Bose–Hubbard simulator with long-range hopping

Nature Physics (2026)Cite this article Quantum simulation that combines condensed-matter systems with quantum optical phenomena currently drives intense research efforts, particularly in an attempt to introduce collective quantum correlations. Here we show that confining dipolar excitons in a nanoscopic lattice emulates a version of the Bose–Hubbard model with long-range hopping and nearest-neighbour dipolar repulsions. Long-range hopping is evidenced by the spontaneous build-up of many-body sub-radiance, signalled by an algebraic slowdown of the radiative dissipation of excitons. In addition, we observe a threshold increase in the temporal coherence for only dipolar quantum solids. This suggests that excitons condense in a single sub-radiant state for Mott-like phases. These combine spatial order and collectively extended coherence in a single degree of freedom. Our study shows that nanoscopic exciton arrays provide a platform to design strongly correlated lattice models with long-range correlations.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutData that support the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.Combescot, M. & Shiau, S. Y. Excitons and Cooper Pairs: Two Composite Bosons in Many-Body Physics (Oxford Univ. Press, 2015).Hopfield, J. Theory of the contribution of excitons to the complex dielectric constant of crystals. Phys. Rev. 112, 1555–1567 (1958).Article ADS Google Scholar Combescot, M., Dubin, F. & Shiau, S.-Y. Signature of electromagnetic quantum fluctuations in exciton physics. Europhys. Lett. 138, 36002 (2022).Article ADS Google Scholar Tiranov, A. et al. Collective super- and subradiant dynamics between distant optical quantum emitters. Science 379, 389–393 (2023).Article ADS Google Scholar Gao, W. B., Fallahi, P., Togan, E., Miguel-Sanchez, J. & Imamoglu, A. Observation of entanglement between a quantum dot spin and a single photon. Nature 491, 426–430 (2012).Article ADS Google Scholar Moskalenko, S. & Snoke, D. Bose-Einstein Condensation of Excitons and Biexcitons: And Coherent Nonlinear Optics with Excitons (Cambridge Univ. Press, 2000).Park, H. et al. Dipole ladders with large Hubbard interaction in a moiré exciton lattice. Nat. Phys. 19, 1286–1292 (2023).Article Google Scholar Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).Article ADS Google Scholar Xiong, R. et al. Correlated insulator of excitons in WSe2/WS2 moiré superlattices. Science 380, 860–864 (2023).Lagoin, C., Suffit, S., Baldwin, K., Pfeiffer, L. & Dubin, F. Mott insulator of strongly interacting two-dimensional semiconductor excitons. Nat. Phys. 18, 149–153 (2022).Baranov, M. A., Dalmonte, M., Pupillo, G. & Zoller, P. Condensed matter theory of dipolar quantum gases. Chem. Rev. 112, 5012–5061 (2012).Article Google Scholar Dutta, O. et al. Non-standard Hubbard models in optical lattices: a review. Rep. Progr. Phys. 78, 066001 (2015).Article ADS Google Scholar Chanda, T., Barbiero, L., Lewenstein, M., Mark, M. J. & Zakrzewski, J. Recent progress on quantum simulations of non-standard Bose–Hubbard models. Rep. Prog. Phys. 88, 044501 (2025).Lagoin, C. et al. Extended Bose–Hubbard model with dipolar excitons. Nature 609, 485–489 (2022).Article ADS Google Scholar Lagoin, C., Baldwin, K., Pfeiffer, L. & Dubin, F. Superlattice quantum solid of dipolar excitons. Phys. Rev. Lett. 132, 176001 (2024).Asenjo-Garcia, A., Moreno-Cardoner, M., Albrecht, A., Kimble, H. & Chang, D. E. Exponential improvement in photon storage fidelities using subradiance and `selective radiance' in atomic arrays. Phys. Rev. X 7, 031024 (2017).

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Introductory Fourier Transform Spectroscopy (Elsevier, 2012).Lagoin, C., Suffit, S., Baldwin, K., Pfeiffer, L. & Dubin, F. Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers. Nat. Mater. 22, 170–174 (2023).ADS Google Scholar Download referencesWe would like to thank P. Filloux, D. Hrabovsky and S. Suffit for support and M. Holzmann and G. Pupillo for stimulating discussions. We are also grateful to J. Bloch, D. Chang, J. Dalibard, T. Grass, M. Lewenstein, H. J. Park and X. Xu for their critical reading of the paper. Our research has been financially supported by the French Agency for Research, contract numbers ANR-20-CE30-0032 and ANR-23-CE30-0022 to F.D.

The Princeton University portion of this research is funded in part by Gordon and Betty Moore Foundation’s EPiQS Initiative grant number GBMF9615.01 to L.P.Université Côte d’Azur, CNRS, CRHEA, Valbonne, FranceCamille Lagoin, Corentin Morin & François DubinPRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ, USAKirk Baldwin & Loren PfeifferSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarK.B. and L.P. realized the epitaxial growth of the GaAs heterostructure, and F.D. and C.L. designed and nanofabricated the electrostatic lattice. Experimental works, data analysis and numerical simulations were performed by C.L., C.M. and F.D. who also directed the research.Correspondence to François Dubin.The authors declare no competing interests.Nature Physics thanks Na Young Kim and the other, anonymous, reviewer(s) for their contribution to the peer review of this workPublisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a-c PL decay, in log-log scale, measured in electrostatic lattices with a period equal to 800 nm (a), 400 nm (b) and 250 nm (c) at 330 mK. The 3 devices were studied in a regime where the average filling is around 1 when Δt is set to about 250 ns (blue rectangle), by suitably tuning the laser excitation power and the gate voltage Vg. In a the complete dynamics is quantitatively reproduced by a single exponential decay with a time constant 1/Γ0 = 158 ns (black line). For the 400 nm period lattice (b) the PL decay is initially exponential, with a time constant 1/Γ0 = 214 ns (solid line), and then slows towards an algebraic dynamics Δt−1 for Δt≥400 ns (dashed line). Measurements shown in c are obtained with the device discussed in the main text, exhibiting a pronounced algebraic decay at long delays scaling like Δt−0.3 (dashed line). d Range accessible to the imaginary eigen-values of HLR for each studied lattice period (see colors), computed by assuming a infinite size two-dimensional array. The black lines provide a guide for the eye.a-b Integrated intensity of the PL as a function of the average laser excitation power P. The panel a corresponds to the experiments reported in Fig. 2. The integrated intensity is measured in a 100 ns long time interval starting 250 ns after extinction of the loading laser pulse repeated at 600 kHz. Panel b corresponds to the measurements shown in Fig. 3, acquired 400 ns after extinction of the loading pulse and averaged in a 200 ns long time interval at 900 kHz. c Exciton compressibility normalised to the level of poissonian fluctuations for the experiments shown in b. Experimental data (gray) were all acquired at the lowest 330 mK bath temperature while the red lines in a display saturation functions adjusting the measurements. In b-c orange and blue shaded areas underline CB and MI regimes respectively.Supplementary Sections I–IV, Figs. 1–6 and discussion.Data for each panel in .xls format.Data for each panel in .xls format.Data for each panel in .xls format.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsLagoin, C., Morin, C., Baldwin, K. et al. Bose–Hubbard simulator with long-range hopping. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03213-7Download citationReceived: 24 September 2024Accepted: 05 February 2026Published: 17 March 2026Version of record: 17 March 2026DOI: https://doi.org/10.1038/s41567-026-03213-7Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative