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arxiv: 2605.17797 · v1 · pith:NYSCEZFKnew · submitted 2026-05-18 · ⚛️ physics.atom-ph · quant-ph

Photon-Atom Granularity Noise Thermometry

Chen-Rong Liu , Yixuan Wang , Xiaowei Wang , Chuang Li , Mingti Zhou , Runxia Tao , Hongwei Chen , Ying Dong This is my paper

Pith reviewed 2026-05-20 01:01 UTC · model grok-4.3

classification ⚛️ physics.atom-ph quant-ph
keywords granularity noiseoptical thermometryatomic ensemblesphoton-atom ratioplasma dispersion functiontemperature scalingfluctuation spectroscopysusceptibility fluctuations
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The pith

Atomic temperature is read from the slope of excess light noise that scales linearly with the photon-to-atom ratio.

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

This paper proposes granularity noise thermometry as a way to determine temperature in atomic ensembles by observing fluctuations in transmitted light. The power spectral density shows noise above the shot-noise level that increases in direct proportion to the ratio of incident photons to atoms. Changing the light intensity and tracking the rate of this increase produces a slope whose value depends on temperature through explicit formulas. For thermal vapors the slope follows a vapor-pressure function divided by temperature squared, while for cold atoms the slope grows with the square of temperature. A sympathetic reader would see this as turning an unavoidable source of atomic discreteness noise into a direct temperature readout.

Core claim

The authors establish that the excess noise in transmitted light arising from atomic discreteness scales linearly with the photon-to-atom ratio R. The slope K of this scaling directly encodes the ensemble temperature, with closed-form expressions for the relevant polarizability moments obtained via the plasma dispersion function; these expressions produce the distinct relations K proportional to P_v(T) over T squared for thermal vapors and K proportional to T squared for cold atoms.

What carries the argument

The linear scaling of excess noise power spectral density with photon-to-atom ratio R, whose slope K functions as the temperature readout through derived polarizability moments.

If this is right

  • For thermal vapors the extracted slope follows the explicit form proportional to P_v(T) divided by T squared.
  • For cold atoms the extracted slope follows the explicit form proportional to T squared.
  • Temperature extraction proceeds without additional fitting parameters once the closed-form moments are used.
  • The approach supplies a noise-based optical thermometry route that relies on atomic ensembles.

Where Pith is reading between the lines

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

  • Spatially resolved noise measurements could map temperature variations inside an inhomogeneous atomic cloud without separate imaging steps.
  • The same light beam used for thermometry could simultaneously support other optical diagnostics such as phase-shift imaging.
  • Applying the method across a temperature range that spans both thermal and cold regimes would test whether the predicted change in scaling exponent appears.
  • Similar granularity-noise analysis might apply to other discrete-particle systems where susceptibility fluctuations are measurable.

Load-bearing premise

The measured excess noise above shot noise arises solely from the intrinsic fluctuations due to discrete atom positions rather than from technical noise sources or detection imperfections, and the closed-form polarizability expressions capture the full temperature dependence.

What would settle it

Vary the incident power over a wide range, extract the noise slope at a fixed analysis frequency, and compare the implied temperature against an independent measurement such as absorption spectroscopy or time-of-flight expansion; disagreement would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.17797 by Chen-Rong Liu, Chuang Li, Hongwei Chen, Mingti Zhou, Runxia Tao, Xiaowei Wang, Ying Dong, Yixuan Wang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: illustrates this linear scaling at several represen￾tative temperatures spanning 173–473 K. For 𝑃in ≲ 1 𝜇W [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

We propose granularity noise thermometry (GNT), a fluctuation-based optical thermometry scheme that exploits the intrinsic fluctuations of susceptibility arising from atomic discreteness. The power spectral density of transmitted light exhibits an excess noise above the shot-noise limit that scales linearly with the photon-to-atom ratio $\mathcal{R}$. Consequently, varying the incident power (hence $\mathcal{R}$) yields the slope $\mathcal{K}$ of this linear scaling, which directly encodes the temperature. Closed-form expressions for the polarizability moments are derived via the plasma dispersion function, which yield distinct temperature scalings: $\mathcal{K}\propto P_{\mathrm{v}}(T)/T^2$ for thermal vapors and $\mathcal{K}\propto T^{2}$ for cold atoms. While practical implementation requires careful control of technical noise and system parameters, the present framework provides a noise-based pathway for optical thermometry using atomic ensembles.

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 paper proposes granularity noise thermometry (GNT), an optical method that extracts temperature from the slope K of excess power spectral density (above shot noise) in transmitted light as a function of the photon-to-atom ratio R. This excess arises from intrinsic susceptibility fluctuations due to atomic discreteness. Closed-form expressions for the relevant polarizability moments are obtained via the plasma dispersion function, producing distinct scalings: K ∝ P_v(T)/T² for thermal vapors and K ∝ T² for cold atoms. Practical use requires control of technical noise.

Significance. If the noise-dominance assumption holds and the derivations are verified, the method would supply a fluctuation-based thermometry route with closed-form, regime-specific temperature scalings that do not require direct fitting to temperature data. This could complement existing optical techniques for atomic ensembles, particularly where distinct scalings help identify the physical regime.

major comments (2)
  1. [Abstract and practical-implementation discussion] The central claim that the measured slope K directly encodes temperature via the derived polarizability moments requires that excess PSD above shot noise is dominated by granularity noise from atomic discreteness rather than technical sources. The manuscript provides no quantitative bounds or example parameter regimes (density, detuning, bandwidth, laser RIN, detector noise) in which granularity noise exceeds technical contributions by a sufficient margin to preserve the linear scaling with R and the claimed distinct T-dependencies. This assumption is load-bearing for the extraction of K and for the practical utility stated in the abstract.
  2. [Theory/derivation section] The abstract asserts closed-form expressions for the polarizability moments via the plasma dispersion function, yet the manuscript does not display the explicit derivations, intermediate steps, or error analysis that would allow verification of the stated scalings K ∝ P_v(T)/T² and K ∝ T². Without these steps, it is unclear whether the expressions are truly parameter-free or contain hidden assumptions that affect the temperature mapping.
minor comments (2)
  1. [Abstract] Notation for the photon-to-atom ratio (script R) and slope (script K) should be introduced with a clear definition and units on first use to improve readability.
  2. [Introduction or Discussion] The manuscript would benefit from a brief comparison table or paragraph contrasting GNT with existing optical thermometry methods (e.g., absorption spectroscopy or fluorescence) in terms of sensitivity, applicable temperature range, and technical requirements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major points below and have revised the manuscript to strengthen the presentation of the practical requirements and theoretical derivations.

read point-by-point responses

  1. Referee: [Abstract and practical-implementation discussion] The central claim that the measured slope K directly encodes temperature via the derived polarizability moments requires that excess PSD above shot noise is dominated by granularity noise from atomic discreteness rather than technical sources. The manuscript provides no quantitative bounds or example parameter regimes (density, detuning, bandwidth, laser RIN, detector noise) in which granularity noise exceeds technical contributions by a sufficient margin to preserve the linear scaling with R and the claimed distinct T-dependencies. This assumption is load-bearing for the extraction of K and for the practical utility stated in the abstract.

    Authors: We agree that explicit demonstration of granularity-noise dominance is necessary for the method's practical utility. The original manuscript notes the requirement for technical-noise control but does not supply quantitative bounds. In the revised version we have added a new subsection with order-of-magnitude estimates for representative thermal-vapor and cold-atom parameters (density, detuning, bandwidth, RIN, detector noise). These calculations identify regimes in which granularity noise exceeds technical contributions by a factor of several, thereby preserving the linear scaling with R and the reported temperature dependencies. We also outline experimental strategies (balanced detection, low-RIN sources) to reach those regimes. revision: yes

  2. Referee: [Theory/derivation section] The abstract asserts closed-form expressions for the polarizability moments via the plasma dispersion function, yet the manuscript does not display the explicit derivations, intermediate steps, or error analysis that would allow verification of the stated scalings K ∝ P_v(T)/T² and K ∝ T². Without these steps, it is unclear whether the expressions are truly parameter-free or contain hidden assumptions that affect the temperature mapping.

    Authors: The closed-form expressions appear in the theory section, but the intermediate algebraic steps were condensed. We have expanded the main text and added a dedicated appendix that walks through the derivation from susceptibility fluctuations to the polarizability moments via the plasma dispersion function. The appendix also includes an error analysis of the approximations (low-density limit, far-detuned regime, neglect of higher-order correlations) and confirms that the reported scalings remain parameter-free within the stated validity range. revision: yes

Circularity Check

0 steps flagged

No circularity: temperature scalings derived from standard plasma dispersion function

full rationale

The derivation chain starts from the plasma dispersion function (a standard external mathematical object) to obtain closed-form polarizability moments, which then produce the distinct scalings K ∝ P_v(T)/T² and K ∝ T². These steps are not self-definitional, do not rename a fitted parameter as a prediction, and do not rely on load-bearing self-citations or ansatzes imported from the authors' prior work. The slope K is extracted from measured linear scaling with R and mapped via the independent derivation; no equation reduces K to a quantity defined in terms of itself or the target temperature. The paper is self-contained against external benchmarks for this part of the claim.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the plasma dispersion function as a standard mathematical tool for atomic response and on the assumption that atomic discreteness produces measurable susceptibility fluctuations separable from technical noise. No free parameters or new invented entities are introduced in the abstract.

axioms (2)
  • standard math The plasma dispersion function provides closed-form expressions for the polarizability moments that govern the susceptibility fluctuations.
    Invoked to derive the temperature scalings for K in both thermal vapors and cold atoms.
  • domain assumption Excess noise above shot noise arises solely from intrinsic atomic discreteness fluctuations when technical noise is controlled.
    Required for the linear scaling with R to encode temperature without contamination.

pith-pipeline@v0.9.0 · 5695 in / 1405 out tokens · 41993 ms · 2026-05-20T01:01:25.923431+00:00 · methodology

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Works this paper leans on

55 extracted references · 55 canonical work pages · 1 internal anchor

  1. [1]

    (18) The temperature dependence of var𝑣 [𝛼𝐼 ] is thus entirely con- tained in 𝑏0

    and ℑ𝑍0 = √𝜋 𝑒𝑏2 0/2 erfc 𝑏0√ 2 . (18) The temperature dependence of var𝑣 [𝛼𝐼 ] is thus entirely con- tained in 𝑏0. Its asymptotic analysis, presented in Appendix C, provides the explicit scalings used throughout Sec. IV. Unless stated otherwise, we adopt these conditions throughout the re- mainder of this work. IV . FROM SCALING LA W TO TEMPERATURE EXTRA...

    work page

  2. [2]

    Atomic vapor In an atomic vapor, the effective interaction time per atom is the transit time 𝜏tr = 2𝑤0 ¯𝑣 = 2 Γ𝑡 , (19) where Γ𝑡 is defined in Sec. III. From kinetic theory, the atomic flux through the transverse cross section of the probe beam is Φat = 1 4 𝑛 ¯𝑣 𝐴, (20) with 𝐴 = 2𝜋𝑤 0𝐿 the lateral area, and the corresponding probe volume is 𝑉bm = 𝜋𝑤 2 0𝐿....

    work page

  3. [3]

    The cloud volume 𝑉cl is determined from absorption imaging [ 26, 36, 37]

    Cold atom cloud In a cold atomic cloud, the atoms are confined by external potentials, so the atom number 𝑁at is fixed during the measure- ment. The cloud volume 𝑉cl is determined from absorption imaging [ 26, 36, 37]. We assume the probe beam fully en- compasses the cloud and that the cloud size is small compared to the Rayleigh range, so the probe inten...

    work page

  4. [4]

    For atomic vapors near room temper- ature, one finds 𝑏0 ≈ 0.016 using the parameters for a typical alkali D2 transition (Table I), thereby confirming that 𝑏0 ≪ 1

    The 𝑏0 ≪ 1 and 𝑏0 ≫ 1 limits The 𝑏0 ≪ 1 regime. For atomic vapors near room temper- ature, one finds 𝑏0 ≈ 0.016 using the parameters for a typical alkali D2 transition (Table I), thereby confirming that 𝑏0 ≪ 1. In this regime, the Doppler width far exceeds the homogeneous linewidth. Expanding erfc for small argument (Appendix C) yields var𝑣 [𝛼𝐼 ] ≈ √ 2𝜋 𝐶...

    work page

  5. [5]

    The inset shows 1/𝑏0 versus tem- perature 𝑇, with the black solid line including transit and collision broadening ( Γ𝑡 , Γ𝑐) and the gray dashed line corresponding to the ideal case Γ → 0 (i.e., Γ𝑡 = Γ 𝑐 = 0)

    work page

  6. [6]

    Atomic vapor

    Temperature scalings Inserting the approximate and asymptotic forms of the vari- ance obtained above into the slope expressions ( 23) and ( 24) reveals how K depends on temperature in the two physical set- tings. Atomic vapor. Substituting the 𝑏0 ≪ 1 approximation Eq. (25) into Eq. ( 23) yields Kv = 𝐿 𝑤0 | 𝝐 · 𝒅21| 4 2𝜖 2 0 ℏ3𝑐 𝑛(𝑇) [𝛾2 + 2Γ(𝑇)] 𝑣2 th(𝑇) ...

    work page

  7. [7]

    The three rates 𝛾2, Γ𝑡 , and Γ𝑐 are defined in Sec

    Master equation and steady-state solution We start from the master equation including spontaneous decay, transit-time broadening, and collision-induced dephas- ing [29–32]: 𝜕 𝜌 𝜕𝑡 = 1 𝑖ℏ [𝐻𝑅, 𝜌] + L decay𝜌 + Ltran 𝜌 + Lcoll 𝜌, (B1) with Ldecay𝜌 = 𝛾2 𝜎12 𝜌𝜎 † 12 − 1 2 { 𝜎† 12𝜎12, 𝜌} , (B2) Ltran 𝜌 = −Γ𝑡 (𝜌12| 1⟩⟨2| + 𝜌21| 2⟩⟨1|) , (B3) Lcoll 𝜌 = −Γ𝑐 (𝜌12| ...

    work page

  8. [8]

    Introducing 𝑣th and the dimensionless velocity 𝜉 = 𝑣/𝑣th, Eq

    Partial-fraction decomposition To obtain a form suitable for integration over the velocity distribution, we perform a partial-fraction decomposition of 𝜌21 (𝑣). Introducing 𝑣th and the dimensionless velocity 𝜉 = 𝑣/𝑣th, Eq. ( 11) becomes a rational function of 𝜉: 𝜌21 (𝜉) = 𝑀1𝜉 + 𝑀0 𝐷2𝜉2 + 𝐷1𝜉 + 𝐷0 , (B10) with 𝑀1 = −2𝛾2Ω𝑘𝑣 th, 𝑀0 = 𝛾2Ω[2Δ − 𝑖(𝛾2 + 2Γ)] , 𝐷...

    work page

  9. [9]

    Polarizability from the steady-state coherence The single-atom polarizability follows from the linear re- sponse of the induced dipole moment to the applied electric field. For a two-level atom without permanent dipole moment, the induced dipole moment in the steady state is given by ⟨𝒅⟩ = Tr(𝜌 𝒅) = 𝒅12 𝜌12 + 𝒅21 𝜌21, (B14) where 𝒅𝑖 𝑗 = ⟨𝑖| 𝒅| 𝑗⟩ are the ...

    work page

  10. [10]

    III, reduce to integrals of rational functions

    Statistical moments The statistical moments of 𝛼(𝜉) over the Maxwell- Boltzmann distribution, required for evaluating var𝑣 [𝛼𝐼 ] in Sec. III, reduce to integrals of rational functions. These are expressed compactly via the plasma dispersion function 𝑍 (𝑧) [21], defined as 𝑍 (𝑧) = 1√𝜋 ¹ ∞ −∞ 𝑒−𝑡 2 𝑡 − 𝑧 𝑑𝑡, ℑ𝑧 > 0, and analytically continued to the whole c...

    work page

  11. [11]

    (B22) The variance of the imaginary part 𝛼𝐼 follows as var𝑣 [𝛼𝐼 ] = 1 2 E[| 𝛼| 2] − ℜ E[𝛼2] − (ℑE[𝛼])2

    − 1√ 2 (𝑐2 1𝑟1𝑍1 + 𝑐2 2𝑟2𝑍2). (B22) The variance of the imaginary part 𝛼𝐼 follows as var𝑣 [𝛼𝐼 ] = 1 2 E[| 𝛼| 2] − ℜ E[𝛼2] − (ℑE[𝛼])2 . (B23) Appendix C: Asymptotic expansions of the polarizability variance The exact variance var𝑣 [𝛼𝐼 ] under resonant, weak-probe conditions is given by Eq. ( 17) of Sec. III. We now derive its leading asymptotic behavior in...

    work page

  12. [12]

    The 𝑏0 ≪ 1 Taylor expansion In the small-argument limit, the complementary error func- tion admits the Taylor expansion erfc(𝑦) = 1 − 2𝑦√𝜋 1 − 𝑦2 3 + 𝑦4 10 − 𝑦6 42 + · · · , 𝑦 ≪ 1. (C1) Substituting 𝑦 = 𝑏0/ √ 2 and expanding the exponential pref- actor 𝑒𝑏2 0/2 = 1 + 𝑏2 0/2 + 𝑏4 0/8 + · · · , we obtain ℑ𝑍0 = √𝜋 𝑒 𝑏2 0 2 erfc 𝑏0√ 2 = √𝜋 1 + 𝑏2 0 2 + 𝑏4 0 8 ...

    work page

  13. [13]

    (C4) Setting 𝑦 = 𝑏0/ √ 2 gives directly ℑ𝑍0 = √ 2 𝑏0 1 − 1 𝑏2 0 + 3 𝑏4 0 − 15 𝑏6 0 + · · · !

    The 𝑏0 ≫ 1 asymptotic expansion For large 𝑏0, the complementary error function is more con- veniently handled via its asymptotic expansion erfc(𝑦) = 𝑒−𝑦2 𝑦 1√𝜋 1 − 1 2𝑦2 + 3 4𝑦4 − 15 8𝑦6 + · · · , 𝑦 ≫ 1. (C4) Setting 𝑦 = 𝑏0/ √ 2 gives directly ℑ𝑍0 = √ 2 𝑏0 1 − 1 𝑏2 0 + 3 𝑏4 0 − 15 𝑏6 0 + · · · ! . (C5) To evaluate the variance, we need the combination ℑ𝑍0...

    work page

  14. [14]

    P . J. Mohr, D. B. Newell, and B. N. Taylor, CODATA recom- mended values of the fundamental physical constants: 2014, Rev. Mod. Phys. 88, 035009 (2016)

    work page 2014

  15. [15]

    Fischer, B

    J. Fischer, B. Fellmuth, C. Gaiser, T. Zandt, L. Pitre, F. Sparasci, M. D. Plimmer, M. de Podesta, R. Underwood, G. Sutton, G. Machin, R. M. Gavioso, D. Madonna Ripa, P . P . M. Steur, J. Qu, X. J. Feng, J. Zhang, M. R. Moldover, S. P . Benz, D. R. White, L. Gianfrani, A. Castrillo, L. Moretti, B. Darquié, E. Mo- ufarej, C. Daussy, S. Briaudeau, O. Kozlov...

    work page 2018

  16. [16]

    Stock, R

    M. Stock, R. Davis, E. de Mirandés, and M. J. T. Milton, The revision of the SI—the result of three decades of progress in metrology, Metrologia 56, 022001 (2019)

    work page 2019

  17. [17]

    Pearce, G

    J. Pearce, G. Machin, A. Todd, M. J. Martin, Y . Pan, K. Zhou, Å. Olsen, A. Kowal, C. Gaiser, Y . Kawamura, et al. , Fu- ture traceability of practical primary thermometry and self- validating thermometry, Philos. Trans. R. Soc. A384, 20240453 (2026)

    work page 2026

  18. [18]

    M. R. Moldover, J. P . M. Trusler, T. J. Edwards, J. B. Mehl, and R. S. Davis, Measurement of the Universal Gas Constant 𝑅 Using a Spherical Acoustic Resonator, Phys. Rev. Lett. 60, 249 (1988)

    work page 1988

  19. [19]

    M. R. Moldover, R. M. Gavioso, J. B. Mehl, L. Pitre, M. de Podesta, and J. T. Zhang, Acoustic gas thermometry, Metrologia 51, R1 (2014)

    work page 2014

  20. [20]

    Nyquist, Thermal Agitation of Electric Charge in Conduc- tors, Phys

    H. Nyquist, Thermal Agitation of Electric Charge in Conduc- tors, Phys. Rev. 32, 110 (1928)

    work page 1928

  21. [21]

    White, R

    D. White, R. Galleano, A. Actis, H. Brixy, M. De Groot, J. Dubbeldam, A. Reesink, F. Edler, H. Sakurai, R. Shepard, et al., The status of Johnson noise thermometry, Metrologia 33, 325 (1996)

    work page 1996

  22. [22]

    P . R. Childs, J. Greenwood, and C. Long, Review of temperature measurement, Rev. Sci. Instrum. 71, 2959 (2000)

    work page 2000

  23. [23]

    Spietz, K

    L. Spietz, K. Lehnert, I. Siddiqi, and R. Schoelkopf, Primary electronic thermometry using the shot noise of a tunnel junction, Science 300, 1929 (2003)

    work page 1929

  24. [24]

    S. P . Benz, A. Pollarolo, J. Qu, H. Rogalla, C. Urano, W. L. Tew, P . D. Dresselhaus, and D. R. White, An electronic measurement of the Boltzmann constant, Metrologia 48, 142 (2011)

    work page 2011

  25. [25]

    J. Qu, S. Benz, H. Rogalla, W. Tew, D. White, and K. Zhou, Johnson noise thermometry, Meas. Sci. Technol. 30, 112001 (2019)

    work page 2019

  26. [26]

    S. P . Benz, K. J. Coakley, N. E. Flowers-Jacobs, H. Rogalla, W. L. Tew, J. Qu, D. R. White, C. Gaiser, A. Pollarolo, and C. Urano, Practical realisation of the kelvin by Johnson noise thermometry, Metrologia 61, 022001 (2024)

    work page 2024

  27. [27]

    J. T. Zhang, Y . R. Sun, C. F. Cheng, and S. M. Hu, Doppler broadening thermometry: recent advances and applications, Phys. Rev. A 105, 033111 (2022)

    work page 2022

  28. [28]

    Huang, J

    Q. Huang, J. Wang, R.-H. Yin, Y . Tan, C.-F. Cheng, Y . R. Sun, A.-W . Liu, and S.-M. Hu, Cavity-enhanced doppler-broadening thermometry via all-frequency metrology, Phys. Rev. Lett. 135, 223002 (2025)

    work page 2025

  29. [29]

    Dimarcq, V

    N. Dimarcq, V . Giordano, and P . Cerez, Statistical properties of laser-induced fluorescence signals, Applied Physics B 59, 135 (1994)

    work page 1994

  30. [30]

    Greiner, C

    M. Greiner, C. A. Regal, J. T. Stewart, and D. S. Jin, Prob- ing pair-correlated fermionic atoms through correlations in atom shot noise, Physical Review Letters 94, 110401 (2005)

    work page 2005

  31. [31]

    Roscilde, Thermometry of cold atoms in optical lattices via artificial gauge fields, Phys

    T. Roscilde, Thermometry of cold atoms in optical lattices via artificial gauge fields, Phys. Rev. Lett. 112, 110403 (2014)

    work page 2014

  32. [32]

    Dixmerias, J

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

    work page arXiv 2025

  33. [33]

    C.-R. Liu, C. Li, R. Tao, Y . Wang, M. Zhou, X. Wang, and Y . Dong, Granularity Noise Limit in Atomic-Ensemble-Based Metrology (2026), arXiv:2604.05420 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  34. [34]

    B. D. Fried and S. D. Conte, The Plasma Dispersion Function: The Hilbert Transform of the Gaussian (Academic Press, New Y ork, 1961)

    work page 1961

  35. [35]

    C. L. Degen, F. Reinhard, and P . Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017)

    work page 2017

  36. [36]

    C.-R. Liu, R. Tao, X. Lv, Y . Dong, C. Li, B. Wei, and M. Zhou, Fisher-based sensitivity framework for Rydberg-atom microwave electrometry, Phys. Rev. Appl. 25, 034052 (2026)

    work page 2026

  37. [37]

    J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999)

    work page 1999

  38. [38]

    H. J. Metcalf and P . Van der Straten, Laser Cooling and Trap- ping, Graduate Texts in Contemporary Physics (Springer, 1999)

    work page 1999

  39. [39]

    Wolswijk et al

    L. Wolswijk et al. , Trapping, manipulating and probing ultra- cold atoms: a quantum technologies tutorial, arXiv (2025) , arXiv:2510.20790 [physics.atom-ph]

    work page arXiv 2025

  40. [40]

    A. V . Oppenheim, R. W. Schafer, and J. R. Buck,Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, 1999)

    work page 1999

  41. [41]

    Mandel and E

    L. Mandel and E. Wolf,Optical Coherence and Quantum Optics (Cambridge University Press, 1995)

    work page 1995

  42. [42]

    Sagle, R

    J. Sagle, R. Namiotka, and J. Huennekens, Measurement and modelling of intensity dependent absorption and transit relax- ation on the Cesium line, J. Phys. B: At. Mol. Opt. Phys. 29, 2629 (1996)

    work page 1996

  43. [43]

    Jabbour, J

    Z. Jabbour, J. Sagle, R. Namiotka, and J. Huennekens, Mea- surement of the self-broadening rate coefficients of the Cesium resonance lines, J. Quant. Spectrosc. Radiat. Transfer 54, 767 12 (1995)

    work page 1995

  44. [44]

    G. A. Pitz, C. D. Fox, and G. P . Perram, Pressure broadening and shift of the cesium D 2 transition by the noble gases and N 2, H2, HD, D 2, CH4, C2H6, CF4, and 3He with comparison to the D1 transition, Phys. Rev. A 82, 042502 (2010)

    work page 2010

  45. [45]

    D. A. Steck, Cesium D Line Data , Online (2025)

    work page 2025

  46. [46]

    B. N. Miller, D. H. Meyer, T. Virtanen, C. M. O’Brien, and K. C. Cox, Rydiqule: A graph-based paradigm for modeling Ryd- berg and atomic sensors, Comput. Phys. Commun. 294, 108952 (2024)

    work page 2024

  47. [47]

    Nagib and T

    O. Nagib and T. G. Walker, Exact steady state of perturbed open quantum systems, Phys. Rev. Res. 7, 033076 (2025)

    work page 2025

  48. [48]

    D. A. Steck, Quantum and Atom Optics , revision 0.16.6 ed. (2025) available online at https://atomoptics.uoregon. edu/~dsteck/teaching/quantum-optics/

    work page 2025

  49. [49]

    Reinaudi, T

    G. Reinaudi, T. Lahaye, Z. Wang, and D. Guéry-Odelin, Strong saturation absorption imaging of dense clouds of ultracold atoms, Opt. Lett. 32, 3143 (2007)

    work page 2007

  50. [50]

    Vibel, M

    T. Vibel, M. B. Christensen, M. A. Kristensen, J. J. Thuesen, L. N. Stokholm, C. A. Weidner, and J. J. Arlt, Spatial calibration of high-density absorption imaging, J. Phys. B: At. Mol. Opt. Phys. 57, 145301 (2024)

    work page 2024

  51. [51]

    Lemonde, O

    P . Lemonde, O. Morice, E. Peik, J. Reichel, H. Perrin, W . Hänsel, and C. Salomon, An opto-electric trap for cold atoms, Europhys. Lett. 32, 555 (1995)

    work page 1995

  52. [52]

    G. Li, S. Zhang, L. Isenhower, K. Maller, and M. Saffman, Crossed vortex bottle beam trap for single-atom qubits, Opt. Lett. 37, 851 (2012)

    work page 2012

  53. [53]

    J. He, J. Wang, B.-D. Y ang, T.-C. Zhang, and J.-M. Wang, Single atoms transferring between a magneto-optical trap and a far-off- resonance optical dipole trap, Chin. Phys. B 18, 3404 (2009)

    work page 2009

  54. [54]

    D. B. Percival and A. T. Walden, Spectral Analysis for Uni- variate Time Series (Cambridge University Press, Cambridge, 2020)

    work page 2020

  55. [55]

    Stoica and R

    P . Stoica and R. L. Moses,Spectral Analysis of Signals (Pearson Prentice Hall, Upper Saddle River, NJ, 2005)

    work page 2005