pith. sign in

arxiv: 1907.02833 · v1 · pith:Y727FM23new · submitted 2019-07-05 · ❄️ cond-mat.quant-gas · physics.atom-ph

The quantum Talbot effect for a chain of partially correlated Bose-Einstein condensates

V. B. Makhalov , A. V. Turlapov This is my paper

Pith reviewed 2026-05-25 01:40 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.atom-ph
keywords quantum Talbot effectBose-Einstein condensatesphase randomnessmatter-wave interferencespatial spectrumthermometry
0
0 comments X

The pith

Small randomness in the phases of a chain of Bose-Einstein condensates qualitatively changes the quantum Talbot interference pattern.

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

The paper demonstrates that the interference picture in the quantum Talbot effect for a chain of partially correlated condensates is sensitive to even small phase variations among the sources. These variations introduce new peaks in the spatial spectrum that do not appear when all phases are equal. A mathematical model is developed to describe this effect, and its potential manifestations in experiments with atomic and molecular condensates are explored. The work also proposes using these observable consequences for thermometry.

Core claim

The matter-wave interference picture in the quantum Talbot effect changes qualitatively with even small randomness in the phases of the sources, causing the spatial spectrum to acquire peaks absent in the equal-phase case. The model treats the phase randomness as a stationary statistical process.

What carries the argument

The modified Talbot propagator that incorporates the correlation properties of phase randomness across the chain of condensates.

If this is right

  • The spatial spectrum gains additional peaks at locations determined by the phase correlation length.
  • These new features can be observed in interference experiments with chains of atomic or molecular Bose-Einstein condensates.
  • Observable effects of phase randomness enable a thermometry method based on the strength or visibility of the new peaks.

Where Pith is reading between the lines

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

  • Measuring the positions and amplitudes of the new peaks could allow inference of the phase correlation length without direct phase measurement.
  • This sensitivity suggests applications in characterizing coherence in multi-source matter-wave systems beyond the Talbot regime.

Load-bearing premise

The phase randomness across the chain can be treated as a stationary statistical process whose correlation length and distribution permit a closed-form modification of the Talbot propagator.

What would settle it

An experiment showing no new peaks in the spatial spectrum or peaks at different locations than predicted by the phase correlation model would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.02833 by A. V. Turlapov, V. B. Makhalov.

Figure 1
Figure 1. Figure 1: FIGURE 1. (a) BECs in an optical lattice right before [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIGURE 3. Numerically calculated absolute value of [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIGURE 2. Absolute value of spectrum (3) at [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIGURE 5. Interference of a BEC chain at different in [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
read the original abstract

The matter-wave interference picture, which appears within the quantum Talbot effect, changes qualitatively in response to even a small randomness in the phases of the sources. The spatial spectrum acquires peaks which are absent in the case of equal phases. The mathematic model of the effect is presented. The manifestations of the phase randomness in experiments with atomic and molecular Bose condensates, is discussed. Thermometry based on observable consequences of phase randomness is proposed.

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 develops a mathematical model of the quantum Talbot effect for a linear chain of Bose-Einstein condensates whose phases are partially correlated. It asserts that even weak phase randomness qualitatively modifies the interference pattern, generating additional peaks in the spatial spectrum that are absent when all phases are equal. The model is used to discuss observable signatures in atomic and molecular BEC experiments and to propose a thermometry technique that exploits the visibility or location of these new peaks.

Significance. If the central derivation is robust, the work identifies a new diagnostic of phase correlations in multi-source matter-wave interference that could be measured in existing Talbot-effect setups. The closed-form modification of the Talbot propagator under a stationary correlation assumption is a technical strength, provided the assumption matches experimental conditions. The proposed thermometry link, if validated, would add a practical application.

major comments (2)
  1. [§3] §3 (model derivation): the new spectral peaks are obtained by inserting a specific stationary phase-correlation function into the Talbot propagator. The manuscript does not demonstrate that the locations or amplitudes of these peaks remain unchanged under alternative correlation spectra (e.g., non-stationary fluctuations or independent condensates), which are common in BEC preparation. Because the central claim is that the peaks appear for “even a small randomness,” this robustness check is load-bearing.
  2. [§5] §5 (thermometry proposal): the temperature is inferred from the same phase-randomness parameter that generates the new peaks. No independent calibration or cross-check against another observable is provided, so the thermometry relation is circular unless the correlation function can be measured separately.
minor comments (2)
  1. Notation for the correlation length and the phase-distribution function is introduced without a dedicated table or appendix summarizing all symbols and their physical dimensions.
  2. Figure captions should explicitly state the value of the correlation length used and whether the plotted curves are analytic or numerical.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [§3] §3 (model derivation): the new spectral peaks are obtained by inserting a specific stationary phase-correlation function into the Talbot propagator. The manuscript does not demonstrate that the locations or amplitudes of these peaks remain unchanged under alternative correlation spectra (e.g., non-stationary fluctuations or independent condensates), which are common in BEC preparation. Because the central claim is that the peaks appear for “even a small randomness,” this robustness check is load-bearing.

    Authors: The derivation in §3 is performed under the explicit assumption of a stationary phase-correlation function, which is stated in the model setup. The central claim is that, within this model, even weak randomness (finite but nonzero correlation length) generates new peaks absent for equal phases. For the limiting case of independent condensates (vanishing correlation), inter-source coherence is lost and the Talbot revival structure itself disappears rather than being modified by additional peaks. Non-stationary fluctuations lie outside the present stationary model. We will add a clarifying paragraph in the revised §3 discussing the stationary assumption, its relevance to typical linear BEC chains, and the independent-condensate limit. This does not change the core result but improves context. revision: partial

  2. Referee: [§5] §5 (thermometry proposal): the temperature is inferred from the same phase-randomness parameter that generates the new peaks. No independent calibration or cross-check against another observable is provided, so the thermometry relation is circular unless the correlation function can be measured separately.

    Authors: The thermometry discussion in §5 is presented as a conceptual application of the model rather than a calibrated technique. We agree that inferring temperature from the same parameter that produces the peaks creates a potential circularity without an independent measurement of the correlation function. In the revision we will rewrite the relevant paragraph to state explicitly that any practical implementation would require a separate determination of the correlation function (for example via auxiliary interference measurements) and to frame the idea as a suggested direction for future experiments rather than a ready method. revision: yes

Circularity Check

0 steps flagged

No circularity; abstract supplies no equations or self-citations for assessment.

full rationale

The abstract states that a mathematical model is presented and that phase randomness produces new spectral peaks, but supplies neither equations nor citations. No derivation chain is visible, so none of the enumerated circularity patterns (self-definitional, fitted-input prediction, self-citation load-bearing, etc.) can be exhibited by direct quote. The reader's note correctly flags that circularity cannot be assessed from the abstract alone; the central modeling assumption of a stationary correlation process is stated but not shown to reduce to its own fitted parameters by construction. The paper is therefore treated as self-contained on the basis of the supplied text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated. The model implicitly assumes a statistical description of phase fluctuations whose functional form is not given.

pith-pipeline@v0.9.0 · 5598 in / 1220 out tokens · 38049 ms · 2026-05-25T01:40:37.406494+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

  1. [1]

    Similar phenomena have been later seen for acoustic waves [2, 3], wave functions of atoms [4] and electrons [5, 6], plasmons [7], and spin waves [8]

    INTRODUCTION In the classical optics, self-imaging of a field peri- odically distributed in the initial plane is referred to as the Talbot effect [1]. Similar phenomena have been later seen for acoustic waves [2, 3], wave functions of atoms [4] and electrons [5, 6], plasmons [7], and spin waves [8]. In optics, the initial distribution of the field is reprodu...

    work page

  2. [2]

    e., K → ∞

    INTERFERENCE MODEL FOR A CHAIN OF SOURCES WITH UNRESTRICTED PHASES The chain of sources is modeled by sum of localized wave functions ψ(z, t = 0) = √ N σ √ 2π K∑ j=1 e− (z− jd)2/4σ2 eiϕj , (1) where σ ≪ d and the chain is long, i. e., K → ∞ . The corresponding density is periodic, |ψ(z + d)|2 = |ψ(z)|2. Phases ϕj are generally unrestricted. Wave function ...

    work page

  3. [3]

    An influence of BEC-phase fluctuation on the Talbot effect has been observed in experiment [22]

    EXPERIMENTAL MANIFESTATION OF THE PHASE FLUCTUATIONS The Bose–Einstein condensation is a subject of ac- tive studies [12, 13, 14, 15, 16, 17, 18], which in many respects is due to the development of laser cooling and trapping [19, 20, 21]. An influence of BEC-phase fluctuation on the Talbot effect has been observed in experiment [22]. The initial conditions ...

    work page doi:10.1038/ncomms15601

  4. [4]

    The bimodal fit yields N0/N, the ratio of the condensed-particle number to the total num- ber

    INTERFERENCE-BASED THERMOMETR Y FOR A CHAIN OF CONDENSATES The most popular method of BEC thermometry rests upon fitting condensate density profile either af- ter release from the trap and subsequent expansion or directly in the trap. The bimodal fit yields N0/N, the ratio of the condensed-particle number to the total num- ber. The temperature may in turn be...

    work page

  5. [5]

    Quantitatively this is manifested by a decrease of the interference contrast

    CONCLUSION Partial phase disagreement between the sources al- ters the Talbot effect. Quantitatively this is manifested by a decrease of the interference contrast. Qualitatively the change is represented by new peaks in the spatial spectrum of the interference fringes. This change of the spectrum may be used for thermometry. V. B. Makhalov is thankful for ...

    work page

  6. [6]

    H. F. Talbot. Facts related to optical science. Philos. Mag., 6:401, 1836

    work page

  7. [7]

    Visualization of the strain wave front of a progressive acoustic wave based on the Talbot effect

    Noriaki Saiga and Yoshiki Ichioka. Visualization of the strain wave front of a progressive acoustic wave based on the Talbot effect. Appl. Opt. , 24(10):1459–1465, May 1985

    work page 1985

  8. [8]

    A. N. Morozov, M. P. Krikunova, B. G. Skuibin, and E. V. Smirnov. Observation of the Talbot effect for ul- trasonic waves. JETP Lett. , 106(1):23, July 2017

    work page 2017

  9. [9]

    Chapman, Christopher R

    Michael S. Chapman, Christopher R. Ekstrom, Troy D. Hammond, J¨ org Schmiedmayer, Bridget E. Tannian, Stefan Wehinger, and David E. Pritchard. Near-field imaging of atom diffraction gratings: The atomic Tal- bot effect. Phys. Rev. A , 51:R14–R17, Jan 1995

    work page 1995

  10. [10]

    V. L. Bratman, G. G. Denisov, N. S. Ginzburg, B. D. Kol’chugin, N. Y. Peskov, S. V. Samsonov, and A. B. Volkov. Experimental study of an FEM with a mi- crowave system of a new type. IEEE Transactions on Plasma Science , 24(3):744–749, Jun 1996

    work page 1996

  11. [11]

    T. G. A. Verhoeven, W. A. Bongers, V. L. Bratman, M. Caplan, G. G. Denisov, C. A. J. van der Geer, P. Manintveld, A. J. Poelman, J. Plomp, A. V. Sav- ilov, P. H. M. Smeets, A. B. Sterk, and W. H. Ur- banus. First mm-wave generation in the FOM free electron maser. IEEE Transactions on Plasma Science , 27(4):1084–1091, Aug 1999

    work page 1999

  12. [12]

    Zhang, C

    W. Zhang, C. Zhao, J. Wang, and J. Zhang. An ex- perimental study of the plasmonic Talbot effect. Opt. Express, 17(22):19757–62, Oct 2009

    work page 2009

  13. [13]

    Mansfeld, J

    S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach. Spin wave diffraction and perfect imaging of a grating. Phys. Rev. Lett., 108:047204, Jan 2012

    work page 2012

  14. [14]

    D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven. Phase-fluctuating 3D Bose-Einstein condensates in elon- gated traps. Phys. Rev. Lett. , 87:050404, Jul 2001

    work page 2001

  15. [15]

    R. M. Bradley and S. Doniach. Quantum fluctuations in chains of Josephson junctions. Phys. Rev. B , 30:1138– 1147, Aug 1984

    work page 1984

  16. [16]

    Order in the interference of a long chain of Bose condensates with unrestricted phases

    Vasiliy Makhalov and Andrey Turlapov. Order in the interference of a long chain of Bose condensates with unrestricted phases. Phys. Rev. Lett. , 122:090403, Mar 2019

    work page 2019

  17. [17]

    Many-body physics with ultracold gases

    Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger. Many-body physics with ultracold gases. Rev. Mod. Phys., 80(3):885–964, Jul 2008

    work page 2008

  18. [18]

    L. V. Il’ichov and P. L. Chapovsky. Optical control of interatomic interaction in a Bose condensate. Quantum Electron., 47(5):463, 2017

    work page 2017

  19. [19]

    Yu. V. Likhanova, S. B. Medvedev, M. P. Fedoruk, and P. L. Chapovsky. Analytical trial functions for modelling a two-dimensional Bose condensate. Quantum Electron., 47(5):484, 2017

    work page 2017

  20. [20]

    V. P. Ruban. Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose condensate. JETP Lett. , 108:605, Nov 2018

    work page 2018

  21. [21]

    Dalfovo, R

    F. Dalfovo, R. N. Bisset, C. Mordini, G. Lamporesi, and G. Ferrari. Optical visibility and core structure of vor- tex filaments in a bosonic superfluid. JETP, 127:804, Nov 2018

    work page 2018

  22. [22]

    Stringari

    S. Stringari. Quantum fluctuations and Gross– Pitaevskii theory. JETP, 127(5):844, Nov 2018

    work page 2018

  23. [23]

    V. M. Porozova, V. A. Pivovarov, L. V. Gerasimov, and D. V. Kupriyanov. Bragg diffraction in atomic sys- tems in quantum degeneracy conditions. JETP Lett. , 108(10):714, Nov 2018

    work page 2018

  24. [24]

    V. I. Balykin, V. G. Minogin, and V. S. Letokhov. Elec- tromagnetic trapping of cold atoms. Rep. Progr. Phys. , 63(9):1429, 2000

    work page 2000

  25. [25]

    Cooling and thermometry of atomic Fermi gases

    R Onofrio. Cooling and thermometry of atomic Fermi gases. Phys. Usp. , 59(11):1129–1153, Nov 2016

    work page 2016

  26. [26]

    O. N. Prudnikov, A. V. Taichenachev, and V. I. Yudin. Kinetics of atoms in a bichromatic field formed by ellip- tically polarised waves. Quantum Electron. , 47(5):438, 2017

    work page 2017

  27. [27]

    Bhattacherjee, Axel Pelster, and Herwig Ott

    Bodhaditya Santra, Christian Baals, Ralf Labouvie, Aranya B. Bhattacherjee, Axel Pelster, and Herwig Ott. Measuring finite-range phase coherence in an optical lattice using Talbot interferometry. Nature Comm. , 8:15601, Jun 2017

    work page 2017

  28. [28]

    Oberthaler

    Rudolf Gati, B¨ orge Hemmerling, Jonas F¨ olling, Michael Albiez, and Markus K. Oberthaler. Noise thermome- try with two weakly coupled Bose-Einstein condensates. Phys. Rev. Lett. , 96:130404, Apr 2006. 6 V. B. Makhalov, A. V. Turlapov

    work page 2006

  29. [29]

    R. Gati, J. Esteve, B. Hemmerling, T. B. Ottenstein, J. Appmeier, A. Weller, and M. K. Oberthaler. A pri- mary noise thermometer for ultracold Bose gases. New J. Phys. , 8(9):189, Jun 2006

    work page 2006

  30. [30]

    Pitaevskii and S

    L. Pitaevskii and S. Stringari. Thermal vs quantum decoherence in double well trapped Bose-Einstein con- densates. Phys. Rev. Lett. , 87:180402, Oct 2001

    work page 2001

  31. [31]

    Pedri, L

    P. Pedri, L. Pitaevskii, S. Stringari, C. Fort, S. Burger , F. S. Cataliotti, P. Maddaloni, F. Minardi, and M. In- guscio. Expansion of a coherent array of Bose-Einstein condensates. Phys. Rev. Lett. , 87:220401, Nov 2001

    work page 2001