Pith. sign in

REVIEW 2 major objections 5 minor 83 references

Fluctuation thermometry of an atom-resolved quantum gas: Beyond the fluctuation-dissipation theorem

T0 review · 2 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Atom-count noise alone fixes the temperature of a quantum gas.

desk verdict A convincing demonstration of correlation-based fluctuation thermometry on an ideal Fermi gas, with the main caveat that the advertised universality and out-of-equilibrium reach outpace the evidence. read the letter →

arxiv 2502.05132 v1 pith:CMTZOLMV submitted 2025-02-07 cond-mat.quant-gas cond-mat.stat-mechphysics.atom-phquant-ph

Maxime Dixmerias , Joris Verstraten , Cyprien Daix , Bruno Peaudecerf , Tim de Jongh , Tarik Yefsah This is my paper · ORCID
classification cond-mat.quant-gascond-mat.stat-mechphysics.atom-phquant-ph
keywords ultracoldFermigasquantummicroscopyfluctuationthermometrydensity-densitycorrelationssub-extensivefluctuationslocalgrand-canonicalensembleg2correlationfunction
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 introduces a thermometer for ultracold quantum gases that reads the temperature directly from single-atom-resolved images, without fitting the trapping potential and without assuming the whole cloud is one thermal sample. The central quantity is the exact relation between the atom-number variance $\Delta N^2$ in a small probe volume and the two-atom correlation function $g_2$; when $g_2$ is known as a function of density and temperature, a measured pair $(\langle N\rangle, \Delta N^2)$ corresponds to exactly one temperature. On a quasi-two-dimensional ideal Fermi gas, the authors demonstrate this over reduced temperatures $T/T_F$ from $0.29(1)$ to $3.6(3)$, and show that the same variance curve gives consistent global and local temperatures down to the scale of the inter-particle spacing. The method also separates the fluctuation-dissipation contribution from a sub-extensive part $\Delta Q$, which is shown to match an exact cross-correlation formula without fitting. If these results hold, thermometry of quantum gases becomes local, calibration-free, and applicable to homogeneous or out-of-equilibrium systems.

What carries the argument

The load-bearing identity is Eq. (2): the variance of the atom number in $S$ is rewritten exactly as $\langle N\rangle$ minus the integrated pair-exclusion integral $n^2\int_S\int_S[1-g_2(r_1,r_2)]\,dr_1dr_2$, where $g_2$ is the normalized two-point density-density correlation function. Because $g_2$ for the ideal Fermi gas is known and depends on the dimensionless products $k_F r$ and $T/T_F$, the variance becomes a function of $\langle N\rangle$ and $T$ only, and the monotone rise of $\Delta N^2$ with $T$ at fixed $\langle N\rangle$ makes the inversion unique. The local-density approximation then reads the trapped cloud as many homogeneous samples, so a single modulation-time preparation yields a full $\Delta N^2$-versus-$\langle N\rangle$ curve, and the vertical motion is handled by summing the variances of the occupied $z$-levels with populations $p_\nu$ fixed by $\mu$, $T$, and $\omega_z$. For the sub-extensive part, the same correlation function is integrated across the boundary between $S$ and its complement, giving Eq. (5) for $\Delta Q$.

What would settle it

Prepare the same cloud, modulate the light sheet for 160 ms, but hold for only a short time (well under the measured 1.4 s relaxation) before removing one spin and imaging; under local equilibrium the temperatures extracted from probe volumes at different positions should disagree and track the vertical-energy imbalance, so any single consistent temperature across all probes would contradict the assumption and invalidate the inversion.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the exact identity $$\$\Delta$ $N^{2}$ = \langle N\rangle - $n^{2}$ \int_S \int_S [1-g_2(r_1,r_2)]\,dr_1 dr_2$$ turns two measured numbers, the average atom number $\langle N\rangle$ and the variance $\Delta N^2$ in a probe volume $S$, into a one-to-one thermometer. For an ideal Fermi gas, $g_2$ depends only on $k_F r$ and $T/T_F$, hence only on $\langle N\rangle$ and $T$, so each measured pair selects a unique temperature. The authors verify their temperatures by computing $g_2$ from the same images at the extracted $T$ and finding agreement without any fitting parameter, and they apply the method at probe sizes down to the Fermi-hole diameter. Separately, they isolate the sub-extensive correction $\Delta Q = \Delta N^2 - k_B T\, \partial\langle N\rangle/\partial\mu|_T$, derive the exact expression $\Delta Q = n^2 \int_S dr_1 \int_{\overline S} dr_2\,[1-g_2(r_1,r_2)]$, and show that the measured $\Delta Q$ follows that expression from the quantum-degenerate to the classical regime. The paper's broader assertion is that any system whose density-density correlation function can be computed, analytically or numerically, inherits a local and global thermometer from this relation alone.

Load-bearing premise

The method assumes each atom-resolved probe volume is locally at thermal equilibrium at one temperature, so the two-atom correlation function $g_2$ depends only on density and that temperature; if local equilibrium fails, the measured pair $(\langle N\rangle, \Delta N^2)$ cannot be inverted to a unique $T$.

Editorial extensions

If this is right

  • The global temperature of a trapped cloud is obtained from one fit of all probe volumes simultaneously, making the result stable against local deviations and sensitive to incomplete thermalization.
  • Local thermometry at the scale of the Fermi hole is demonstrated for $T/T_F$ from $0.29(1)$ to $2.6(2)$, so temperature maps can be built across a spatially inhomogeneous sample.
  • Because the method requires neither global equilibrium nor trap calibration, it extends to homogeneous systems and to out-of-equilibrium configurations such as quenches or heat-transport experiments, where standard density-profile fitting fails.
  • The measured $\Delta Q$ and the exact formula (5) give an experimental window on sub-extensive fluctuations, showing that the fluctuation-dissipation term alone is insufficient in small probe volumes at low temperature.
  • Any system with a computable $g_2$, including interacting one-dimensional gases, two-dimensional BKT superfluids, and lattice or continuum models accessible to quantum Monte Carlo, inherits this thermometer, as do phase-separated systems whose outer trivial reservoir can serve as the probe.

Reading between the lines

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

  • A natural extension the authors leave implicit: at known temperature, the variance curve can be inverted to constrain $g_2$ itself, turning the apparatus into a correlation-function microscope for interacting systems where $g_2$ is not known analytically.
  • The uniqueness of the inversion relies on monotonicity of $\Delta N^2$ with $T$ at fixed $\langle N\rangle$; systems with non-monotonic variance, for instance near a phase transition, would need a third joint observable to select $T$.
  • Because $\Delta Q$ is a cross-correlation between the probe and its complement, spatially resolved measurements of it could map non-local or entanglement-related fluctuations across a sample, connecting this thermometer to quantum-information observables.
  • A direct testable extension is to apply the method while the cloud is still relaxing after the heating modulation and check whether the local-temperature map tracks the vertical-energy imbalance; disagreement would quantify how far the local-equilibrium assumption is from holding.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper introduces a thermometry method for ultracold quantum gases based on the exact relation between atom-number fluctuations in a probe volume and the two-particle density correlation function g2 (Eq. (2)). The authors demonstrate the method on a quasi-two-dimensional ideal Fermi gas imaged with continuum quantum gas microscopy. They extract global temperatures from fits of the variance-versus-mean curve with temperature as the sole free parameter, over reduced temperatures T/T_F from 0.29(1) to 3.6(3), and verify the results by comparing the measured g2 to theory without additional fitting. They further demonstrate local thermometry down to probe volumes comparable to the Fermi-hole diameter, and use the method to isolate a sub-extensive contribution ΔQ to the number fluctuations beyond the fluctuation-dissipation term, comparing it to numerical and asymptotic predictions.

Significance. If the central claims hold, the paper provides a valuable addition to ultracold-atom thermometry: it replaces the fluctuation-dissipation approximation with an exact correlation-based identity, works for arbitrary trapping geometries without precise trap calibration, and gives local temperatures at the scale of the correlation length. The experimental validation is notably strong in several respects: the Eq. (2) identity is exact and cleanly derived; the classical-gas data fall on the parameter-free Poissonian line; the g2 comparison in Fig. S2 is made without fitting parameters; and the dynamic range of degeneracy is broad. These strengths make the core method credible for locally equilibrated ideal Fermi gases.

major comments (2)
  1. [Abstract, Discussion, Conclusion; after Eq. (2)] The claims that the method does not require global thermal equilibrium and extends thermometry to gases 'far out-of-equilibrium' overstate what is demonstrated. The inversion of Eq. (2) to a temperature is valid only 'provided it is locally at thermal equilibrium' (stated immediately after Eq. (2)), and this condition is checked in Fig. S1 only for the longest modulation time (160 ms) and only through the in-plane width σxy. The collapse of the variance data onto a single curve is an indirect necessary condition, not a sufficient test of local equilibrium; a non-thermal momentum distribution would make g2 depend on more than (n, T) and render the extracted 'temperature' ambiguous. The authors should qualify the universality claims to locally equilibrated systems or provide additional evidence supporting the broader 'far out-of-equilibrium' statement.
  2. [Fig. 4 and Eq. (5)] The agreement between the measured ΔQ and the theoretical prediction from Eq. (5) is partly by construction. The measured ΔQ is obtained by subtracting kBT ∂⟨N⟩/∂μ|T from the measured ΔN², using the temperature T extracted from the variance fit to Eq. (2). Because Eq. (4) is an exact identity, this construction forces the measured ΔQ to match the right-hand side of Eq. (5) evaluated at the same T and density. The 'without fitting parameter' statement in the Fig. 4 caption is technically true but the comparison is a consistency check, not an independent validation of the theory. The empirical observation that ΔQ is positive and decreases with T remains valid, but the claim of 'excellent agreement' should be reframed, or an independently determined T (for example from the g2 comparison in Fig. S2) should be used to construct both the data points and the theory curve.
minor comments (5)
  1. [Fig. 3 caption] Typo: 'reprents' should be 'represents'.
  2. [Supplementary Materials, 'Influence of the Probe Volume'] Typo: 'spacial' should be 'spatial'.
  3. [Fig. 1b caption] The assertion that 'for a given ⟨N⟩, ΔN² monotonically increases with T' is used to justify the uniqueness of the inversion, but no proof or reference is provided; a brief derivation or citation would make the uniqueness claim rigorous.
  4. [Local Thermometry section] The statement that 'there is no formal limitation to how small the system S can be' is later qualified in the Supplementary Materials by the pinning-lattice constraint (L ≳ aL); the wording in the main text should be reconciled with this practical limitation.
  5. [Fig. S2] The g2 comparison in the first row of Fig. S2 is shown only for the central region of the cloud; a sentence stating whether the agreement holds across the full cloud would clarify the spatial robustness of the temperature determination.

Circularity Check

1 steps flagged · score 6.0 of 10

Sub-extensive fluctuation 'measurement' in Fig. 4 reduces to the fit: ΔQ data and Eq. (5) theory are identical functions of the same fitted T and g2.

  1. fitted input called prediction [Main text, 'Sub-extensive fluctuation measurement', page 5, and Fig. 4 caption; Supplementary Eqs. (S3)-(S6)]
    "The ∆Q data is obtained by subtracting the extensive term kBT ∂⟨N ⟩/∂µ |T from the total fluctuation in Eq. (4). ... the solid lines going through the ∆Q = f (⟨N ⟩) data is the theoretical prediction from Eq. (5) without fitting parameter."

    T is first obtained by fitting Eq. (2) to the measured ΔN² using the theoretical g2, so T already encodes the g2-based relation between variance and density. The extensive term subtracted to define the ΔQ 'data' is computed from this same fitted T. The Supplementary then proves (Eq. S3 to S6) that ΔQ is exactly n²∫S∫S̄ [1−g2], i.e. Eq. (5). Therefore the solid 'theory' line and the 'measured' ΔQ points are the same function of the same fitted T and the same g2; the agreement is forced up to fit residuals and is not an independent confirmation of the sub-extensive fluctuation theory.

full rationale

The core thermometer is not circular: Eq. (2) uses an independently known g2 for the ideal Fermi gas, T is the sole fitting parameter, and the classical Poissonian limit and the measured g2(r) comparison provide genuine external checks. Self-citations for the imaging method and g2 are not load-bearing for the thermodynamic derivation. The local-equilibrium requirement is a scope limitation, not a circular step. However, the paper's sub-extensive fluctuation result is circular: 'measured' ΔQ is defined by subtracting kBT∂⟨N⟩/∂μ evaluated at the T fitted from the same variance data, while Eq. (5) is an exact identity expressing ΔQ as an integral of the same g2 at that T. The excellent agreement in Fig. 4b is therefore a restatement of the fit plus the identity, not a new prediction. This warrants partial circularity: the headline thermometry stands, but one central claim reduces by construction.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The derivation is mathematically economical: it uses exact identities and known correlation functions, and the only fitted number is the temperature itself, which is the measured output. The main burden lies in the domain assumptions: local density approximation, local thermal equilibrium, grand-canonical description, quasi-2D level populations, and imaging fidelity. No new physical entities are introduced.

free parameters (1)
  • global temperature T = 33(1) to 136(14) nK across tmod=0 to 160 ms
    Sole fitting parameter in the variance-versus-mean fit based on Eq. (2) and Eq. (S2). It is the measured output of the thermometer, not a hidden nuisance parameter, but the central claim depends on it and its uncertainty propagates into all derived quantities.
assumptions (6)
  • standard math The variance of atom number in a subsystem equals ⟨N⟩ - n² ∫∫_S [1 - g2(r1,r2)] dr1 dr2 (Eq. 2).
    Exact identity from the definition of variance in terms of density-density correlations; it is the foundation of the thermometer.
  • domain assumption For a non-interacting Fermi gas, g2 depends only on kF r and T/TF and satisfies g2 = 1 - g1² via Wick's theorem.
    Used to map a measured pair (⟨N⟩, ΔN²) to a unique temperature. This is exact for the ideal Fermi gas considered but is not universal.
  • domain assumption The local density approximation applies in the shallow xy-plane trap, so each probe volume behaves as a homogeneous system.
    Used throughout Global Thermometry to interpret spatial regions as homogeneous samples with different densities.
  • domain assumption Each probe volume is locally at thermal equilibrium and the total system is described by the grand-canonical ensemble.
    Required for Eq. (2) to act as a thermometer and for the derivation of ΔQ in Eq. (5). The paper states this as 'provided it is locally at thermal equilibrium'.
  • domain assumption The quasi-2D gas is treated with discrete vertical harmonic oscillator levels, and the populations pν are given by Eq. (S1).
    Used to generalize the purely 2D g2 calculation to the measured quasi-2D gas; depends on the experimentally measured ωz and on thermalization.
  • domain assumption Pinning and Raman sideband cooling preserve the in-situ density distribution with near-100% fidelity.
    The measured images are assumed to reflect the in-situ gas; the supplementary reports a pinning fidelity exceeding 99.9%, but the variance analysis relies on this.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Fluctuation thermometry of an atom-resolved quantum gas: Beyond the fluctuation-dissipation theorem." pith.science (2026). https://pith.science/paper/CMTZOLMV

@misc{pith2026250205132,
  author       = {Pith},
  title        = {Pith review of: Fluctuation thermometry of an atom-resolved quantum gas: Beyond the fluctuation-dissipation theorem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CMTZOLMV}},
  note         = {Machine review of arXiv:2502.05132}
}
read the original abstract

Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in-situ density profiles or standard fluctuation thermometry, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this work, we introduce a novel in-situ thermometry for quantum gases, leveraging single-atom resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes with approximately one atom on average, we extract both global and local temperatures over a broad dynamic range. Unlike traditional fluctuation thermometry, our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering sub-extensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This nearly universal thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.

Figures

Figures reproduced from arXiv: 2502.05132 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: a we report the measurement of ∆Q as a function of ⟨N⟩ for the different preparations discussed above. The results confirm that the sub-extensive fluctuations constitute an important fraction of the variance at low temperature. To quantify the temperature dependence of…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 70 canonical work pages

  1. [1]

    K¨ ohl, Physical Review A73, 031601 (2006)

    M. K¨ ohl, Physical Review A73, 031601 (2006)

    2006

  2. [2]

    Zhou and T.-L

    Q. Zhou and T.-L. Ho, Physical Review Letters 106, 225301 (2011)

    2011

  3. [3]

    Roscilde, Physical Review Letters 112, 110403 (2014)

    T. Roscilde, Physical Review Letters 112, 110403 (2014)

    2014

  4. [4]

    McDonald, B

    M. McDonald, B. H. McGuyer, G. Z. Iwata, and T. Zelevinsky, Physical Review Letters 114, 023001 (2015)

    work page 2015

  5. [5]

    M. T. Mitchison, T. Fogarty, G. Guarnieri, S. Campbell, T. Busch, and J. Goold, Physical Review Letters 125, 080402 (2020)

    work page 2020

  6. [6]

    Ketterle, D

    W. Ketterle, D. S. Durfee, and D. M. Stamper-Kurn, Making, probing and understanding Bose-Einstein con- densates (1999), arXiv:cond-mat/9904034

    arXiv 1999

  7. [7]

    Gemelke, X

    N. Gemelke, X. Zhang, C.-L. Hung, and C. Chin, Nature 460, 995 (2009)

    work page 2009

  8. [8]

    D. M. Weld, P. Medley, H. Miyake, D. Hucul, D. E. Pritchard, and W. Ketterle, Physical Review Letters 103, 245301 (2009)

    work page 2009

Show all 83 references
  1. [9]

    Sanner, E

    C. Sanner, E. J. Su, A. Keshet, R. Gommers, Y.-i. Shin, W. Huang, and W. Ketterle, Physical Review Letters 105, 040402 (2010)

    2010

  2. [10]

    M¨ uller, B

    T. M¨ uller, B. Zimmermann, J. Meineke, J.-P. Brantut, T. Esslinger, and H. Moritz, Physical Review Letters 105, 040401 (2010)

    2010

  3. [11]

    M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, Science 335, 563 (2012)

    2012

  4. [12]

    Desbuquois, T

    R. Desbuquois, T. Yefsah, L. Chomaz, C. Weitenberg, L. Corman, S. Nascimb` ene, and J. Dalibard, Physical Review Letters 113, 020404 (2014)

    2014

  5. [13]

    W. G. Tobias, K. Matsuda, G. Valtolina, L. De Marco, J.-R. Li, and J. Ye, Physical Review Letters124, 033401 (2020)

    2020

  6. [14]

    Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Physical Review Letters 122, 093401 (2019)

    2019

  7. [15]

    Z. Yan, P. B. Patel, B. Mukherjee, C. J. Vale, R. J. Fletcher, and M. W. Zwierlein, Science 383, 629 (2024)

    2024

  8. [16]

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

    2011

  9. [17]

    Yefsah, R

    T. Yefsah, R. Desbuquois, L. Chomaz, K. J. G¨ unter, and J. Dalibard, Physical Review Letters 107, 130401 (2011)

    2011

  10. [18]

    Yefsah, Thermodynamique du gaz de Bose ` a deux di- mensions, Ph.D

    T. Yefsah, Thermodynamique du gaz de Bose ` a deux di- mensions, Ph.D. thesis, Universit´ e Pierre et Marie Curie - Paris VI (2011)

    2011

  11. [19]

    J. H. Drewes, E. Cocchi, L. A. Miller, C. F. Chan, D. Pertot, F. Brennecke, and M. K¨ ohl, Physical Review Letters 117, 135301 (2016)

    2016

  12. [20]

    Pasqualetti, O

    G. Pasqualetti, O. Bettermann, N. Darkwah Oppong, E. Ibarra-Garc ´ ıa-Padilla, S. Dasgupta, R. T. Scalettar, K. R. A. Hazzard, I. Bloch, and S. F¨ olling, Physical Review Letters 132, 083401 (2024)

    2024

  13. [21]

    Hartke, B

    T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Physical Review Letters 125, 113601 (2020)

    2020

  14. [22]

    Gring, M

    M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. A. Smith, E. Dem- ler, and J. Schmiedmayer, Science 337, 1318 (2012)

    2012

  15. [23]

    Trotzky, Y.-A

    S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollw¨ ock, J. Eisert, and I. Bloch, Nature Physics 8, 325 (2012)

    2012

  16. [24]

    Cheneau, P

    M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schauß, T. Fukuhara, C. Gross, I. Bloch, C. Kollath, and S. Kuhr, Nature 481, 484 (2012)

    2012

  17. [25]

    Eigen, J

    C. Eigen, J. A. P. Glidden, R. Lopes, E. A. Cornell, R. P. Smith, and Z. Hadzibabic, Nature 563, 221 (2018)

    2018

  18. [26]

    Kim and D

    H. Kim and D. A. Huse, Physical Review A 86, 053607 (2012)

    2012

  19. [27]

    Samland, N

    J. Samland, N. Wurz, M. Gall, and M. K¨ ohl, Thermo- dynamics and density fluctuations in a bilayer Hubbard system of ultracold atoms (2024), arXiv:2407.11863

    2024 arXiv

  20. [28]

    Castin, in Lecture Notes of the 2006 Varenna Enrico Fermi School on Fermi Gases , edited by M

    Y. Castin, in Lecture Notes of the 2006 Varenna Enrico Fermi School on Fermi Gases , edited by M. Inguscio, W. Ketterle, and C. Salomon (IOS Press, 2007) pp. 289– 349

    2006

  21. [29]

    Verstraten, K

    J. Verstraten, K. Dai, M. Dixmerias, B. Peaudecerf, T. de Jongh, and T. Yefsah, In-situ Imaging of a Single-Atom Wave Packet in Continuous Space (2024), arXiv:2404.05699

    2024

  22. [30]

    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

    2024

  23. [31]

    The symbolˆis omitted for readability

  24. [32]

    G. E. Astrakharchik, R. Combescot, and L. P. 7 Pitaevskii, Physical Review A 76, 063616 (2007)

    2007

  25. [33]

    Klawunn, A

    M. Klawunn, A. Recati, L. P. Pitaevskii, and S. Stringari, Physical Review A 84, 033612 (2011)

    2011

  26. [34]

    Omran, M

    A. Omran, M. Boll, T. A. Hilker, K. Kleinlein, G. Sa- lomon, I. Bloch, and C. Gross, Physical Review Letters 115, 263001 (2015)

    2015

  27. [35]

    Additional details can be found in the Supplementary Materials, which includes Ref. [82]

  28. [36]

    Fr´ erot and T

    I. Fr´ erot and T. Roscilde, Physical Review B94, 075121 (2016)

    2016

  29. [37]

    Gioev and I

    D. Gioev and I. Klich, Physical Review Letters 96, 100503 (2006)

    2006

  30. [38]

    N. R. Smith, P. Le Doussal, S. N. Majumdar, and G. Schehr, Physical Review E 103, L030105 (2021)

    2021

  31. [39]

    M. M. Wolf, Physical Review Letters 96, 010404 (2006)

    2006

  32. [40]

    H. F. Song, S. Rachel, C. Flindt, I. Klich, N. Laflorencie, and K. Le Hur, Physical Review B 85, 035409 (2012)

    2012

  33. [41]

    Calabrese, M

    P. Calabrese, M. Mintchev, and E. Vicari, EPL (Euro- physics Letters) 98, 20003 (2012)

    2012

  34. [42]

    Fr´ erot and T

    I. Fr´ erot and T. Roscilde, Physical Review B92, 115129 (2015)

    2015

  35. [43]

    A. V. Zabrodin and A. A. Ovchinnikov, (1985)

    1985

  36. [44]

    Berkovich and J

    A. Berkovich and J. H. Lowenstein, Nuclear Physics B 285, 70 (1987)

    1987

  37. [45]

    Leclair, F

    A. Leclair, F. Lesage, S. Sachdev, and H. Saleur, Nuclear Physics B 482, 579 (1996)

    1996

  38. [46]

    LeClair and G

    A. LeClair and G. Mussardo, Nuclear Physics B 552, 624 (1999)

    1999

  39. [47]

    K. V. Kheruntsyan, D. M. Gangardt, P. D. Drummond, and G. V. Shlyapnikov, Physical Review Letters 91, 040403 (2003)

    2003

  40. [48]

    Caux and P

    J.-S. Caux and P. Calabrese, Physical Review A 74, 031605 (2006)

    2006

  41. [49]

    I. E. Dzyaloshinski ˘I and A. I. Larkin, Correlation func- tions for a one-dimensional Fermi system with long- range interaction (Tomonaga model), in World Scien- tific Series in 20th Century Physics , Vol. 11 (WORLD SCIENTIFIC, 1996) pp. 95–101

    1996

  42. [50]

    D. M. Ceperley, Reviews of Modern Physics 67, 279 (1995)

    1995

  43. [51]

    Pilati, J

    S. Pilati, J. Boronat, J. Casulleras, and S. Giorgini, Physical Review A 71, 023605 (2005)

    2005

  44. [52]

    Holzmann and Y

    M. Holzmann and Y. Castin, The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics 7, 425 (1999)

    1999

  45. [53]

    Capogrosso-Sansone, S ¸

    B. Capogrosso-Sansone, S ¸. G. S¨ oyler, N. Prokof’ev, and B. Svistunov, Physical Review A 77, 015602 (2008)

    2008

  46. [54]

    Caleffi, M

    F. Caleffi, M. Capone, C. Menotti, I. Carusotto, and A. Recati, Physical Review Research 2, 033276 (2020)

    2020

  47. [55]

    G. G. Batrouni and R. T. Scalettar, Physical Review Letters 84, 1599 (2000)

    2000

  48. [56]

    Capogrosso-Sansone, C

    B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, and G. Pupillo, Physical Review Letters 104, 125301 (2010)

    2010

  49. [57]

    Yamamoto, A

    D. Yamamoto, A. Masaki, and I. Danshita, Physical Re- view B 86, 054516 (2012)

    2012

  50. [58]

    Zhang, Physical Review Letters 83, 2777 (1999)

    S. Zhang, Physical Review Letters 83, 2777 (1999)

    1999

  51. [59]

    C. N. Varney, C.-R. Lee, Z. J. Bai, S. Chiesa, M. Jar- rell, and R. T. Scalettar, Physical Review B 80, 075116 (2009)

    2009

  52. [60]

    Paiva, R

    T. Paiva, R. Scalettar, M. Randeria, and N. Trivedi, Physical Review Letters 104, 066406 (2010)

    2010

  53. [61]

    L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein, Science 353, 1260 (2016)

    2016

  54. [62]

    Y.-Y. He, M. Qin, H. Shi, Z.-Y. Lu, and S. Zhang, Phys- ical Review B 99, 045108 (2019)

    2019

  55. [63]

    C. F. Chan, M. Gall, N. Wurz, and M. K¨ ohl, Physical Review Research 2, 023210 (2020)

    2020

  56. [64]

    Pollet, Reports on Progress in Physics 75, 094501 (2012)

    L. Pollet, Reports on Progress in Physics 75, 094501 (2012)

    2012

  57. [65]

    Chang, S

    C.-C. Chang, S. Gogolenko, J. Perez, Z. Bai, and R. T. Scalettar, Philosophical Magazine 95, 1260 (2015)

    2015

  58. [66]

    Alexandru, G

    A. Alexandru, G. Ba¸ sar, P. F. Bedaque, and N. C. War- rington, Reviews of Modern Physics 94, 015006 (2022)

    2022

  59. [67]

    Carlson, S

    J. Carlson, S. Gandolfi, K. E. Schmidt, and S. Zhang, Physical Review A 84, 061602 (2011)

    2011

  60. [68]

    Van Houcke, F

    K. Van Houcke, F. Werner, E. Kozik, N. Prokof’ev, B. Svistunov, M. J. H. Ku, A. T. Sommer, L. W. Cheuk, A. Schirotzek, and M. W. Zwierlein, Nature Physics 8, 366 (2012)

    2012

  61. [69]

    Rossi, T

    R. Rossi, T. Ohgoe, K. Van Houcke, and F. Werner, Physical Review Letters 121, 130405 (2018)

    2018

  62. [70]

    Y. Shin, M. W. Zwierlein, C. H. Schunck, A. Schirotzek, and W. Ketterle, Physical Review Letters 97, 030401 (2006)

    2006

  63. [71]

    M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, Science 311, 492 (2006)

    2006

  64. [72]

    Y.-i. Shin, C. H. Schunck, A. Schirotzek, and W. Ket- terle, Nature 451, 689 (2008)

    2008

  65. [73]

    Mitra, P

    D. Mitra, P. T. Brown, P. Schauß, S. S. Kondov, and W. S. Bakr, Physical Review Letters 117, 093601 (2016)

    2016

  66. [74]

    Mazurenko, C

    A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kan´ asz-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, Nature 545, 462 (2017)

    2017

  67. [75]

    C. S. Chiu, G. Ji, A. Mazurenko, D. Greif, and M. Greiner, Physical Review Letters 120, 243201 (2018)

    2018

  68. [76]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. L¨ uschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Science 349, 842 (2015)

    2015

  69. [77]

    J.-y. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio- Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Science 352, 1547 (2016)

    2016

  70. [78]

    Alet and N

    F. Alet and N. Laflorencie, Comptes Rendus Physique Quantum Simulation / Simulation Quantique, 19, 498 (2018)

    2018

  71. [79]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Reviews of Modern Physics 91, 021001 (2019)

    2019

  72. [80]

    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]

    2024

  73. [81]

    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]

    2024 arXiv

  74. [82]

    S. Jin, K. Dai, J. Verstraten, M. Dixmerias, R. Alhyder, C. Salomon, B. Peaudecerf, T. De Jongh, and T. Yefsah, Physical Review Research 6, 013158 (2024). 8 SUPPLEMENT AR Y MA TERIALS Experimental Sequence Our experimental setup was described in [29]. For this work, we start b...

    2024

  75. [83]

    (S7) We used the expression above to numerically inte- grate ∆Q in Fig

    Using that relation we obtain: 11 ∆Q = n2 Z S dr1 Z ¯S dr2 g1(r1, r2)2. (S7) We used the expression above to numerically inte- grate ∆Q in Fig. 4. For T /TF → ∞, one can show that: g1(kFr) ≃ e−πr2/λ2 T . If then we consider for S a square volume of size L ≫ λT , we get for the...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.