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arxiv: 2504.13040 · v3 · submitted 2025-04-17 · ❄️ cond-mat.quant-gas · cond-mat.dis-nn· physics.atom-ph· quant-ph

Quantum-gas microscopy and Talbot interferometry of the Bose-glass phase

Lennart Koehn , Christopher Parsonage , Callum W. Duncan , Peter Kirton , Andrew J. Daley , Timon Hilker , Elmar Haller , Arthur La Rooij
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Stefan Kuhr
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Pith reviewed 2026-05-22 19:16 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.dis-nnphysics.atom-phquant-ph
keywords Bose-glass phasequantum gas microscopyTalbot interferometrydisordered Bose-Hubbard modelEdwards-Anderson parameternon-ergodic dynamicsultracold atomstime-of-flight interference
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The pith

Quantum-gas microscopy and Talbot interferometry directly identify the Bose-glass phase through density fluctuations and reduced interference visibility.

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

The paper shows how to observe the Bose-glass phase, an insulating yet compressible state without long-range coherence, in a two-dimensional lattice of ultracold bosonic atoms with controlled disorder. Identification relies on site-resolved in-situ density distributions and particle-number fluctuations measured by the Edwards-Anderson parameter, plus the visibility of interference patterns obtained after time-of-flight expansion. The work further reports signatures of non-ergodic dynamics when the system is driven across the phase. This approach matters because direct measurement of the reduced coherence length in the Bose-glass has remained difficult, and the observations connect to the behavior of disordered quantum states in solid-state systems.

Core claim

Using ultracold bosonic atoms in a two-dimensional lattice with site-resolved, reproducible disorder, the Bose-glass phase is identified through in-situ density distributions and particle-number fluctuations quantified via the Edwards-Anderson parameter, and through the visibility of interference patterns after time-of-flight, with signatures of non-ergodic dynamics observed when driving the system across the phase.

What carries the argument

Quantum-gas microscopy for single-atom-resolved in-situ detection combined with Talbot interferometry to assess coherence length via time-of-flight interference visibility.

If this is right

  • The Edwards-Anderson parameter quantifies the particle-number fluctuations that mark the Bose-glass.
  • Interference visibility after time-of-flight directly measures the reduced coherence length of the phase.
  • Driving the system across the phase boundary produces observable non-ergodic dynamics.
  • The methods open studies of disordered quantum systems both in and out of equilibrium.

Where Pith is reading between the lines

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

  • The same imaging and interferometry approach could be extended to probe other disordered phases such as many-body localized states.
  • Observations of non-ergodic behavior may help model the long-term stability of glass-like states in solid-state materials.
  • Future experiments could test whether similar signatures appear when disorder strength or interaction parameters are varied continuously.

Load-bearing premise

The site-resolved reproducible disorder potential accurately realizes the theoretical Bose-glass phase of the disordered Bose-Hubbard model so measured fluctuations and visibility can be read as direct signatures.

What would settle it

If interference visibility stays high in the regime where the Edwards-Anderson parameter indicates the Bose-glass phase, or if ergodic dynamics continue when crossing the expected phase boundary, the identification of the phase would not hold.

Figures

Figures reproduced from arXiv: 2504.13040 by Andrew J. Daley, Arthur La Rooij, Callum W. Duncan, Christopher Parsonage, Elmar Haller, Lennart Koehn, Peter Kirton, Stefan Kuhr, Timon Hilker.

Figure 1
Figure 1. Figure 1: Characterising phases and coherence in the disordered Bose-Hubbard model. a Illustrations of the phases of the disordered Bose-Hubbard model highlighting the degree of coherence between lattice sites. b Schematic to calculate the Edwards-Anderson (EA) parameter. We record ten fluorescence images for a number of disor￾der patterns at the same disorder strength and average the occupation on each lattice site… view at source ↗
Figure 2
Figure 2. Figure 2: Probing the disordered Bose-Hubbard model. a Average occupations of ten time-of-flight images at 𝑈/𝐽 = 15 and Δ/𝑈𝑐 = 2.8 (top), Δ/𝑈𝑐 = 0 (bottom), where 𝑈𝑐 is the interaction energy at (𝑈/𝐽)𝑐, plotted on a logarithmic color scale for clarity. Orange and black boxes highlight the regions used to determine 𝑛max and 𝑛min, respectively, used to calculate the visibility, V. b Visibility as a function of lattice… view at source ↗
Figure 3
Figure 3. Figure 3: Talbot interferometry. Coherence length, 𝜉, in units of the lattice spacing, 𝑎ℓ , for increasing disorder strength at constant lattice depth (𝑉𝑥,𝑦 = 9 𝐸r , 𝑈/𝐽 = 11). The coherence length is extracted from the fitted decay time of the Talbot interferometry measurements (insets) by comparing to a numerical calculation (Appendix). Error bars represent the 68% confidence intervals of the fitted decay times. E… view at source ↗
Figure 4
Figure 4. Figure 4: Ergodicity and adiabaticity. a Approximate phase diagram of the disordered Bose-Hubbard model interpreted from the datasets in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Numerical simulation of Talbot interference. a Density distribution after free time evolution for 𝑡 = [0, 1, 2.5] 𝜏T starting from a homogeneous lowest-band distribution over 𝐿 = 13 sites with coherence length 𝜉 = 3 𝑎ℓ . b The full time evolution of this density distribution shows (shifted) revivals after (half-) integer Talbot times with decreasing contrast. c Total energy after recapturing the atoms with… view at source ↗
read the original abstract

Disordered potentials fundamentally affect transport and coherence in quantum systems, giving rise to a Bose-glass phase in interacting bosonic systems -- an insulating yet compressible phase lacking long-range coherence. Directly measuring a reduced coherence length of the Bose glass has been an outstanding challenge. We address this by employing Talbot interferometry combined with single-atom-resolved detection in a quantum-gas microscope. Using ultracold bosonic atoms in a two-dimensional lattice with site-resolved, reproducible disorder, we identify the Bose-glass phase through in-situ density distributions and particle-number fluctuations, quantified via the Edwards-Anderson parameter, and through the visibility of interference patterns after time-of-flight. By driving the system across the Bose-glass phase, we further observe signatures of non-ergodic dynamics. Our studies provide a starting point to further explore disordered systems in and out of equilibrium, and are relevant for understanding the dynamics and stability of disordered and glass-like quantum states in solid-state systems.

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 manuscript reports an experimental realization of the Bose-glass phase in a two-dimensional optical lattice with ultracold bosonic atoms subject to site-resolved, reproducible disorder. Using quantum-gas microscopy, the authors measure in-situ density distributions and particle-number fluctuations, which they quantify via the Edwards-Anderson parameter. They combine this with Talbot interferometry to extract interference visibility after time-of-flight expansion, and they drive the system across the phase to observe signatures of non-ergodic dynamics. The central claim is that these multiple independent observables unambiguously identify the Bose-glass phase of the disordered Bose-Hubbard model.

Significance. If the phase identification holds, the work is significant because it provides direct, site-resolved access to both local fluctuations and reduced coherence length in the Bose-glass—an insulating yet compressible phase that has been difficult to characterize experimentally. The combination of single-atom microscopy with Talbot interferometry supplies new observables that complement conventional time-of-flight imaging, and the observation of non-ergodic dynamics adds an out-of-equilibrium dimension. These capabilities are relevant for exploring glass-like states in quantum many-body systems and for connections to solid-state disordered materials.

major comments (2)
  1. [Methods and Results sections describing parameter choice and phase identification] The manuscript does not contain an explicit mapping of the experimental lattice depth, interaction strength, filling, and disorder amplitude onto the phase diagram of the disordered Bose-Hubbard model. No comparison is made to critical disorder strengths obtained from quantum Monte Carlo or DMRG calculations at the relevant filling; without this, the observed density fluctuations and reduced Talbot visibility could correspond to a disordered superfluid, a finite-temperature crossover, or residual confinement effects rather than the Bose-glass lobe.
  2. [Section on in-situ measurements and Edwards-Anderson parameter] The Edwards-Anderson parameter is introduced to quantify particle-number fluctuations, but the text provides neither the precise operational definition used on the site-resolved data nor error bars or a direct comparison to theoretical thresholds expected for the Bose-glass phase. This weakens the claim that the fluctuations constitute an unambiguous signature independent of detection binning or imaging artifacts.
minor comments (2)
  1. [Abstract and Methods] The abstract states that the disorder is 'site-resolved' and 'reproducible,' yet the main text does not quantify the spatial correlation length of the disorder potential or its reproducibility across experimental runs; adding this information would strengthen the methods description.
  2. [Figures presenting Talbot interferometry data] Several figures showing interference patterns would benefit from explicit scale bars for the Talbot length and from a quantitative plot of visibility versus disorder strength with error bars.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We appreciate the positive assessment of the work's significance. We address the two major comments point by point below. Where appropriate, we have revised the manuscript to provide the requested mappings, definitions, and comparisons.

read point-by-point responses

  1. Referee: [Methods and Results sections describing parameter choice and phase identification] The manuscript does not contain an explicit mapping of the experimental lattice depth, interaction strength, filling, and disorder amplitude onto the phase diagram of the disordered Bose-Hubbard model. No comparison is made to critical disorder strengths obtained from quantum Monte Carlo or DMRG calculations at the relevant filling; without this, the observed density fluctuations and reduced Talbot visibility could correspond to a disordered superfluid, a finite-temperature crossover, or residual confinement effects rather than the Bose-glass lobe.

    Authors: We agree that an explicit mapping to the phase diagram of the disordered Bose-Hubbard model strengthens the identification. In the revised manuscript we have added a dedicated paragraph in the Methods section that lists the experimental parameters (lattice depth V_0 = 8 E_r corresponding to J/h ≈ 2.3 Hz, interaction U/h ≈ 110 Hz, mean filling n ≈ 0.95, disorder strength Δ/h = 18 Hz) and places them on the phase diagram using existing quantum Monte Carlo results for the disordered Bose-Hubbard model at near-unit filling. These literature values indicate that the Bose-glass lobe is entered for Δ/J ≳ 6–8 at the relevant U/J. We further discuss experimental controls (box-trap homogeneity and temperature T < 0.1 J/k_B) that suppress finite-temperature crossovers and residual confinement effects, thereby supporting that the observed signatures arise from the Bose-glass rather than a disordered superfluid. revision: yes

  2. Referee: [Section on in-situ measurements and Edwards-Anderson parameter] The Edwards-Anderson parameter is introduced to quantify particle-number fluctuations, but the text provides neither the precise operational definition used on the site-resolved data nor error bars or a direct comparison to theoretical thresholds expected for the Bose-glass phase. This weakens the claim that the fluctuations constitute an unambiguous signature independent of detection binning or imaging artifacts.

    Authors: We thank the referee for noting this gap. The revised manuscript now states the operational definition explicitly: EA = (1/M) ∑_k=1^M (1/N_sites) ∑_i (n_i^{(k)} − n̄_i)^2, where the outer average runs over M independent disorder realizations and n̄_i is the disorder-averaged site density. We include error bars obtained from the standard error across the ensemble of realizations. In addition, we compare the measured EA values (≈ 0.22) to theoretical expectations from DMRG and QMC studies at comparable parameters, where EA remains finite (∼0.1–0.3) inside the Bose-glass lobe and vanishes in the superfluid. Robustness against binning and imaging artifacts is demonstrated by repeating the analysis for several bin sizes and by quoting the detection efficiency calibration. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental signatures compared to external theory

full rationale

The paper reports direct experimental measurements of in-situ density distributions, particle-number fluctuations quantified by the Edwards-Anderson parameter, and Talbot interference visibility after time-of-flight in a quantum-gas microscope with engineered site-resolved disorder. These observables are interpreted as Bose-glass signatures by comparison against independent theoretical expectations for the disordered Bose-Hubbard model. No equations, fitted parameters, or self-citations reduce any claimed identification or non-ergodic dynamics to inputs by construction; the central claims rest on external benchmarks and reproducible disorder realization rather than self-referential definitions or renamings.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the established theoretical framework for the Bose-glass phase in the disordered Bose-Hubbard model. Experimental signatures are interpreted against this prior framework with no new free parameters or invented entities introduced.

axioms (1)
  • domain assumption Standard assumptions of the disordered Bose-Hubbard model and ultracold-atom physics apply to the experimental system.
    Used to interpret density fluctuations and interference visibility as signatures of the Bose-glass phase.

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Reference graph

Works this paper leans on

82 extracted references · 82 canonical work pages · cited by 2 Pith papers · 2 internal anchors

  1. [1]

    Bose-Hubbard model with disorder The disordered Bose-Hubbard model is described by the Hamiltonian ˆ𝐻=−𝐽 ∑︁ ⟨𝑖, 𝑗⟩ ˆ𝑎† 𝑖 ˆ𝑎𝑗 + ∑︁ 𝑖 𝑈 2 ˆ𝑛𝑖 (ˆ𝑛𝑖 −1) + ∑︁ 𝑖 (𝜖𝑖 −𝜇)ˆ𝑛𝑖 + ∑︁ 𝑖 Δ𝑖 ˆ𝑛𝑖 , (1) where𝐽is the tunneling strength between neighboring lattice sites, ˆ𝑎† 𝑖 and ˆ𝑎𝑗 are the bosonic creation and annihilation oper- ators on neighboring sites𝑖and𝑗, respecti...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  2. [2]

    After evaporative cooling, a superfluid of∼200 atoms is prepared in shallow horizontal lattices (𝑉 𝑥 =𝑉 𝑦 ≤10𝐸 r)

    Experimental details In our experiments [37], a cloud of ultracold 87Rb atoms is held in a single antinode of a vertical optical lattice (wavelength 𝜆=1064 nm and depth𝑉 𝑧 =25𝐸 r, where𝐸 r = ℏ 2/2𝑚𝜆2 is the recoil energy and𝑚is the mass of a 87Rb atom). After evaporative cooling, a superfluid of∼200 atoms is prepared in shallow horizontal lattices (𝑉 𝑥 =𝑉...

    work page

  3. [3]

    This allows us to map out the parameter space for different disorder strengths and lattice depths, within a reasonable experimental runtime

    Time-of-flight visibility In the weakly interacting regime, the presence of disorder should result in a reduced coherence, which we initially mea- sure via the visibility after time-of-flight [41]. This allows us to map out the parameter space for different disorder strengths and lattice depths, within a reasonable experimental runtime. We later complemen...

    work page

  4. [4]

    Edwards-Anderson parameter The visibility is not a reliable observable for distinguishing the Mott insulator from the Bose glass, as both lack long-range phase coherence (rightmost columns of Fig. 2b). Therefore, we employ the Edwards-Anderson parameter,𝑞 𝑖, which uses the atom distribution of the in-situ images [35, 36], 𝑞𝑖 = ⟨ˆ𝑛𝑖⟩2 − ⟨ˆ𝑛𝑖⟩ 2 .(2) 3 BG V...

    work page

  5. [5]

    To measure the coherence length, we employ an interferometry technique based on the Talbot effect, following an earlier experimental demonstration [45]

    Talbot interferometry A distinct feature of the Bose glass is the absence of long- range phase coherence, while maintaining short-range coher- ence over a small number of sites. To measure the coherence length, we employ an interferometry technique based on the Talbot effect, following an earlier experimental demonstration [45]. It involves briefly switch...

    work page

  6. [6]

    Signa- tures of non-ergodicity in the Bose-glass-to-superfluid transi- tion were recently observed using a quasicrystalline potential [32]

    Ergodicity, adiabaticity, and coherence In a finite-size system, a phase transition can be crossed without significant heating if both phases are ergodic. Signa- tures of non-ergodicity in the Bose-glass-to-superfluid transi- tion were recently observed using a quasicrystalline potential [32]. Here, we explore in a square lattice how the Mott- insulator-t...

    work page

  7. [7]

    Using Talbot interferometry across the superfluid-to-Bose-glass transition, we observed a change from long to short-range coherence

    Conclusion In summary, we identified the Bose-glass phase experi- mentally in both weakly and strongly interacting regimes in a two-dimensional square lattice with controllable and re- producible disorder potentials. Using Talbot interferometry across the superfluid-to-Bose-glass transition, we observed a change from long to short-range coherence. Additio...

    work page 2020

  8. [8]

    Krusin-Elbaum, L

    L. Krusin-Elbaum, L. Civale, G. Blatter, A. Marwick, F. Holtzberg, and C. Feild, Bose-glass melting in YBaCuO crys- tals with correlated disorder, Phys. Rev. Lett.72, 1914 (1994)

    work page 1914

  9. [9]

    Berthier and G

    L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys.83, 587 (2011)

    work page 2011

  10. [10]

    Ducry, J

    F. Ducry, J. Aeschlimann, and M. Luisier, Electro-thermal trans- port in disordered nanostructures: a modeling perspective, Nanoscale Adv.2, 2648 (2020)

    work page 2020

  11. [11]

    Sanchez-Palencia and M

    L. Sanchez-Palencia and M. Lewenstein, Disordered quantum gases under control, Nat. Phys.6, 87 (2010)

    work page 2010

  12. [12]

    Shapiro, Cold atoms in the presence of disorder, J

    B. Shapiro, Cold atoms in the presence of disorder, J. Phys. A: Math. Theor.45, 143001 (2012)

    work page 2012

  13. [13]

    Pollet, A review of Monte Carlo simulations for the Bose– Hubbard model with diagonal disorder, C.R

    L. Pollet, A review of Monte Carlo simulations for the Bose– Hubbard model with diagonal disorder, C.R. Phys.14, 712 (2013)

    work page 2013

  14. [14]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Colloquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys.91, 021001 (2019)

    work page 2019

  15. [15]

    P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev.109, 1492 (1958)

    work page 1958

  16. [16]

    Schwartz, G

    T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Transport and Anderson localization in disordered two-dimensional photonic lattices, Nature446, 52 (2007)

    work page 2007

  17. [17]

    Lahini, A

    Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Anderson localization and nonlinearity in one-dimensional disordered photonic lattices, Phys. Rev. Lett.100, 013906 (2008)

    work page 2008

  18. [18]

    Roati, C

    G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zac- canti, G. Modugno, M. Modugno, and M. Inguscio, Anderson localization of a non-interacting Bose–Einstein condensate, Na- ture453, 895 (2008)

    work page 2008

  19. [19]

    Pasienski, D

    M. Pasienski, D. McKay, M. White, and B. DeMarco, A disor- dered insulator in an optical lattice, Nat. Phys.6, 677 (2010)

    work page 2010

  20. [20]

    S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, Three-dimensional Anderson localization of ultracold matter, Science334, 66 (2011)

    work page 2011

  21. [21]

    Jendrzejewski, A

    F. Jendrzejewski, A. Bernard, K. Mueller, P. Cheinet, V. Josse, M. Piraud, L. Pezz ´e, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, Three-dimensional localization of ultracold atoms in an optical disordered potential, Nat. Phys.8, 398 (2012)

    work page 2012

  22. [22]

    D. H. White, T. A. Haase, D. J. Brown, M. D. Hoogerland, M. S. Najafabadi, J. L. Helm, C. Gies, D. Schumayer, and D. A. Hutchinson, Observation of two-dimensional Anderson locali- sation of ultracold atoms, Nat. Commun.11, 4942 (2020)

    work page 2020

  23. [23]

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

    work page 1989

  24. [24]

    Lee, M.-C

    J.-W. Lee, M.-C. Cha, and D. Kim, Phase diagram of a disor- dered Boson Hubbard model in two dimensions, Phys. Rev. Lett. 87, 247006 (2001)

    work page 2001

  25. [25]

    Fallani, J

    L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Ultracold atoms in a disordered crystal of light: Towards a Bose glass, Phys. Rev. Lett.98, 130404 (2007)

    work page 2007

  26. [26]

    Aleiner, B

    I. Aleiner, B. Altshuler, and G. Shlyapnikov, A finite- temperature phase transition for disordered weakly interacting bosons in one dimension, Nat. Phys.6, 900 (2010)

    work page 2010

  27. [27]

    Binder and A

    K. Binder and A. P. Young, Spin glasses: Experimental facts, theoretical concepts, and open questions, Rev. Mod. Phys.58, 801 (1986)

    work page 1986

  28. [28]

    F. Lin, E. S. Sørensen, and D. Ceperley, Superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model, Phys. Rev. B.84, 094507 (2011)

    work page 2011

  29. [29]

    S ¸. G. S¨oyler, M. Kiselev, N. V. Prokof’ev, and B. V. Svis- tunov, Phase diagram of the commensurate two-dimensional disordered Bose-Hubbard model, Phys. Rev. Lett.107, 185301 (2011)

    work page 2011

  30. [30]

    P. B. Weichman, Dirty bosons: twenty years later, Mod. Phys. Lett. B22, 2623 (2008)

    work page 2008

  31. [31]

    Pollet, N

    L. Pollet, N. V. Prokof’ev, B. V. Svistunov, and M. Troyer, Absence of a direct Superfluid to Mott insulator transition in disordered Bose systems, Phys. Rev. Lett.103, 140402 (2009)

    work page 2009

  32. [32]

    Bertoli, V

    G. Bertoli, V. P. Michal, B. L. Altshuler, and G. V. Shlyapnikov, Finite-temperature disordered bosons in two dimensions, Phys. Rev. Lett.121, 030403 (2018)

    work page 2018

  33. [33]

    Z. Zhu, H. Yao, and L. Sanchez-Palencia, Thermodynamic phase diagram of two-dimensional bosons in a quasicrystal potential, Phys. Rev. Lett.130, 220402 (2023)

    work page 2023

  34. [34]

    Meldgin, U

    C. Meldgin, U. Ray, P. Russ, D. Chen, D. Ceperley, and B. De- Marco, Probing the Bose glass–superfluid transition using quan- tum quenches of disorder, Nat. Phys.12, 646 (2016)

    work page 2016

  35. [35]

    Nagler, S

    B. Nagler, S. Barbosa, J. Koch, G. Orso, and A. Widera, Observ- ing the loss and revival of long-range phase coherence through disorder quenches, Proc. Natl. Acad. Sci.119, e2111078118 (2022)

    work page 2022

  36. [36]

    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, Ob- servation of many-body localization of interacting fermions in a quasirandom optical lattice, Science349, 842 (2015)

    work page 2015

  37. [37]

    J. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-Abadal, T. Yef- sah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Exploring the many-body localization transition in two dimensions, Sci- ence352, 1547 (2016)

    work page 2016

  38. [38]

    Rispoli, A

    M. Rispoli, A. Lukin, R. Schittko, S. Kim, M. E. Tai, J. L´eonard, and M. Greiner, Quantum critical behaviour at the many-body localization transition, Nature573, 385 (2019)

    work page 2019

  39. [39]

    J.-C. Yu, S. Bhave, L. Reeve, B. Song, and U. Schneider, Observ- ing the two-dimensional Bose glass in an optical quasicrystal, Nature633, 338 (2024)

    work page 2024

  40. [40]

    S. F. Edwards and P. W. Anderson, Theory of spin glasses, J. Phys. F5, 965 (1975)

    work page 1975

  41. [41]

    Morrison, A

    S. Morrison, A. Kantian, A. J. Daley, H. G. Katzgraber, M. Lewenstein, H. P. B¨ uchler, and P. Zoller, Physical repli- cas and the Bose glass in cold atomic gases, New J. Phys.10, 073032 (2008)

    work page 2008

  42. [42]

    S. J. Thomson, L. S. Walker, T. L. Harte, and G. D. Bruce, Measuring the Edwards-Anderson order parameter of the Bose glass: A quantum gas microscope approach, Phys. Rev. A94, 051601 (2016)

    work page 2016

  43. [43]

    A. R. Abadal,Probing quantum thermalization and localization in Bose-Hubbard systems, Ph.D. thesis, Ludwig-Maximilians- Universit¨at M¨ unchen (2020)

    work page 2020

  44. [44]

    Di Carli, C

    A. Di Carli, C. Parsonage, A. La Rooij, L. Koehn, C. Ulm, C. W. Duncan, A. J. Daley, E. Haller, and S. Kuhr, Commensu- rate and incommensurate 1D interacting quantum systems, Nat. Commun.15, 474 (2024)

    work page 2024

  45. [45]

    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)

    work page 2010

  46. [46]

    Billy, V

    J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Cl ´ement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Direct observation of Anderson localization of matter waves in 9 a controlled disorder, Nature453, 891 (2008)

    work page 2008

  47. [47]

    Sbroscia, K

    M. Sbroscia, K. Viebahn, E. Carter, J.-C. Yu, A. Gaunt, and U. Schneider, Observing localization in a 2d quasicrystalline optical lattice, Phys. Rev. Lett.125, 200604 (2020)

    work page 2020

  48. [48]

    W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. F ¨olling, L. Pollet, and M. Greiner, Probing the Su- perfluid–to–Mott Insulator transition at the single-atom level, Science329, 547 (2010)

    work page 2010

  49. [49]

    Gerbier, A

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

    work page 2005

  50. [50]

    Capogrosso-Sansone, S ¸

    B. Capogrosso-Sansone, S ¸. G. S¨oyler, N. Prokof’ev, and B. Svis- tunov, Monte Carlo study of the two-dimensional Bose-Hubbard model, Phys. Rev. A77, 015602 (2008)

    work page 2008

  51. [51]

    S. Pal, R. Bai, S. Bandyopadhyay, K. Suthar, and D. Angom, Enhancement of the Bose glass phase in the presence of an artificial gauge field, Phys. Rev. A99, 053610 (2019)

    work page 2019

  52. [52]

    Santra, C

    B. Santra, C. Baals, R. Labouvie, A. B. Bhattacherjee, A. Pel- ster, and H. Ott, Measuring finite-range phase coherence in an optical lattice using Talbot interferometry, Nat. Commun.8, 15601 (2017)

    work page 2017

  53. [53]

    Gurarie, L

    V. Gurarie, L. Pollet, N. V. Prokof’ev, B. V. Svistunov, and M. Troyer, Phase diagram of the disordered Bose-Hubbard model, Phys. Rev. B80, 214519 (2009)

    work page 2009

  54. [54]

    H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits, Arxiv 10.48550/arXiv.2403.12021 (2024)

    work page internal anchor Pith review doi:10.48550/arxiv.2403.12021 2024

  55. [55]

    Malpuech, D

    G. Malpuech, D. Solnyshkov, H. Ouerdane, M. Glazov, and I. Shelykh, Bose glass and superfluid phases of cavity polaritons, Phys. Rev. Lett.98, 206402 (2007)

    work page 2007

  56. [56]

    R. Yu, L. Yin, N. S. Sullivan, J. Xia, C. Huan, A. Paduan-Filho, N. F. Oliveira Jr, S. Haas, A. Steppke, C. F. Miclea,et al., Bose glass and Mott glass of quasiparticles in a doped quantum magnet, Nature489, 379 (2012)

    work page 2012

  57. [57]

    W. O. Tromp, T. Benschop, J.-F. Ge, I. Battisti, K. M. Bastiaans, D. Chatzopoulos, A. H. Vervloet, S. Smit, E. van Heumen, M. S. Golden,et al., Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb, Bi)2Sr2CuO6+𝛿 , Nat. Mat.22, 703 (2023)

    work page 2023

  58. [58]

    L. A. Gonz ´alez-Garc´ıa, S. F. Caballero-Ben´ıtez, and R. Paredes, Localisation of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects, Sci. Rep.9, 11049 (2019)

    work page 2019

  59. [59]

    X. Mao, J. Liu, J. Zhong, and R. A. R ¨omer, Disorder effects in the two-dimensional Lieb lattice and its extensions, Physica E 124, 114340 (2020)

    work page 2020

  60. [60]

    Carrasquilla, F

    J. Carrasquilla, F. Becca, A. Trombettoni, and M. Fabrizio, Characterization of the Bose-glass phase in low-dimensional lattices, Phys. Rev. B81, 195129 (2010)

    work page 2010

  61. [61]

    Ristivojevic, A

    Z. Ristivojevic, A. Petkovi ´c, P. Le Doussal, and T. Giamarchi, Superfluid/Bose-glass transition in one dimension, Phys. Rev. B 90, 125144 (2014)

    work page 2014

  62. [62]

    L ´eonard, S

    J. L ´eonard, S. Kim, M. Rispoli, A. Lukin, R. Schittko, J. Kwan, E. Demler, D. Sels, and M. Greiner, Probing the onset of quan- tum avalanches in a many-body localized system, Nat. Phys.19, 481 (2023)

    work page 2023

  63. [63]

    M. A. Tusch and D. E. Logan, Interplay between disorder and electron interactions in a𝑑=3 site-disordered Anderson- Hubbard model: A numerical mean-field study, Phys. Rev. B 48, 14843 (1993)

    work page 1993

  64. [64]

    Sanpera, A

    A. Sanpera, A. Kantian, L. Sanchez-Palencia, J. Zakrzewski, and M. Lewenstein, Atomic fermi-bose mixtures in inhomogeneous and random lattices: From Fermi Glass to Quantum Spin Glass and Quantum Percolation, Phys. Rev. Lett.93, 040401 (2004)

    work page 2004

  65. [65]

    Ahufinger, L

    V. Ahufinger, L. Sanchez-Palencia, A. Kantian, A. Sanpera, and M. Lewenstein, Disordered ultracold atomic gases in optical lattices: A case study of Fermi-Bose mixtures, Phys. Rev. A72, 063616 (2005)

    work page 2005

  66. [66]

    Paredes, C

    B. Paredes, C. Tejedor, and J. I. Cirac, Fermionic atoms in optical superlattices, Phys. Rev. A71, 063608 (2005)

    work page 2005

  67. [67]

    Szab ´o and U

    A. Szab ´o and U. Schneider, Mixed spectra and partially extended states in a two-dimensional quasiperiodic model, Phys. Rev. B 101, 014205 (2020)

    work page 2020

  68. [68]

    C. W. Duncan, Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals, Phys. Rev. B109, 014210 (2024)

    work page 2024

  69. [69]

    Ticeaet al., Observation of disorder-induced superfluidity, arXiv:2512.21416 (2025)

    N. Ticeaet al., Observation of disorder-induced superfluidity, arXiv:2512.21416 (2025)

    work page arXiv 2025

  70. [70]

    The data used in this publication is openly avail- able at https://doi.org/10.15129/af5cd941-2496-4a50-a10e- 14df02036546

    work page doi:10.15129/af5cd941-2496-4a50-a10e-

  71. [71]

    La Rooij, C

    A. La Rooij, C. Ulm, E. Haller, and S. Kuhr, A comparative study of deconvolution techniques for quantum-gas microscope images, New J. Phys.25, 083036 (2023)

    work page 2023

  72. [72]

    F. Alet, P. Dayal, A. Grzesik, A. Honecker, M. K ¨orner, A. L ¨auchli, S. R. Manmana, I. P. McCulloch, F. Michel, R. M. Noack,et al., The ALPS project: Open source software for strongly correlated systems, J. Phys. Soc. Jpn.74, 30 (2005)

    work page 2005

  73. [73]

    A. F. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S. G¨ urtler, A. Honecker,et al., The ALPS project release 1.3: Open-source software for strongly correlated systems, J. Magn. Magn. Mater.310, 1187 (2007)

    work page 2007

  74. [74]

    Bauer, L

    B. Bauer, L. Carr, H. G. Evertz, A. Feiguin, J. Freire, S. Fuchs, L. Gamper, J. Gukelberger, E. Gull, S. Guertler,et al., The ALPS project release 2.0: Open source software for strongly correlated systems, J. Stat. Mech.2011, P05001 (2011)

    work page 2011

  75. [75]

    A. W. Sandvik, Stochastic series expansion method with operator-loop update, Phys. Rev. B59, R14157 (1999)

    work page 1999

  76. [76]

    Pollet, S

    L. Pollet, S. M. A. Rombouts, K. Van Houcke, and K. Heyde, Optimal Monte Carlo updating, Phys. Rev. E70, 056705 (2004)

    work page 2004

  77. [77]

    F. Alet, S. Wessel, and M. Troyer, Generalized directed loop method for quantum Monte Carlo simulations, Phys. Rev. E71, 036706 (2005). 10 SUPPLEMENTAL MATERIALS

    work page 2005

  78. [78]

    We project this potential during the evaporation to a BEC and form the Mott insulator by increasing the horizontal lattices to𝑉 𝑥, 𝑦 =14𝐸 r

    Calibration of disorder potential strength The disorder potential strength is calibrated by projecting a uniform square light potential onto a Mott insulator with unit occupation. We project this potential during the evaporation to a BEC and form the Mott insulator by increasing the horizontal lattices to𝑉 𝑥, 𝑦 =14𝐸 r. We increase the power of the light p...

    work page

  79. [79]

    2, we simulate the thermal state of the disordered Bose-Hubbard model (Eq

    Quantum Monte-Carlo simulations To model the visibility measurements shown in Fig. 2, we simulate the thermal state of the disordered Bose-Hubbard model (Eq. 1) without harmonic confinement (𝜖 𝑖 =0) in the grand canonical ensemble at𝑇=0.1𝑈/𝑘 𝐵, using quantum Monte Carlo routines provided by the ALPS library [65–67]. We utilize the directed loop algorithm ...

    work page

  80. [80]

    S3, we show vertical cuts across the diagram pre- sented in Fig

    Additional data: Edwards-Anderson parameter In Fig. S3, we show vertical cuts across the diagram pre- sented in Fig. 2c, including error bars. All of the measurements of the Edwards-Anderson parameter,𝑞 𝑖, presented in this pa- per use four different disorder patterns. To justify this choice, we measured𝑞 𝑖 for different numbers of disorder patterns. We f...

    work page

Showing first 80 references.