in every extracted l_z and N_s/N. The agreement with homogeneous N_s/N data after trap averaging is reassuring, but it is not fully independent because those extractions also rely on the two-fluid Doppler formalism. Please provide an explicit estimate or experimental upper bound for v_n a","section":"Main text, Eq. (1)/(2) and Eq. (28) of Methods; Fig. 4"},{"comment":"The fitting model, Eq. (23), keeps only the first-sound pole and neglects second sound. The suppression of the second-sound contribution relies on the smallness of χ2/χ1 ≈ (γ−1)(1+2c2^2/c1^2), Eq. (22), and the power spectra in Fig. 2c confirm this for the non-rotating, low-temperature cases shown. However, the finite-temperature runs (up to T/T_c ≈ 0.6) and the BCS data point sit closer to T_c, where the Landau–Placzek ratio grows and second sound can couple more strongly to density. If a small second-sound component were present, the two-mode fit, Eq. (10), would still yield a visually good fit but with an effective precession frequency biased relative to f_s v_s. Please state the expected χ2/χ1 at the highest T and at 1/k_Fa = −0.55, or show power spectral densities for those conditions, to demonstrate that the one-sound approximation is adequate for the reported error bars.","section":"Methods, Eqs. (17)–(23) and Fig. 2c"}],"minor_comments":[{"comment":"The acronym for the Gorkov–Melik–Barkhudarov approach is written as both 'GMB' and 'GBM'; please use one consistently.","section":"Fig. 4 and Methods"},{"comment":"The weights χ± are used in Eq. (8) before their definition in the main text following Eq. (2). Define them at first use in the Methods, or refer back to the main-text definition.","section":"Methods, Eq. (8)"},{"comment":"Minor language: 'clock- and anticlock-wise' should be 'clockwise and counterclockwise' for consistency with the rest of the text.","section":"Abstract and main text"},{"comment":"N_p is introduced as the number of atoms per spin component in the main text but the symbol is reused in Eqs. (3)–(5) without restating its meaning; please clarify the notation.","section":"Methods, Eq. (3)–(5)"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First: this is the first direct in-situ measurement of the h/2m circulation quantum in a fermionic superfluid. That claim holds up. The BEC and unitary data show ℓ_z/ℏw = 1/2 within errors, in contrast to the h/m of bosons, and the step-like dependence of the Doppler shift on the imprinted phase is good evidence that you are seeing the quantized supercurrent, not a smooth normal-fluid moment of inertia. The derivation in Methods connecting Δc to the f-sum rule and the m2− moment is a genuine strength: the Doppler relation is not being fit to the data, it is derived from linear response.\n\nThe paper also does solid housekeeping: sound speed across the crossover, quality factors, a Bertsch parameter consistent with previous work, and a finite-temperature superfluid fraction that agrees with established results once trap averaging is applied.\n\nThe soft spots. The load-bearing assumption is v_n ≈ 0. The sentence in the main text after Eq. (2) – \"any residual incoherent motion of the normal component is damped...\" – is an assertion, not a measurement. Through Eq. (28), Δc = f_s v_s + f_n v_n, so a finite normal-fluid velocity would shift every ℓ_z and N_s/N point by a temperature- and interaction-dependent offset. The step-like response in Fig. 3c,d shows the carrier is quantized, but it does not put a bound on a constant v_n offset. The comparison with the homogeneous superfluid fraction in Fig. 4 is reassuring, but it shares the same two-fluid Doppler ansatz, so it is not fully independent. This matters most for the quantitative N_s/N extraction; the low-temperature h/2m claim is less exposed because f_n is small there, though not negligible at T/Tc ≈ 0.4, and the BEC data are the cleanest.\n\nI also noticed the data availability statement says data \"will be available in a Zenodo repository\" – no link, no release date. For a paper making a first-measurement claim, that is a missing piece, and an easy one to fix.\n\nWho is it for: the cold-atom and quantum-fluid communities will want this, and it also belongs in the rotation-sensing/atom-interferometry discussion. It deserves a serious referee. I would send it out, with the request that the authors either bound v_n more directly or soften the quantitative finite-temperature claims — and release the data.","headline":"First direct in-situ measurement of the h/2m circulation quantum in a Fermi superfluid; solid central result with one load-bearing assumption on the normal component.","tokens_in":20882,"tokens_out":4326,"would_cite":true,"duration_ms":46212,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.75.Ss","67.85.-d"],"model":"deepseek-v4-flash","headline":"A ring-shaped Sagnac phonon interferometer measures the circulation quantum h/2m in Fermi superfluids, half the bosonic value.","keywords":["quantum of circulation","Fermi superfluidity","BEC-BCS crossover","Sagnac phonon interferometry","angular momentum per particle","superfluid fraction","persistent currents","unitary Fermi gas"],"falsifier":"Quench the perturbing potential before the equilibration period is complete, or deliberately launch a second-sound entropy wave while the supercurrent flows, and look for a change in the extracted ℓ_z/w at fixed temperature; if the slope moves away from ℏ/2 at a temperature where the superfluid fraction is independently known, the identification Δc = v_s at zero temperature or Δc = f_s v_s at finite temperature is falsified.","tokens_in":19895,"feed_emoji":"🌀","tokens_out":6966,"duration_ms":73928,"temperature":0.7,"pith_summary":"This paper claims that the quantum of superfluid circulation in a Fermi superfluid is h/2m, half the value h/m familiar from bosonic condensates, and that this factor of two holds across the entire BEC–BCS crossover. The evidence comes from a new in-situ probe: a sonic Sagnac interferometer that excites two counter-propagating phonons in an annular cloud of paired fermions and watches the standing-wave pattern precess when a quantized supercurrent is imprinted. From the Doppler splitting of the two sound modes, the authors extract the angular momentum per particle, finding ℓ_z/ℏw = 1/2 in both the molecular-BEC regime and the unitary Fermi gas. At finite temperature the same measurement yields the superfluid fraction, since the Doppler shift measures f_s v_s when the normal component is at rest. A sympathetic reader would care because this turns the old vortex-lattice estimate of circulation into a direct, equation-of-state-independent measurement and establishes pair-based transport as a general signature of Fermi superfluidity.","feed_headline":"Fermi superfluids circulate in units of h/2m, not h/m","feed_subtitle":"A ring-shaped phonon interferometer reads the angular momentum per particle across the BEC-BCS crossover.","key_machinery":"The key object is the sonic Sagnac interferometer: a ring trap with periodic boundary conditions in which two counter-propagating first-sound phonons are excited by a weak cosθ potential. A persistent supercurrent of winding number w splits their frequencies by a Doppler shift Δc, which shows up as precession of the standing-wave density pattern at Ω = Δc/R̄. The paper derives the central identity Δc = f_s v_s + f_n v_n by matching the high-frequency expansion of the density-response function to model-independent sum rules; with v_n ≈ 0 this gives ℓ_z = (m w/2π)(N_s/N)κ. Phase imprinting provides the quantized currents, and a linear-response fit to the density modulations extracts the phonon","core_discovery":"The central discovery is that the circulation quantum of a fermionic pair condensate—measured directly rather than inferred from vortex spacing—is κ = h/2m, with m the mass of a single atom. Injecting persistent currents of winding number w into a ring of lithium-6 atoms and recording the precession of a two-phonon standing wave gives ℓ_z, the angular momentum per particle, through ℓ_z = m R̄ Δc. In the BEC and unitary regimes the data collapse onto ℓ_z/ℏw = 1/2; in the BCS regime the slope drops, which the authors attribute to the finite-temperature reduction of the superfluid fraction. Because the Doppler shift of first sound in a weakly compressible two-fluid system is Δc = f_s v_s + f_n","pith_inferences":["The finite-temperature superfluid-fraction extraction inherits the paper's own caveat that measured sound speed and N_s/N sit below homogeneous-system values before trap corrections; testing the same protocol in a 3D box trap would remove those corrections and either confirm or revise the apparent agreement.","Since the whole finite-temperature readout rests on v_n ≈ 0, a deliberate measurement with a controlled heat (second-sound) wave would check whether the normal component truly stays at rest; this is the most direct probe of the paper's weakest link.","The same Doppler identity should make the second-sound frequency shift anomalously velocity-dependent; locating that shift in the ring would extend the interferometer from a circulation meter into a two-fluid velocimeter.","The step-like Doppler shift versus imprinted phase could become a fast, in-situ winding-number detector for fermionic atomtronic circuits, eliminating the need for time-of-flight interferometry in future devices."],"forward_implications":["The factor-of-two reduction in the circulation quantum, κ = h/2m, is established as a general hallmark of Fermi superfluidity, independent of interaction strength from tightly bound molecules to unitarity.","The Sagnac phonon interferometer measures angular momentum per particle without requiring the equation of state, so it can probe systems where thermodynamic input is unavailable.","At finite temperature the Doppler shift directly encodes f_s v_s, making the same apparatus a quantitative superfluid-fraction thermometer at unitarity.","The method is designed to extend to two-dimensional, disordered, periodically modulated, and supersolid superfluids, where vortex-based probes are harder.","The observed quantum-limited sound damping near unitarity supports the use of strongly interacting Fermi superfluids as durable atom-interferometric sensors."],"fun_headline_variants":["Fermi superfluid circulation quantized at h/2m, not h/m","Sagnac phonon interferometry reads angular momentum per fermion","Ring interferometer measures h/2m circulation in Fermi gas","Phonon Sagnac effect reveals pair condensate circulation quantum"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing assumption is that the normal (non-superfluid) component is at rest when the phonon measurement begins, so the measured Doppler shift reflects only the superfluid flow; if a residual normal-fluid velocity survives the 50 ms equilibration, the inferred angular momentum and the h/2m quantum would be systematically biased.","fun_headline_variants_meta":{"raw":{"variants":["Fermi superfluid circulation quantized at h/2m, not h/m","Sagnac phonon interferometry reads angular momentum per fermion","Ring interferometer measures h/2m circulation in Fermi gas","Phonon Sagnac effect reveals pair condensate circulation quantum"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000162,"raw_usage":{"total_tokens":1148,"prompt_tokens":886,"completion_tokens":262,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":630,"completion_tokens_details":{"reasoning_tokens":184}},"tokens_in":630,"tokens_out":262,"duration_ms":3292,"temperature":1.0,"reasoning_tokens":184,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T00:04:01.613909+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Quench the perturbing potential before the equilibration period is complete, or deliberately launch a second-sound entropy wave while the supercurrent flows, and look for a change in the extracted ℓ_z/w at fixed temperature; if the slope moves away from ℏ/2 at a temperature where the superfluid fraction is independently known, the identification Δc = v_s at zero temperature or Δc = f_s v_s at finite temperature is falsified.","supporting_citations":[],"review_version":1}