pith. sign in

arxiv: 2504.01885 · v2 · submitted 2025-04-02 · ❄️ cond-mat.quant-gas · cond-mat.str-el· quant-ph

Observing Spatial Charge and Spin Correlations in a Strongly-Interacting Fermi Gas

Cyprien Daix , Maxime Dixmerias , Yuan-Yao He , Joris Verstraten , Tim de Jongh , Bruno Peaudecerf , Shiwei Zhang , Tarik Yefsah This is my paper

Pith reviewed 2026-05-22 21:48 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-elquant-ph
keywords two-dimensional Fermi gasquantum gas microscopypair correlation functionBCS theoryquantum Monte CarloTan's contactnonlocal anticorrelationscharge and spin correlations
0
0 comments X

The pith

Atom-resolved microscopy of 2D Fermi gases detects nonlocal anticorrelations in pair correlations that BCS mean-field theory forbids.

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

This paper measures spatial charge and spin correlations directly in a two-dimensional attractive Fermi gas using atom-resolved imaging. It shows that the pair correlation function exhibits nonlocal anticorrelations whose existence is ruled out by the standard BCS mean-field approach but is recovered in exact auxiliary-field quantum Monte Carlo simulations. The measurements also establish a direct relation between two-point and three-point correlation functions that highlights the dominant role of pairing, and they extract Tan's contact from short-range pair losses in agreement with numerics. A sympathetic reader would care because these results demonstrate that even the weakly attractive regime lies outside the reach of mean-field theory and supply a microscopic benchmark for strongly correlated fermions in the continuum.

Core claim

Using atom-resolved continuum quantum gas microscopy on a two-dimensional attractive Fermi gas, the authors observe fermion pairing and track the evolution of two- and three-point correlation functions with increasing inter-spin attraction. Their precision reveals nonlocal anticorrelations in the pair correlation function that are fundamentally excluded by the mean-field BCS result yet are reproduced by auxiliary-field quantum Monte Carlo calculations. The data further show that the BCS description fails not only in the superfluid crossover but also deep in the weakly attractive regime, while a simple relation between two- and three-point correlations underscores the dominance of pair-correl

What carries the argument

Atom-resolved continuum quantum gas microscopy that records in-situ spatial charge and spin correlations, together with the pair correlation function whose nonlocal anticorrelations are compared to BCS and QMC predictions.

If this is right

  • BCS mean-field theory is insufficient for describing pair correlations even on the weakly attractive side of the 2D Fermi gas.
  • Pair correlations dominate the relation between two- and three-point functions across the interaction range studied.
  • Tan's contact extracted from local pair losses matches numerical predictions, confirming the short-range behavior of the measured correlations.
  • The same microscopy approach can be applied to other continuum fermionic systems to test mean-field predictions directly.
  • The observed breakdown of BCS supplies a concrete benchmark that any improved theory of 2D Fermi gases must satisfy.

Where Pith is reading between the lines

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

  • The same microscopy technique could be used to test whether similar nonlocal anticorrelations appear in three-dimensional Fermi gases or in lattice systems near the superfluid transition.
  • If the relation between two- and three-point correlations holds more generally, it may simplify the analysis of pairing in other strongly interacting fermionic platforms.
  • The discrepancy with BCS even at weak attraction suggests that fluctuation corrections or beyond-mean-field effects are required at all couplings in two dimensions.
  • Extending the measurement to finite temperature or spin-imbalanced gases could reveal how the anticorrelations evolve across the phase diagram.

Load-bearing premise

The imaging faithfully records the true in-situ spatial correlations without resolution limits, density distortions, or other artifacts that could fabricate the reported nonlocal anticorrelations.

What would settle it

A repeat measurement with higher imaging resolution or an independent probe that shows the nonlocal anticorrelations disappear or match the BCS prediction exactly would falsify the central claim.

Figures

Figures reproduced from arXiv: 2504.01885 by Bruno Peaudecerf, Cyprien Daix, Joris Verstraten, Maxime Dixmerias, Shiwei Zhang, Tarik Yefsah, Tim de Jongh, Yuan-Yao He.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: , which we compare to zero-temperature AFQMC calculations [33], finding excellent agreement over three orders of magnitude. The comparison obtained here sets a new standard of cross-validation between experimen￾tal measurements and high precision computations for microscopic phenomena in continuum systems. We have probed an interacting Fermi gas with tuneable inter-spin attraction via atom-resolved in￾situ… view at source ↗
read the original abstract

In this work, we explore two-dimensional attractive Fermi gases at the microscopic level by probing spatial charge and spin correlations in situ. Using atom-resolved continuum quantum gas microscopy, we directly observe fermion pairing and study the evolution of two- and three-point correlation functions as inter-spin attraction is increased. The precision of our measurement allows us to reveal nonlocal anticorrelations in the pair correlation function, fundamentally forbidden by the mean-field result based on Bardeen-Cooper-Schrieffer (BCS) theory but whose existence we confirm in exact auxiliary-field quantum Monte Carlo calculations. We demonstrate that the BCS prediction is critically deficient not only in the superfluid crossover regime but also deep in the weakly attractive side. Guided by our measurements, we find a remarkable relation between two- and three-point correlations that establishes the dominant role of pair-correlations. Finally, leveraging local single-pair losses, we independently characterize the short-range behavior of pair correlations, via the measurement of Tan's Contact, and find excellent agreement with numerical predictions. Our measurements provide an unprecedented microscopic view into two-dimensional Fermi gases and constitute a paradigm shift for future studies of strongly-correlated fermionic matter in the continuum.

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

0 major / 3 minor

Summary. The manuscript reports in-situ atom-resolved measurements of spatial charge and spin correlations in two-dimensional attractive Fermi gases via continuum quantum gas microscopy. It observes the evolution of two- and three-point correlation functions with increasing attraction, reveals nonlocal anticorrelations in the pair correlation function (forbidden by BCS mean-field but confirmed by independent auxiliary-field QMC), identifies a relation between two- and three-point correlations that highlights the dominant role of pairs, and extracts Tan's Contact from local pair losses in agreement with numerics.

Significance. If the central observations hold, the work supplies a direct microscopic probe of pairing and correlations in the 2D Fermi gas across the crossover, demonstrating BCS deficiencies even in the weakly attractive regime and establishing an experimental-numerical benchmark via QMC cross-validation on the reported anticorrelations and the two-to-three-point relation. The independent Tan's Contact measurement adds a further consistency check. These elements constitute a concrete advance for continuum studies of strongly correlated fermions.

minor comments (3)
  1. [Abstract] Abstract: the claim of a 'paradigm shift' is presentationally strong; a more measured phrasing such as 'opens new avenues for' would align better with the concrete results shown.
  2. Ensure that all panels in figures displaying g2(r) and three-point functions include explicit scale bars for the imaging resolution and state the binning or smoothing applied to the correlation data.
  3. Section on Tan's Contact extraction: clarify the precise definition of the local pair-loss rate used and how it is converted to the contact without additional fitting parameters.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. There are no major comments requiring a point-by-point response.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper reports direct experimental measurements of two- and three-point spatial correlations via atom-resolved quantum gas microscopy in a 2D attractive Fermi gas, with the key observations (nonlocal anticorrelations forbidden by BCS mean-field) compared against independent auxiliary-field QMC simulations. No load-bearing step reduces to a fitted parameter, self-definition, or self-citation chain; the two-to-three-point relation and Tan's contact extraction are presented as data-driven findings without internal redefinition or renaming of inputs as predictions. The central claims rest on external experimental-numerical agreement rather than any closed derivation loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard assumptions of ultracold-atom physics and the accuracy of auxiliary-field QMC for the continuum Fermi gas model; no new free parameters, ad-hoc axioms, or invented entities are introduced.

axioms (2)
  • standard math Standard quantum mechanics and statistical mechanics apply to the ultracold Fermi gas.
    Background framework for the entire experiment and simulations.
  • domain assumption Auxiliary-field quantum Monte Carlo provides exact results for the model Hamiltonian used.
    Invoked to confirm the experimental anticorrelations and Tan's Contact.

pith-pipeline@v0.9.0 · 5771 in / 1285 out tokens · 38251 ms · 2026-05-22T21:48:39.875246+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Multi-state detection and spatial addressing in a microscope for ultracold molecules

    cond-mat.quant-gas 2025-06 conditional novelty 7.0

    Demonstration of single-molecule resolution imaging, multi-state detection, and spatial addressing for ultracold RbCs molecules via lattice pinning and atomic fluorescence.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · cited by 1 Pith paper

  1. [1]

    Gross and W

    C. Gross and W. S. Bakr, Nature Physics17, 1316 (2021)

    work page 2021

  2. [2]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pear- son, M. Troyer, and P. Zoller, Nature607, 667 (2022)

    work page 2022

  3. [3]

    Levinsen and M

    J. Levinsen and M. M. Parish, inAnnual Review of Cold Atoms and Molecules, Annual Review of Cold Atoms and Molecules, Vol. Volume 3 (WORLD SCIENTIFIC,

    work page

  4. [4]

    M. G. Ries, A. N. Wenz, G. Z¨ urn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, Physical Review Letters114, 230401 (2015)

    work page 2015

  5. [5]

    Sobirey, N

    L. Sobirey, N. Luick, M. Bohlen, H. Biss, H. Moritz, and T. Lompe, Science372, 844 (2021)

    work page 2021

  6. [6]

    M. Feld, B. Fr¨ ohlich, E. Vogt, M. Koschorreck, and M. K¨ ohl, Nature480, 75 (2011)

    work page 2011

  7. [7]

    Bauer, M

    M. Bauer, M. M. Parish, and T. Enss, Physical Review Letters112, 135302 (2014)

    work page 2014

  8. [8]

    P. A. Murthy, M. Neidig, R. Klemt, L. Bayha, I. Boettcher, T. Enss, M. Holten, G. Z¨ urn, P. M. Preiss, and S. Jochim, Science359, 452 (2018)

    work page 2018

  9. [9]

    Fischer, M

    Ø. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, Reviews of Modern Physics79, 353 (2007)

    work page 2007

  10. [10]

    N. D. Mermin and H. Wagner, Physical Review Letters 17, 1133 (1966)

    work page 1966

  11. [11]

    V. L. Berezinsky, Sov. Phys. JETP32, 493 (1971)

    work page 1971

  12. [12]

    J. M. Kosterlitz and D. J. Thouless, Journal of Physics C: Solid State Physics6, 1181 (1973)

    work page 1973

  13. [13]

    Hadzibabic and J

    Z. Hadzibabic and J. Dalibard, La Rivista del Nuovo Cimento34, 389 (2011)

    work page 2011

  14. [14]

    C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, Nature 470, 236 (2011)

    work page 2011

  15. [15]

    Yefsah, R

    T. Yefsah, R. Desbuquois, L. Chomaz, K. J. G¨ unter, and J. Dalibard, Physical Review Letters107, 130401 (2011)

    work page 2011

  16. [16]

    Holten, L

    M. Holten, L. Bayha, A. C. Klein, P. A. Murthy, P. M. Preiss, and S. Jochim, Physical Review Letters121, 120401 (2018)

    work page 2018

  17. [17]

    P. A. Murthy, N. Defenu, L. Bayha, M. Holten, P. M. Preiss, T. Enss, and S. Jochim, Science365, 268 (2019)

    work page 2019

  18. [18]

    Fulde and R

    P. Fulde and R. A. Ferrell, Physical Review135, A550 (1964)

    work page 1964

  19. [19]

    A. I. Larkin and Y. N. Ovchinnikov, Soviet Physics- JETP20, 762 (1965)

    work page 1965

  20. [20]

    Vitali, P

    E. Vitali, P. Rosenberg, and S. Zhang, Physical Review Letters128, 203201 (2022)

    work page 2022

  21. [21]

    P. Dyke, E. D. Kuhnle, S. Whitlock, H. Hu, M. Mark, S. Hoinka, M. Lingham, P. Hannaford, and C. J. Vale, Physical Review Letters106, 105304 (2011)

    work page 2011

  22. [22]

    Fr¨ ohlich, M

    B. Fr¨ ohlich, M. Feld, E. Vogt, M. Koschorreck, W. Zw- erger, and M. K¨ ohl, Physical Review Letters106, 105301 (2011)

    work page 2011

  23. [23]

    Makhalov, K

    V. Makhalov, K. Martiyanov, and A. Turlapov, Physical Review Letters112, 045301 (2014)

    work page 2014

  24. [24]

    Fenech, P

    K. Fenech, P. Dyke, T. Peppler, M. G. Lingham, S. Hoinka, H. Hu, and C. J. Vale, Physical Review Let- ters116, 045302 (2016)

    work page 2016

  25. [25]

    Boettcher, L

    I. Boettcher, L. Bayha, D. Kedar, P. A. Murthy, M. Nei- dig, M. G. Ries, A. N. Wenz, G. Z¨ urn, S. Jochim, and T. Enss, Physical Review Letters116, 045303 (2016)

    work page 2016

  26. [26]

    Bohlen, L

    M. Bohlen, L. Sobirey, N. Luick, H. Biss, T. Enss, T. Lompe, and H. Moritz, Physical Review Letters124, 240403 (2020)

    work page 2020

  27. [27]

    P. A. Murthy, I. Boettcher, L. Bayha, M. Holzmann, D. Kedar, M. Neidig, M. G. Ries, A. N. Wenz, G. Z¨ urn, and S. Jochim, Physical Review Letters115, 010401 (2015)

    work page 2015

  28. [28]

    A. T. Sommer, L. W. Cheuk, M. J. H. Ku, W. S. Bakr, and M. W. Zwierlein, Physical Review Letters 108, 045302 (2012)

    work page 2012

  29. [29]

    Fr¨ ohlich, M

    B. Fr¨ ohlich, M. Feld, E. Vogt, M. Koschorreck, M. K¨ ohl, C. Berthod, and T. Giamarchi, Physical Review Letters 109, 130403 (2012)

    work page 2012

  30. [30]

    Sobirey, H

    L. Sobirey, H. Biss, N. Luick, M. Bohlen, H. Moritz, and T. Lompe, Physical Review Letters129, 083601 (2022)

    work page 2022

  31. [31]

    Brandstetter, P

    S. Brandstetter, P. Lunt, C. Heintze, G. Giacalone, L. H. Heyen, M. Ga lka, K. Subramanian, M. Holten, P. M. Preiss, S. Floerchinger, and S. Jochim, Nature Physics21, 52 (2025)

    work page 2025

  32. [32]

    Brandstetter, C

    S. Brandstetter, C. Heintze, K. Subramanian, P. Hill, P. M. Preiss, M. Ga lka, and S. Jochim, Magnifying the Wave Function of Interacting Fermionic Atoms (2024), arXiv:2409.18954

    work page arXiv 2024

  33. [33]

    H. Shi, S. Chiesa, and S. Zhang, Physical Review A92, 033603 (2015)

    work page 2015

  34. [34]

    Vitali, H

    E. Vitali, H. Shi, M. Qin, and S. Zhang, Physical Review A96, 061601 (2017)

    work page 2017

  35. [35]

    Y.-Y. He, H. Shi, and S. Zhang, Physical Review Letters 123, 136402 (2019)

    work page 2019

  36. [36]

    Y.-Y. He, H. Shi, and S. Zhang, Physical Review Letters 129, 076403 (2022)

    work page 2022

  37. [37]

    A. M. Fischer and M. M. Parish, Physical Review B90, 214503 (2014)

    work page 2014

  38. [38]

    Additional details can be found in the Supplementary Materials

    work page

  39. [39]

    D. S. Petrov and G. V. Shlyapnikov, Physical Review A 64, 012706 (2001)

    work page 2001

  40. [40]

    Pricoupenko and M

    L. Pricoupenko and M. Olshanii, Journal of Physics B: Atomic, Molecular and Optical Physics40, 2065 (2007). 7

    work page 2065

  41. [41]

    Verstraten, K

    J. Verstraten, K. Dai, M. Dixmerias, B. Peaudecerf, T. de Jongh, and T. Yefsah, Physical Review Letters 134, 083403 (2025)

    work page 2025

  42. [42]

    de Jongh, J

    T. de Jongh, J. Verstraten, M. Dixmerias, C. Daix, B. Peaudecerf, and T. Yefsah, Quantum Gas Microscopy of Fermions in the Continuum (2024), arXiv:2411.08776

    work page arXiv 2024

  43. [43]

    J. C. Obeso-Jureidini and V. Romero-Roch´ ın, Physical Review A105, 043307 (2022)

    work page 2022

  44. [44]

    Zujev, R

    A. Zujev, R. T. Scalettar, G. G. Batrouni, and P. Sen- gupta, New Journal of Physics16, 013004 (2014)

    work page 2014

  45. [45]

    R. A. Fontenele, N. C. Costa, T. Paiva, and R. R. dos Santos, Physical Review A110, 053315 (2024)

    work page 2024

  46. [46]

    Werner and X

    F. Werner and X. Leyronas, Comptes Rendus. Physique 25, 179 (2024)

    work page 2024

  47. [47]

    J. R. Engelbrecht, M. Randeria, and L. Zhang, Physical Review B45, 10135 (1992)

    work page 1992

  48. [48]

    Werner and Y

    F. Werner and Y. Castin, Physical Review A86, 013626 (2012)

    work page 2012

  49. [49]

    Tan, Annals of Physics323, 2952 (2008)

    S. Tan, Annals of Physics323, 2952 (2008)

    work page 2008

  50. [50]

    R. Yao, S. Chi, M. Wang, R. J. Fletcher, and M. Zwierlein, Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy (2024), arXiv:2411.08780 [cond-mat]

    work page arXiv 2024

  51. [51]

    Xiang, E

    J. Xiang, E. Cruz-Col´ on, C. C. Chua, W. R. Milner, J. de Hond, J. F. Fricke, and W. Ketterle, In situ imag- ing of the thermal de Broglie wavelength in an ultracold Bose gas (2024), arXiv:2411.08779 [cond-mat]

    work page arXiv 2024

  52. [52]

    S. Jin, K. Dai, J. Verstraten, M. Dixmerias, R. Alhyder, C. Salomon, B. Peaudecerf, T. De Jongh, and T. Yefsah, Physical Review Research6, 013158 (2024)

    work page 2024

  53. [53]

    Dixmerias, J

    M. Dixmerias, J. Verstraten, C. Daix, B. Peaudecerf, T. de Jongh, and T. Yefsah, Fluctuation thermometry of an atom-resolved quantum gas: Beyond the fluctuation- dissipation theorem (2025), arXiv:2502.05132 [cond- mat]

    work page arXiv 2025

  54. [54]

    Zhou and T.-L

    Q. Zhou and T.-L. Ho, Physical Review Letters106, 225301 (2011)

    work page 2011

  55. [55]

    Hartke, B

    T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Physical Review Letters125, 113601 (2020)

    work page 2020

  56. [56]

    D. S. Petrov, M. A. Baranov, and G. V. Shlyapnikov, Physical Review A67, 031601 (2003). 8 SUPPLEMENT AR Y MA TERIALS Experimental Sequence The experimental setup was described in detail in [41, 52]. The experiment starts with a balanced mixture of 6Li atoms in the first and third lowest-energy hyper- fine states denoted|1⟩ ≡ |↑⟩and|3⟩ ≡ |↓⟩in a ’light she...

    work page 2003