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arxiv: 2505.11452 · v2 · submitted 2025-05-16 · ❄️ cond-mat.quant-gas · physics.atom-ph· quant-ph

The fate of the Fermi surface coupled to a single-wave-vector cavity mode

Bernhard Frank , Michele Pini , Johannes Lang , Francesco Piazza This is my paper

Pith reviewed 2026-05-22 14:07 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.atom-phquant-ph
keywords Fermi surfacecavity QEDultracold Fermi gasdensity wavesuperradiancesuperfluid pairinginfinite-range interaction
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The pith

Cavity-induced single-wave-vector interactions always deform the Fermi surface of an ultracold gas and select density-wave order only for attractive coupling while favoring superfluid pairing for repulsive coupling.

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

The paper solves the full set of competing instabilities that arise when a Fermi gas feels an infinite-range interaction modulated at a single wavelength set by a cavity mode. A sympathetic reading shows that the interaction strength and sign can be tuned independently, producing a density-wave instability that wins on the attractive side but vanishes entirely on the repulsive side. In the repulsive regime the ground state is instead a non-superradiant superfluid with fermion pairs that can carry either zero or finite total momentum. Even when no symmetry-breaking order occurs, the Fermi surface itself is always distorted away from a perfect sphere. The authors argue that this entire phenomenology lies within reach of current ultracold-atom experiments.

Core claim

The density-wave (superradiant) instability dominates on the attractive side, yet is absent for repulsive interactions, where the competition is instead won by non-superradiant superfluid phases at low temperatures with Fermion pairs forming at both vanishing and finite center-of-mass momentum. Even in the absence of such symmetry-breaking instabilities, the Fermi surface is always nontrivially deformed from an isotropic shape.

What carries the argument

The single-wave-vector cavity mode that imposes a spatially modulated, infinite-range interaction whose sign and strength are independently tunable.

If this is right

  • The Fermi surface remains deformed even in the absence of any symmetry-breaking order.
  • Repulsive interactions stabilize superfluid pairing at both zero and finite center-of-mass momentum instead of density waves.
  • The full phase diagram, including the location of the various instabilities, is accessible to state-of-the-art cavity-QED setups with ultracold fermions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The persistent deformation could modify collective modes or transport coefficients even above any critical temperature.
  • Engineering analogous single-wavelength infinite-range forces in other itinerant systems might reveal similar competition between pairing and density-wave channels.
  • Finite-temperature crossovers between the superfluid phases could be probed through momentum-resolved spectroscopy.

Load-bearing premise

The cavity produces a purely single-wave-vector, infinite-range interaction whose strength and sign can be adjusted independently of all other parameters.

What would settle it

Time-of-flight imaging that either detects or rules out a density-wave modulation when the cavity-mediated interaction is tuned repulsive, or that measures a non-circular Fermi surface in the normal phase.

Figures

Figures reproduced from arXiv: 2505.11452 by Bernhard Frank, Francesco Piazza, Johannes Lang, Michele Pini.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram for a transversely driven ultracold [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Sketch of the mean-field decouplings evaluated [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Momentum distribution [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic representation of the momentum struc [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

The electromagnetic field of standing-wave or ring cavities induces a spatially modulated, infinite-range interaction between atoms in an ultracold Fermi gas, with a single wavelength comparable to the Fermi length. This interaction has no analog in other systems of itinerant particles and has so far been studied only in the regime where it is attractive at zero distance. Here, we fully solve the problem of competing instabilities of the Fermi surface induced by single-wavelength interactions. We find that while the density-wave (superradiant) instability dominates on the attractive side, it is absent for repulsive interactions, where the competition is instead won by non-superradiant superfluid phases at low temperatures, with Fermion pairs forming at both vanishing and finite center-of-mass momentum. Moreover, even in the absence of such symmetry-breaking instabilities, we find the Fermi surface to be always nontrivially deformed from an isotropic shape. We estimate this full phenomenology to be within reach of dedicated state-of-the-art experimental setups.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes competing instabilities in an ultracold Fermi gas coupled to a single-wave-vector cavity mode that induces a spatially modulated infinite-range interaction. It claims a full solution showing that the density-wave (superradiant) instability dominates for attractive interactions at zero distance, while for repulsive interactions this instability is absent and non-superradiant superfluid phases win at low temperatures, with fermion pairing at both zero and finite center-of-mass momentum. The Fermi surface is reported to be nontrivially deformed from isotropy even without symmetry breaking, with the full phenomenology estimated to be experimentally accessible.

Significance. If the central results hold, the work delivers a complete phase diagram for this cavity-mediated interaction with no direct analog in other itinerant systems, cleanly separating attractive and repulsive regimes and identifying a deformed Fermi surface as a generic feature. Credit is due for the direct solution of the model equations against external physical regimes and for generating falsifiable predictions for state-of-the-art cavity QED experiments with fermions.

major comments (2)
  1. [§2] §2 (model definition): the central claim that the repulsive regime is free of density-wave instability and instead hosts non-superradiant superfluid phases at zero and finite COM momentum requires explicit confirmation that the effective interaction remains purely single-wave-vector and infinite-range when its sign at zero distance is reversed; if the microscopic cavity-QED derivation introduces additional momentum components or range corrections for repulsive detuning, the reported separation of regimes would not follow.
  2. [§4] §4 (repulsive-side results): the statement that the competition is won by superfluid phases rests on the absence of superradiant instability; the specific criterion (e.g., the eigenvalue spectrum of the density-wave susceptibility or the self-consistent gap equations) used to establish this absence must be shown explicitly, together with the numerical or analytic method that locates the superfluid transition lines.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'we fully solve the problem' is strong; a one-sentence summary of the method (mean-field ansatz, functional integral, etc.) would help readers assess the scope of the solution.
  2. [Figure 3] Figure 3 (or equivalent phase diagram): the boundaries between the reported superfluid phases and the normal state should be labeled with the precise order parameters (pairing momentum, etc.) for immediate readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and for identifying points where additional clarification would strengthen the manuscript. We address the two major comments below and will incorporate the requested details in a revised version.

read point-by-point responses

  1. Referee: [§2] §2 (model definition): the central claim that the repulsive regime is free of density-wave instability and instead hosts non-superradiant superfluid phases at zero and finite COM momentum requires explicit confirmation that the effective interaction remains purely single-wave-vector and infinite-range when its sign at zero distance is reversed; if the microscopic cavity-QED derivation introduces additional momentum components or range corrections for repulsive detuning, the reported separation of regimes would not follow.

    Authors: The effective interaction is obtained from the single-mode cavity QED Hamiltonian in the dispersive regime. The atom-cavity coupling generates an infinite-range interaction whose spatial dependence is fixed by the cavity mode function (a single wave vector set by the cavity geometry). The overall sign of the interaction is controlled by the atom-cavity detuning; reversing this sign does not alter the momentum content or introduce additional Fourier components. The same single-wave-vector form therefore applies on both sides of the resonance. We will add a short paragraph in §2 that explicitly states this point and references the microscopic derivation. revision: yes

  2. Referee: [§4] §4 (repulsive-side results): the statement that the competition is won by superfluid phases rests on the absence of superradiant instability; the specific criterion (e.g., the eigenvalue spectrum of the density-wave susceptibility or the self-consistent gap equations) used to establish this absence must be shown explicitly, together with the numerical or analytic method that locates the superfluid transition lines.

    Authors: The density-wave susceptibility is obtained from the static Lindhard response of the deformed Fermi surface; its largest eigenvalue remains finite throughout the repulsive regime, confirming the absence of a superradiant instability. The superfluid transition lines are determined by solving the self-consistent gap equations for both zero-momentum and finite-center-of-mass-momentum pairing channels, with the critical temperature identified as the point where the largest eigenvalue of the linearized gap equation reaches unity. We will include the explicit expressions for the susceptibility and the numerical procedure (including convergence checks) in the revised §4 and the associated supplementary material. revision: yes

Circularity Check

0 steps flagged

No circularity: direct solution of model equations against tunable interaction sign

full rationale

The paper states it fully solves the competing instabilities of the Fermi surface for a single-wave-vector infinite-range interaction whose sign is independently tunable. The attractive-side dominance of density-wave instability versus repulsive-side non-superradiant superfluid phases (zero and finite COM momentum) plus always-deformed Fermi surface follow from solving the model equations under those stated assumptions. No self-definitional steps, no fitted parameters renamed as predictions, and no load-bearing self-citations appear in the derivation chain. The sign tunability is an input of the cavity-QED setup rather than a result derived from the target phenomenology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on a cavity-induced interaction model with single wave vector and infinite range; no free parameters or invented entities are mentioned in the abstract, but the interaction form itself is a domain assumption.

axioms (1)
  • domain assumption Cavity electromagnetic field induces spatially modulated infinite-range interaction with single wavelength comparable to Fermi length
    Stated directly in the abstract as the starting physical setup.

pith-pipeline@v0.9.0 · 5707 in / 1340 out tokens · 48299 ms · 2026-05-22T14:07:19.480551+00:00 · methodology

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Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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Reference graph

Works this paper leans on

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