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A Quantum Coherence Microscope in the Hubbard Regime

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A quantum coherence microscope maps off-diagonal correlations onto site-resolved density images.

desk verdict A genuinely new Talbot-based coherence microscope with site-resolved off-diagonal correlation access, held back from being a clean quantitative tool by a single calibrated efficiency η=0.47 whose universality is asserted more than demonstrated. read the letter →

arxiv 2608.09924 v1 pith:7Y6BWFL2 submitted 2026-08-10 quant-ph cond-mat.quant-gascond-mat.str-elphysics.atom-ph

Lin Su , Michal Szurek , Alec Douglas , Ceren B. Dag , Markus Greiner This is my paper · ORCID
classification quant-phcond-mat.quant-gascond-mat.str-elphysics.atom-ph PACS 03.75.Lm05.30.Jp37.10.Jk67.85.Hj
keywords quantumgasmicroscopeTalboteffectoff-diagonalcorrelationssingle-particledensitymatrixBose-Hubbardmodelsuperfluid-Motttransitionopticallatticecoherencemeasurement
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

Quantum gas microscopes can photograph atoms site by site, but the off-diagonal parts of the single-particle density matrix—the coherence between different lattice sites—have stayed out of reach. This paper claims a microscope for that missing information: after a sudden lattice quench, atoms evolve for a short Talbot time and are recaptured in a phase-tunable lattice, turning coherence at a chosen site separation $r$ into a modulation of the recaptured density. The measured relative amplitude $R$ is related to the normalized coherence by $R = \eta\, g^{(1)}_{i,i+r}$, with a single efficiency $\eta \approx 0.47$ that the authors find independent of separation, filling, interaction strength, and evolution time. Using it, they locally resolve the superfluid-to-Mott-insulator transition across a harmonically trapped cloud and detect next-nearest-neighbor coherence in a two-leg ladder. If the calibration holds, the method turns a quantum gas microscope into a spatially resolving coherence probe.

What carries the argument

The load-bearing mechanism is the matter-wave Talbot effect combined with phase-controlled lattice recapture. After the initial lattice is suddenly turned off, a phase-coherent array of atoms rephases after half a Talbot time (29 microseconds for erbium atoms in a 266 nm lattice), concentrating wavefunction amplitude between the original sites; the atoms are then recaptured in an accordion lattice whose phase is varied shot to shot. For a chosen evolution time, the recaptured filling oscillates with lattice phase, and the relative amplitude of that oscillation encodes the coherence at the corresponding separation $r$, giving near-single-site resolution for nearest neighbors and access to longer separations at coarser resolution. The single global efficiency $\eta$ absorbs all deviations from an ideal instantaneous, non-interacting recapture and is what turns the measured modulation into a quantitative estimate of $g^{(1)}$.

What would settle it

Measure $R$ for a state whose $g^{(1)}$ is known exactly, such as a small array of independent coherent wave packets or a non-interacting band insulator, at several separations and interaction strengths, and check whether $R/g^{(1)}$ remains 0.47 within error bars; a statistically significant deviation at any single condition would falsify the universal mapping. Alternatively, compare the extracted $g^{(1)}$ with an independent local probe such as single-bond kinetic-energy measurements on the same system.

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Extended reading notes

Core claim

The central discovery is that off-diagonal elements of the normalized single-particle density matrix $g^{(1)}_{i,j}$ can be read out locally by combining short Talbot evolution with single-atom-resolved recapture. At evolution times corresponding to a lattice separation $r$, the recapture-filling modulation as the recapture lattice phase is varied has relative amplitude $R = \eta\, g^{(1)}_{i,i+r}$; the global constant $\eta = 0.47$ accounts for the finite efficiency of the protocol and is shown to be independent, within error bars, of lattice separation, filling, interaction strength, and Talbot time. The authors demonstrate the microscope by measuring the spatial profile of coherence across the superfluid-to-Mott transition, where the center of the cloud loses coherence with increasing $U/t$ while the lower-density edge stays superfluid, and by isolating next-nearest-neighbor coherence in an engineered two-leg ladder, where interchain tunneling $t_\perp$ drives a rapid rise in coherence at low $U/t$ but leaves the high-$U/t$ insulating region nearly unchanged. DMRG and TEBD simulations reproduce the measured modulation amplitudes with the same global scaling parameter.

Load-bearing premise

The whole quantitative comparison rests on a single number: the global efficiency $\eta = 0.47$, calibrated from the authors' own DMRG simulations, is assumed to stay the same for every separation, filling, interaction strength, lattice depth, and Talbot time probed; if it drifts with any of these, the agreement between experiment and simulation would no longer be a meaningful test.

Editorial extensions

If this is right

  • A single quantum gas microscope image can now reveal how coherence varies across a cloud, distinguishing coexisting superfluid and Mott-insulating regions that conventional time-of-flight averages blur together.
  • Probing multiple separations $r$ gives the spatial decay of off-diagonal correlations, opening quantitative studies of quasi-long-range order and power-law correlations in strongly interacting matter.
  • The protocol can be targeted at an engineered low-entropy sample region without contamination from a surrounding reservoir, as demonstrated in the ladder geometry.
  • Because the same mapping holds across interaction strengths and fillings, the method offers a path to site-resolved order-parameter measurements in Bose-Hubbard simulators and, as the authors outline, to fermionic systems through programmable pre-imaging evolution.
  • By choosing the Talbot time, the experiment trades spatial resolution for reach, so longer-range coherence can be measured at coarser resolution within the same apparatus.

Reading between the lines

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

  • If $\eta$ is as universal as reported, the protocol could be used as a relative coherence standard: measuring $R$ at fixed $\eta$ effectively measures $g^{(1)}$ without per-experiment recalibration, which would make the method a practical tool rather than a single demonstration.
  • A natural stress test is to push the method toward stronger interactions and higher densities, where interactions during the short expansion could distort the single-particle Talbot picture; the paper's own discussion of interaction-reduced contrast marks this as the likeliest place for $\eta$ to fail.
  • The same recapture idea could be applied after a quench to watch coherence build or decay in real time: varying the hold time before Talbot evolution would give time-resolved, site-resolved snapshots of off-diagonal correlations during thermalization or phase transitions.
  • For fermionic systems, the paper's outlook suggests pairing correlations could become locally accessible; an immediate check would be whether a spin-dependent or species-dependent recapture lattice can map spin-resolved off-diagonal density-matrix elements.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces a 'quantum coherence microscope' for ultracold bosons in an optical lattice. The protocol releases atoms from the lattice for a short time (a fraction of the Talbot time), lets them expand, then recaptures them in a phase-tunable lattice and images with single-site resolution. The authors claim that the relative amplitude R of the resulting filling modulation versus lattice phase is related to the normalized single-particle density matrix by R = η g(1)_{i,i+r}, with a single global efficiency η = 0.47 calibrated from DMRG simulations. They use the method to map out the local superfluid-to-Mott-insulator transition in a harmonically confined cloud (center vs. edge responses) and to measure next-nearest-neighbor coherence along the chains of a two-leg dipolar Bose-Hubbard ladder as a function of interchain tunneling, comparing against DMRG and TEBD simulations.

Significance. If the central relation holds, the technique would provide a genuinely new observable for quantum gas microscopes: spatially resolved off-diagonal correlations, rather than only density snapshots. The qualitative physics is convincing: coherent states show Talbot revivals while incoherent states do not; the center of a trapped cloud loses coherence across the SF-MI transition while the low-density edge does not; and the ladder coherence responds to t_perp as expected. The paper is also careful in using nontrivial tensor-network simulations with explicit ramp dynamics, number fluctuations, and parameter uncertainties, and in displaying experimental error bars. The main weakness is that the one quantitative bridge between measurement and theory, the efficiency η, is calibrated from the very simulations it is then used to test, and its claimed universality is only partially demonstrated.

major comments (3)
  1. [Model and Supplemental Material 'Global scaling parameter'] The central relation R = η g(1)_{i,i+r} is calibrated using η = 0.47 obtained from the authors' own DMRG simulations, and the same η is then used to generate every theoretical curve shown in Figs. 2 and 3. The paper states that η is independent of separation, filling, interaction strength, and Talbot evolution time, but the only quantitative evidence shown is the r-dependence in Fig. 6. The claimed independence from U/t, filling, and lattice depth is asserted without data or quoted bounds. Because the agreement between experiment and DMRG/TEBD curves is the main quantitative claim, the universality of η is load-bearing; the authors should provide direct measurements of η across the parameter ranges of Figs. 2 and 3, or an independent calibration procedure, so that the comparison is not a consistency check of the fit.
  2. [Supplemental Material 'Qualitative interpretation of the global scaling parameter'] The Supplemental Material explicitly disclaims a first-principles prediction of η and identifies dipolar interactions at short interparticle separations (tens of kHz) as a mechanism not included in the estimate, citing refs. [81,82] in which interactions reduce Talbot contrast. Since Fig. 2 varies U/t from 10 to 40 and compares regions of different filling, a drift of η with interaction strength or density would directly change the shape of the predicted curves. The authors need to either estimate the size of this drift or provide experimental bounds on η for the different U/t and filling regimes, rather than relying on a qualitative assertion that no resolvable variation was seen.
  3. [Model (Eq. (2) and surrounding text)] The paper states that at evolution times associated with a separation r, the recapture modulation is 'predominantly sensitive' to g(1)_{i,i+r}, but it does not quantify the sensitivity kernel or the crosstalk from other separations. For a quantitative microscope, one needs to show, for the experimental Wannier functions and lattice depth, how the measured R at a given Talbot time decomposes into contributions from different r, and how the inversion to g(1) is performed. Without this, the claimed spatial resolution of 'approximately r lattice sites' and the mapping R = η g(1)_{i,i+r} are not fully established.
minor comments (5)
  1. [Fig. 1d caption] The sentence 'The recapture filling does not start near unity likely due to imperfect quench transfer from the green to the blue lattice' would benefit from a quantitative description of the expected versus observed initial filling, since it bears on the definition of R.
  2. [Fig. 2, definition of R] The relative amplitude R = |A|/O is defined via a sinusoidal fit; the paper should state how uncertainties in A and O are propagated into the error bars of R, and whether the offset O is corrected for background or average density.
  3. [Fig. 3 axis labels] The horizontal axis in Fig. 3d is labeled 't t_perp /' in the text; this appears to be a typographical artifact and should be 't_perp / t'.
  4. [Abstract and Introduction] The claim of 'near-single-site resolution' is precise only for r = 1; for r = 2 the resolution is two sites. The abstract should clarify that the resolution is set by the separation being probed.
  5. [Data and code availability] The data and code are listed as 'available from the corresponding authors upon request'; for a methods-focused quantum simulation paper, a public repository would substantially strengthen reproducibility.

Circularity Check

1 steps flagged · score 4.0 of 10

The absolute scale of every DMRG/TEBD comparison curve is set by the fitted efficiency eta=0.47, so the absolute agreement is partly constructed by calibration; the trend predictions remain independent.

  1. fitted input called prediction [Supplemental Material, 'Global scaling parameter'; main text, Model section.]
    "To relate the experimentally measured relative recapture modulation R to the normalized coherence g(1)_{i,j}, we introduce a single global scale factor η, such that R=η·g(1)_{i,j}. We determine η=0.47 from a global calibration and use this same value for all theoretical curves shown in the manuscript."

    By construction, every theoretical curve is η·g(1)_{DMRG/TEBD}, and η is calibrated from the ratio between the measured modulation and the simulated coherence. Comparing R_meas to η·g(1)_sim after fixing η from those same data tests the shape of the correlation function but not its absolute scale, so the claimed 'excellent agreement' and 'quantitative reproduction' partly rest on the calibration value. The U/t suppression, the flat edge response, and the t⊥ dependence of next-nearest-neighbor coherence are not forced by the fit and are genuine predictions, so the circularity is partial rather than total.

full rationale

The central mapping R = η·g(1)_{i,i+r} is implemented with a single η=0.47 obtained from the authors' own DMRG simulations and then applied to all theoretical curves in Figs. 2 and 3. This is one-parameter calibration rather than ab initio prediction, so the absolute vertical placement of the DMRG/TEBD bands is partly constructed by the fit. With η fixed, however, the variation of R with U/t, the difference between center and edge regions, and the t⊥-dependent growth of next-nearest-neighbor coherence are nontrivial, parameter-free shape predictions of the Hubbard-model simulations. The paper explicitly disclaims a first-principles calculation of η, and the SM's consistency check across separations in Fig. 6 provides partial supporting evidence for universality. No load-bearing self-citation chain or imported uniqueness theorem is present; self-references such as [59], [60], [68], and [76] supply parameters and apparatus details rather than the main claim. The universality of η across U/t, filling, lattice depth, and geometry is asserted without shown data, which is a robustness concern but not itself a circular step. Overall score 4 reflects the calibration-dependent absolute agreement while acknowledging the independent trend content of the central demonstration.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a calibrated linear relation R = η g(1) with one fitted constant η; the Hamiltonian model and Gaussian wavefunction approximation are standard domain assumptions; no new physical entities are postulated.

free parameters (1)
  • η (global recapture efficiency) = 0.47
    Calibrated from DMRG simulations of g(1) to relate measured recapture modulation R to normalized coherence via R = η g(1); assumed constant across separation, filling, interaction strength, and Talbot time; not derived from first principles.
assumptions (4)
  • domain assumption The single-particle wavefunction on each lattice site is well approximated by a Gaussian in deep lattices.
    Used in the SM 'Connection to the optical Talbot effect' to compute Talbot times and interpret revivals; good in the deep-lattice regime (roughly 25 recoil energies).
  • domain assumption The experimental system is described by the Bose-Hubbard Hamiltonian with dipolar interactions (Eq. 1) with the stated parameters t, U, V.
    The entire comparison to DMRG/TEBD rests on this Hamiltonian; parameters are calibrated using methods from ref [76].
  • ad hoc to paper At half-integer Talbot times, the recapture modulation is predominantly sensitive to g(1) at a specific separation r, i.e., R = η g(1)_{i,i+r}.
    This is the core mapping of the microscope; it is asserted in the main text and calibrated through η, not derived from a microscopic model of the recapture dynamics.
  • domain assumption The DMRG and TEBD simulations faithfully capture the state preparation and measurement conditions.
    Simulations include ramps, number fluctuations, and parameter uncertainties; the stated agreement with the global η supports consistency but is not an independent check.

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Pith. "Pith review of A Quantum Coherence Microscope in the Hubbard Regime." pith.science (2026). https://pith.science/paper/7Y6BWFL2

@misc{pith2026260809924,
  author       = {Pith},
  title        = {Pith review of: A Quantum Coherence Microscope in the Hubbard Regime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7Y6BWFL2}},
  note         = {Machine review of arXiv:2608.09924}
}
read the original abstract

Quantum coherence underlies collective quantum phenomena and emerging quantum technologies. Quantum gas microscopes have transformed quantum simulation by providing projective snapshots of many-body states with single-atom resolution, but spatially resolved measurements of off-diagonal correlations have remained elusive. Here, using the Talbot effect, we introduce a quantum coherence microscope that maps off-diagonal correlations onto site-resolved density signals with near-single-site resolution. We use this technique to locally probe the superfluid-Mott transition in a layer of a three-dimensional optical lattice and to measure coherence beyond nearest neighbors in an engineered potential landscape. By mapping off-diagonal correlations onto density signals through controlled Talbot evolution, this work opens new possibilities for accessing observables beyond the density basis through tailored matter-wave evolution and recapture.

Figures

Figures reproduced from arXiv: 2608.09924 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. b, the modulation amplitude increases immediately with finite interchain tunneling t⊥, indicating a rapid in- [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Works this paper leans on

81 extracted references · 47 canonical work pages

  1. [1]

    Baumgratz, M

    T. Baumgratz, M. Cramer, and M. B. Plenio, Quantify- ing coherence, Phys. Rev. Lett.113, 140401 (2014)

    2014

  2. [2]

    Streltsov, G

    A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource, Rev. Mod. Phys.89, 041003 (2017)

    2017

  3. [3]

    P. W. Shor, Polynomial-time algorithms for prime factor- ization and discrete logarithms on a quantum computer, SIAM review41, 303 (1999)

    1999

  4. [4]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature Photonics5, 222 (2011)

    2011

  5. [5]

    Penrose and L

    O. Penrose and L. Onsager, Bose-Einstein condensation and liquid helium, Phys. Rev.104, 576 (1956)

    1956

  6. [6]

    C. N. Yang, Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors, Rev. Mod. Phys.34, 694 (1962)

    1962

  7. [7]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys.80, 885 (2008)

    2008

  8. [8]

    W. S. Bakr, J. I. Gillen, A. Peng, S. F¨ olling, and M. Greiner, A quantum gas microscope for detecting sin- gle atoms in a Hubbard-regime optical lattice, Nature 462, 74 (2009)

    2009

Show all 81 references
  1. [9]

    J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Single-atom-resolved fluorescence imaging of an atomic Mott insulator, Nature467, 68 (2010)

    2010

  2. [10]

    Gross and W

    C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nature Physics17, 1316 (2021)

    2021

  3. [11]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quantum simulation, Nature607, 667 (2022)

    2022

  4. [12]

    Endres, M

    M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauss, C. Gross, L. Mazza, M. C. Banuls, L. Pollet, I. Bloch, and S. Kuhr, Observation of correlated particle- hole pairs and string order in low-dimensional Mott in- sulators, Science334, 200 (2011)

    2011

  5. [13]

    Islam, R

    R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin, M. Rispoli, and M. Greiner, Measuring entanglement en- tropy in a quantum many-body system, Nature528, 77 (2015)

    2015

  6. [14]

    Andrews, C

    M. Andrews, C. Townsend, H.-J. Miesner, D. Durfee, D. Kurn, and W. Ketterle, Observation of interference between two bose condensates, Science275, 637 (1997)

    1997

  7. [15]

    Greiner, O

    M. Greiner, O. Mandel, T. Esslinger, T. W. H¨ ansch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature415, 39 (2002)

    2002

  8. [16]

    Roth and K

    R. Roth and K. Burnett, Superfluidity and interference pattern of ultracold bosons in optical lattices, Phys. Rev. A67, 031602 (2003)

    2003

  9. [17]

    Gerbier, A

    F. Gerbier, A. Widera, S. F¨ olling, O. Mandel, T. Ger- icke, and I. Bloch, Phase coherence of an atomic Mott insulator, Phys. Rev. Lett.95, 050404 (2005)

    2005

  10. [18]

    F¨ olling, F

    S. F¨ olling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, Spatial quantum noise interferometry in ex- panding ultracold atom clouds, Nature434, 481 (2005)

    2005

  11. [19]

    J. K. Chin, D. Miller, Y. Liu, C. Stan, W. Setiawan, 10 C. Sanner, K. Xu, and W. Ketterle, Evidence for super- fluidity of ultracold fermions in an optical lattice, Nature 443, 961 (2006)

    2006

  12. [20]

    Hadzibabic, P

    Z. Hadzibabic, P. Kr¨ uger, M. Cheneau, B. Battelier, and J. Dalibard, Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas, Nature441, 1118 (2006)

    2006

  13. [21]

    J. Mun, P. Medley, G. K. Campbell, L. G. Marcassa, D. E. Pritchard, and W. Ketterle, Phase diagram for a Bose-Einstein condensate moving in an optical lattice, Phys. Rev. Lett.99, 150604 (2007)

    2007

  14. [22]

    Gericke, P

    T. Gericke, P. W¨ urtz, D. Reitz, T. Langen, and H. Ott, High-resolution scanning electron microscopy of an ultra- cold quantum gas, Nature Physics4, 949 (2008)

    2008

  15. [23]

    Trotzky, L

    S. Trotzky, L. Pollet, F. Gerbier, U. Schnorrberger, I. Bloch, N. Prokof’Ev, B. Svistunov, and M. Troyer, Suppression of the critical temperature for superfluidity near the Mott transition, Nature Physics6, 998 (2010)

    2010

  16. [24]

    Braun, M

    S. Braun, M. Friesdorf, S. S. Hodgman, M. Schreiber, J. P. Ronzheimer, A. Riera, M. Del Rey, I. Bloch, J. Eis- ert, and U. Schneider, Emergence of coherence and the dynamics of quantum phase transitions, Proceedings of the National Academy of Sciences112, 3641 (2015)

    2015

  17. [25]

    Baier, M

    S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Extended Bose-Hubbard models with ultracold magnetic atoms, Science352, 201 (2016)

    2016

  18. [26]

    Bergschneider, V

    A. Bergschneider, V. M. Klinkhamer, J. H. Becher, R. Klemt, L. Palm, G. Z¨ urn, S. Jochim, and P. M. Preiss, Experimental characterization of two-particle entangle- ment through position and momentum correlations, Na- ture Physics15, 640 (2019)

    2019

  19. [27]

    Schumm, S

    T. Schumm, S. Hofferberth, L. M. Andersson, S. Wil- dermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kr¨ uger, Matter-wave interferometry in a double well on an atom chip, Nature Physics1, 57 (2005)

    2005

  20. [28]

    F¨ olling, S

    S. F¨ olling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. M¨ uller, and I. Bloch, Direct observation of second-order atom tunnelling, Nature448, 1029 (2007)

    2007

  21. [29]

    Sebby-Strabley, B

    J. Sebby-Strabley, B. L. Brown, M. Anderlini, P. J. Lee, W. D. Phillips, J. V. Porto, and P. R. Johnson, Preparing and probing atomic number states with an atom inter- ferometer, Phys. Rev. Lett.98, 200405 (2007)

    2007

  22. [30]

    Trotzky, Y.-A

    S. Trotzky, Y.-A. Chen, U. Schnorrberger, P. Cheinet, and I. Bloch, Controlling and detecting spin correlations of ultracold atoms in optical lattices, Phys. Rev. Lett. 105, 265303 (2010)

    2010

  23. [31]

    Greif, T

    D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Short-range quantum magnetism of ultra- cold fermions in an optical lattice, Science340, 1307 (2013)

    2013

  24. [32]

    R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, Observation of antiferromagnetic cor- relations in the Hubbard model with ultracold atoms, Nature519, 211 (2015)

    2015

  25. [33]

    M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. D. Lukin, and E. Demler, Probing real-space and time- resolved correlation functions with many-body Ramsey interferometry, Phys. Rev. Lett.111, 147205 (2013)

    2013

  26. [34]

    Keßler and F

    S. Keßler and F. Marquardt, Single-site-resolved mea- surement of the current statistics in optical lattices, Phys. Rev. A89, 061601 (2014)

    2014

  27. [35]

    L. A. Pena Ardila, M. Heyl, and A. Eckardt, Measuring the single-particle density matrix for fermions and hard- core bosons in an optical lattice, Phys. Rev. Lett.121, 260401 (2018)

    2018

  28. [36]

    P. A. Murthy and S. Jochim, Direct imaging of the or- der parameter of an atomic superfluid using matterwave optics, arXiv preprint arXiv:1911.10824 (2019)

    2019 arXiv

  29. [37]

    Impertro, S

    A. Impertro, S. Karch, J. F. Wienand, S. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Local read- out and control of current and kinetic energy operators in optical lattices, Phys. Rev. Lett.133, 063401 (2024)

    2024

  30. [38]

    Impertro, S

    A. Impertro, S. Huh, S. Karch, J. F. Wienand, I. Bloch, and M. Aidelsburger, Strongly interacting Meissner phases in large bosonic flux ladders, Nature Physics21, 895 (2025)

    2025

  31. [39]

    Talbot, Lxxvi

    H. Talbot, Lxxvi. facts relating to optical science. no. iv, The London, Edinburgh, and Dublin Philosophi- cal Magazine and Journal of Science9, 401 (1836), https://doi.org/10.1080/14786443608649032

    doi

  32. [40]

    J. Wen, Y. Zhang, and M. Xiao, The Talbot effect: re- cent advances in classical optics, nonlinear optics, and quantum optics, Adv. Opt. Photon.5, 83 (2013)

    2013

  33. [41]

    Besold and N

    B. Besold and N. Lindlein, Fractional Talbot effect for periodic microlens arrays, Optical Engineering36, 1099 (1997)

    1997

  34. [42]

    Schlosser, S

    M. Schlosser, S. Tichelmann, D. Sch¨ affner, D. O. de Mello, M. Hambach, J. Sch¨ utz, and G. Birkl, Scal- able multilayer architecture of assembled single-atom qubit arrays in a three-dimensional Talbot tweezer lat- tice, Phys. Rev. Lett.130, 180601 (2023)

    2023

  35. [43]

    J. F. Clauser and S. Li, Talbot-vonLau atom interferom- etry with cold slow potassium, Phys. Rev. A49, R2213 (1994)

    1994

  36. [44]

    M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, Near-field imaging of atom diffraction grat- ings: The atomic Talbot effect, Phys. Rev. A51, R14 (1995)

    1995

  37. [45]

    A. S. Sanz and S. Miret-Art´ es, A causal look into the quantum Talbot effect, J. Chem. Phys.126, 234106 (2007)

    2007

  38. [47]

    L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, Temporal, matter-wave-dispersion Talbot effect, Phys. Rev. Lett.83, 5407 (1999)

    1999

  39. [48]

    Song, H.-B

    X.-B. Song, H.-B. Wang, J. Xiong, K. Wang, X. Zhang, K.-H. Luo, and L.-A. Wu, Experimental observation of quantum Talbot effects, Phys. Rev. Lett.107, 033902 (2011)

    2011

  40. [49]

    Miyake, G

    H. Miyake, G. A. Siviloglou, G. Puentes, D. E. Pritchard, W. Ketterle, and D. M. Weld, Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices, Phys. Rev. Lett.107, 175302 (2011)

    2011

  41. [50]

    M. J. Mark, E. Haller, J. G. Danzl, K. Lauber, M. Gus- tavsson, and H.-C. N¨ agerl, Demonstration of the tempo- ral matter-wave Talbot effect for trapped matter waves, New Journal of Physics13, 085008 (2011)

    2011

  42. [51]

    Buchhold, U

    M. Buchhold, U. Bissbort, S. Will, and W. Hofstetter, Creating exotic condensates via quantum-phase-revival dynamics in engineered lattice potentials, Phys. Rev. A 84, 023631 (2011)

    2011

  43. [52]

    Santra, C

    B. Santra, C. Baals, R. Labouvie, A. B. Bhattacherjee, A. Pelster, and H. Ott, Measuring finite-range phase co- 11 herence in an optical lattice using Talbot interferometry, Nature Communications8, 15601 (2017)

    2017

  44. [53]

    Makhalov and A

    V. Makhalov and A. Turlapov, Order in the interference of a long chain of bose condensates with unrestricted phases, Phys. Rev. Lett.122, 090403 (2019)

    2019

  45. [54]

    Asteria, H

    L. Asteria, H. P. Zahn, M. N. Kosch, K. Sengstock, and C. Weitenberg, Quantum gas magnifier for sub-lattice- resolved imaging of 3D quantum systems, Nature599, 571 (2021)

    2021

  46. [55]

    J. C. Br¨ uggenj¨ urgen, M. S. Fischer, and C. Weitenberg, A phase microscope for quantum gases, Science393, 167 (2026)

    2026

  47. [56]

    Koehn, C

    L. Koehn, C. Parsonage, C. W. Duncan, P. Kirton, A. J. Daley, T. Hilker, E. Haller, A. La Rooij, and S. Kuhr, Quantum-gas microscopy of the bose-glass phase, arXiv preprint arXiv:2504.13040 (2025)

    2025 arXiv

  48. [57]

    Chomaz, I

    L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe- Tolra, B. L. Lev, and T. Pfau, Dipolar physics: a review of experiments with magnetic quantum gases, Reports on Progress in Physics86, 026401 (2023)

    2023

  49. [58]

    M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B40, 546 (1989)

    1989

  50. [59]

    L. Su, A. Douglas, M. Szurek, R. Groth, S. F. Ozturk, A. Krahn, A. H. H´ ebert, G. A. Phelps, S. Ebadi, S. Dick- erson, F. Ferlaino, O. Markovi´ c, and M. Greiner, Dipolar quantum solids emerging in a Hubbard quantum simula- tor, Nature622, 724 (2023)

    2023

  51. [60]

    L. Su, A. Douglas, M. Szurek, A. H. Hebert, A. Krahn, R. Groth, G. A. Phelps, O. Markovic, and M. Greiner, Fast single atom imaging for optical lattice arrays, Nature Communications16, 1017 (2025)

    2025

  52. [61]

    Bernier, C

    J.-S. Bernier, C. Kollath, A. Georges, L. De Leo, F. Ger- bier, C. Salomon, and M. K¨ ohl, Cooling fermionic atoms in optical lattices by shaping the confinement, Phys. Rev. A79, 061601 (2009)

    2009

  53. [62]

    C. S. Chiu, G. Ji, A. Mazurenko, D. Greif, and M. Greiner, Quantum state engineering of a Hubbard system with ultracold fermions, Phys. Rev. Lett.120, 243201 (2018)

    2018

  54. [63]

    Sompet, S

    P. Sompet, S. Hirthe, D. Bourgund, T. Chalopin, J. Bibo, J. Koepsell, P. Bojovi´ c, R. Verresen, F. Pollmann, G. Sa- lomon, C. Gross, T. A. Hilker, and I. Bloch, Realizing the symmetry-protected haldane phase in Fermi-Hubbard ladders, Nature606, 484 (2022)

    2022

  55. [64]

    M. Xu, L. H. Kendrick, A. Kale, Y. Gang, C. Feng, S. Zhang, A. W. Young, M. Lebrat, and M. Greiner, A neutral-atom Hubbard quantum simulator in the cryo- genic regime, Nature642, 909 (2025)

    2025

  56. [65]

    E. G. Dalla Torre, E. Berg, and E. Altman, Hidden or- der in 1D Bose insulators, Phys. Rev. Lett.97, 260401 (2006)

    2006

  57. [66]

    E. Berg, E. G. Dalla Torre, T. Giamarchi, and E. Alt- man, Rise and fall of hidden string order of lattice bosons, Phys. Rev. B77, 245119 (2008)

    2008

  58. [67]

    A. N. Madhusudan, G. C. Santra, I. Kaur, W. Li, and R. Nath, Commensurate supersolids and re-entrant transitions in an extended Bose-Hubbard ladder, arXiv preprint arXiv:2407.20107 (2024)

    2024 arXiv

  59. [68]

    L. Su, R. Sahay, M. Szurek, A. Douglas, O. Markovic, C. B. Dag, R. Verresen, and M. Greiner, Topological phase transitions and mixed-state order in a Hubbard quantum simulator, Nature Physics 10.1038/s41567-026- 03381-6 (2026)

    2026 doi

  60. [69]

    P. A. Murthy, D. Kedar, T. Lompe, M. Neidig, M. G. Ries, A. N. Wenz, G. Z¨ urn, and S. Jochim, Matter-wave fourier optics with a strongly interacting two-dimensional fermi gas, Phys. Rev. A90, 043611 (2014)

    2014

  61. [70]

    Murthy, I

    P. Murthy, I. Boettcher, L. Bayha, M. Holzmann, D. Kedar, M. Neidig, M. Ries, A. Wenz, G. Z¨ urn, and S. Jochim, Observation of the Berezinskii-Kosterlitz- Thouless phase transition in an ultracold fermi gas, Phys. Rev. Lett.115, 010401 (2015)

    2015

  62. [71]

    Brandstetter, C

    S. Brandstetter, C. Heintze, P. Hill, P. M. Preiss, M. Ga lka, and S. Jochim, Magnifying the wave func- tion of interacting fermionic atoms, Phys. Rev. Lett.135, 103401 (2025)

    2025

  63. [72]

    V. Venu, P. Xu, M. Mamaev, F. Corapi, T. Bilitewski, J. P. D’Incao, C. J. Fujiwara, A. M. Rey, and J. H. Thy- wissen, Unitary p-wave interactions between fermions in an optical lattice, Nature613, 262 (2023)

    2023

  64. [73]

    Defossez, L

    A. Defossez, L. Vanderstraeten, L. Peralta Gavensky, and N. Goldman, Dynamic realization of Majorana zero modes in a particle-conserving ladder, Phys. Rev. Re- search7, 023183 (2025)

    2025

  65. [74]

    D. K. Mark, H.-Y. Hu, J. Kwan, C. Kokail, S. Choi, and S. F. Yelin, Efficiently measuring d-wave pairing and beyond in quantum gas microscopes, Phys. Rev. Lett. 135, 123402 (2025)

    2025

  66. [75]

    Weitenberg, L

    C. Weitenberg, L. Asteria, O. Carlsson, A. Bohrdt, and F. Grusdt, Protocols for a many-body phase microscope: From coherences and d-wave superconductivity to green’s functions, arXiv preprint arXiv:2602.12142 (2026)

    2026

  67. [76]

    Su, Quantum simulation of dipolar itinerant lattice models with magnetic erbium atoms, Doctoral disserta- tion (2025)

    L. Su, Quantum simulation of dipolar itinerant lattice models with magnetic erbium atoms, Doctoral disserta- tion (2025)

    2025

  68. [77]

    Patscheider, L

    A. Patscheider, L. Chomaz, G. Natale, D. Petter, M. J. Mark, S. Baier, B. Yang, R. R. W. Wang, J. L. Bohn, and F. Ferlaino, Determination of the scattering length of erbium atoms, Phys. Rev. A105, 063307 (2022)

    2022

  69. [78]

    Aikawa, A

    K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, Bose-Einstein condensation of erbium, Phys. Rev. Lett.108, 210401 (2012)

    2012

  70. [79]

    Korbmacher, G

    H. Korbmacher, G. A. Dom ´ ınguez-Castro, W.-H. Li, J. Zakrzewski, and L. Santos, Transversal effects on the ground state of hard-core dipolar bosons in one- dimensional optical lattices, Phys. Rev. A107, 063307 (2023)

    2023

  71. [80]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calcula- tions, SciPost Phys. Codebases , 4 (2022)

    2022

  72. [81]

    H¨ ollmer, J.-S

    P. H¨ ollmer, J.-S. Bernier, C. Kollath, C. Baals, B. Santra, and H. Ott, Talbot effect in the presence of interactions, Phys. Rev. A100, 063613 (2019)

    2019

  73. [82]

    F. Wei, Z. Zhang, Y. Chen, H. Shui, Y. Liang, C. Li, and X. Zhou, Temporal Talbot interferometer of a strongly interacting molecular Bose-Einstein condensate, Phys. Rev. A109, 043313 (2024)

    2024

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