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Angular momentum of rotating fermionic superfluids by Sagnac phonon interferometry

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Pith's one-line read A ring-shaped Sagnac phonon interferometer measures the circulation quantum h/2m in Fermi superfluids, half the bosonic value.

desk verdict 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. read the letter →

arxiv 2511.02664 v2 pith:BDR4H44Q submitted 2025-11-04 cond-mat.quant-gas physics.atom-phquant-ph

Marcia Frómeta Fernández , Diego Hernández Rajkov , Giulia Del Pace , Nicola Grani , Massimo Inguscio , Francesco Scazza , Sandro Stringari , Giacomo Roati This is my paper · ORCID
classification cond-mat.quant-gasphysics.atom-phquant-ph PACS 03.75.Ss67.85.-d
keywords quantumofcirculationFermisuperfluidityBEC-BCScrossoverSagnacphononinterferometryangularmomentumperparticlesuperfluidfractionpersistentcurrentsunitarygas
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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

What would settle it

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.

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Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

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).

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 (2)
  1. [Main text, Eq. (1)/(2) and Eq. (28) of Methods; Fig. 4] 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
  2. [Methods, Eqs. (17)–(23) and Fig. 2c] 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.
minor comments (4)
  1. [Fig. 4 and Methods] The acronym for the Gorkov–Melik–Barkhudarov approach is written as both 'GMB' and 'GBM'; please use one consistently.
  2. [Methods, Eq. (8)] 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.
  3. [Abstract and main text] Minor language: 'clock- and anticlock-wise' should be 'clockwise and counterclockwise' for consistency with the rest of the text.
  4. [Methods, Eq. (3)–(5)] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found: the h/2m circulation quantum is inferred from an independent phonon-precession measurement plus a sum-rule relation, not assumed as input.

full rationale

The central chain is non-circular. The measured observable is the phonon precession rate Ω extracted from a fit to the two Doppler-shifted density modulations (Eq. (2); Methods Eq. (10)), and the conversion Ω → Δc = Ω R̄ is purely kinematic. The conversion Δc → angular momentum per particle, ℓz = m R̄ Δc, is derived from the m2^- sum rule in Methods Eqs. (24)-(28), yielding Δc = (1/m)⟨Px⟩ = f_s v_s + f_n v_n. No fitted parameter in this chain is defined in terms of the claimed output; κ = h/2m is obtained by comparing the measured ℓz/w with the quantization law ℓz = m w κ/(2π) for the BEC and unitary low-temperature points, not by inserting the answer. The finite-temperature superfluid fraction N_s/N = 2m R̄ Δc/ℏ does use κ = h/2m measured at low T and assumes f_n v_n ≈ 0, as 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." This is an explicit physical assumption and a genuine systematic-risk caveat for the temperature-dependent values, but it is not a circular reduction: it does not define the target result in terms of itself, and the step-like dependence of Δc on imprinted phase plus the agreement with published homogeneous superfluid-fraction data are independent consistency checks. The self-citations (Refs. [4], [30], [64]) supply the phase-imprinting method, the trap T_c normalization, and the Fermi-energy estimate; they are calibrations with independent content, not cited proofs of the h/2m claim. Consequently, no specific circular step can be exhibited.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central measurement is essentially model-independent at T = 0: the Doppler splitting of counter-propagating phonons is related to the momentum per particle by the f-sum rule and the m_2^- sum rule (Methods). The only genuinely ad hoc assumption is that the normal component is at rest; the fit includes nuisance parameters (damping Γ, angular offset) but these do not affect the central physical inference. No new entities are introduced.

free parameters (2)
  • Damping rate Γ = ~30 Hz at unitarity
    Added phenomenologically to Eq. (8) to describe decay of the phonon modes; not predicted by theory and extracted from fits.
  • Angular offset θ_0 = arbitrary initial phase
    Accounts for the unknown initial phase of the standing wave in the interferogram fits.
assumptions (4)
  • standard math Linear response theory: density response χ(k,ω) given by two-fluid hydrodynamic poles and f-sum rule exhaustion by phonons
    Used to derive Eq. (28) relating the Doppler shift to the momentum per particle; standard many-body theory (Refs. 34, 65-68).
  • domain assumption Landau two-fluid hydrodynamics with weakly compressible limit γ ≃ 1
    Underlies first/second sound decomposition and neglect of second-sound contribution to the density response; justified for unitary Fermi gas at T < 0.7 T_c (Refs. 32, 33, 44).
  • ad hoc to paper Normal component at rest: f_n v_n ≈ 0
    Critical assumption for interpreting Δc as f_s v_s and for extracting the superfluid fraction; supported by step-like Δc vs imprinted phase but not directly measured.
  • domain assumption Polytropic approximation for density calibration and V_0 extraction
    Used to set perturbation amplitude V_0/μ ≲ 0.1; standard LDA/polytropic model for trapped gases.

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Pith. "Pith review of Angular momentum of rotating fermionic superfluids by Sagnac phonon interferometry." pith.science (2026). https://pith.science/paper/BDR4H44Q

@misc{pith2026251102664,
  author       = {Pith},
  title        = {Pith review of: Angular momentum of rotating fermionic superfluids by Sagnac phonon interferometry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BDR4H44Q}},
  note         = {Machine review of arXiv:2511.02664}
}
abstract

Fermionic many-body systems provide an unrivaled arena to investigate how interactions drive the emergence of collective quantum behavior, such as macroscopic coherence and superfluidity. Central to these phenomena is the formation of Cooper pairs, correlated states of two fermions that behave as composite bosons and condense below a critical temperature. However, unlike elementary bosons, these pairs retain their internal structure set by underlying fermionic correlations, essential for understanding superfluid properties throughout the so-called Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover -- a cornerstone of strongly correlated fermionic matter. Here, we harness a sonic analog of the optical Sagnac effect to disclose the composite nature of fermionic condensates across the BEC-BCS crossover. We realize an in-situ loop interferometer by coherently exciting two counter-propagating long-wavelength phonons of an annular fermionic superfluid with tuneable interparticle interactions. The frequency degeneracy between clock- and anticlock-wise sound modes is lifted upon controllably injecting a quantized supercurrent in the superfluid ring, resulting in a measurable Doppler shift that enables us to probe the elementary quantum of circulation and the angular momentum carried by each particle in the fermionic fluid. Our observations directly reveal that the superflow circulation is quantized in terms of $h/2m$, where $m$ is the mass of the constituents, in striking contrast to bosonic condensates where $h/m$ is the relevant circulation quantum. Further, by operating our interferometer at tunable temperature, we measure the thermal depletion of the superfluid in the unitary Fermi gas, demonstrating phonon interferometry as a powerful technique for probing fundamental properties of strongly-correlated quantum systems.

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