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  • Letter
  • Open Access

Weak superfluidity in twisted optical potentials

Dean Johnstone1, Shanya Mishra1, Zhaoxuan Zhu1, Hepeng Yao2, and Laurent Sanchez-Palencia1

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Phys. Rev. Research 6, L042066 – Published 23 December, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042066

Abstract

A controlled twist between separate potentials can drastically influence localization properties of quantum particles between ordered and (quasi)disordered limits. Transport properties of single-particle and correlated fermionic materials have been extensively studied in connection with twisted bilayer graphene, but their bosonic counterpart remains largely unexplored. Here, we study bosonic matter in twisted potentials. We use continuous-space quantum Monte Carlo simulations to determine the unique phase diagrams of strongly correlated ultracold bosons in twisted optical lattices. For commensurate twisting angles, spectral gaps govern the formation of insulators, separated by thin superfluid domains. These domains form weak superfluids; with low superfluid fraction at zero temperature and high sensitivity to thermal fluctuations, but may be stabilized under appropriate parameter control. In contrast, slightly changing the twisting angle to an incommensurate value destroys most spectral gaps, leaving behind a prominent Bose glass phase. Our results are directly applicable to current generation experiments that quantum simulate moiré physics.

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References (81)

  1. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  2. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
  3. M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science 363, 1059 (2019).
  4. E. Suárez Morell, J. D. Correa, P. Vargas, M. Pacheco, and Z. Barticevic, Flat bands in slightly twisted bilayer graphene: Tight-binding calculations, Phys. Rev. B 82, 121407(R) (2010).
  5. R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. 108, 12233 (2011).
  6. G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Origin of magic angles in twisted bilayer graphene, Phys. Rev. Lett. 122, 106405 (2019).
  7. H. C. Po, L. Zou, A. Vishwanath, and T. Senthil, Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene, Phys. Rev. X 8, 031089 (2018).
  8. J. González and T. Stauber, Kohn-luttinger superconductivity in twisted bilayer graphene, Phys. Rev. Lett. 122, 026801 (2019).
  9. M. Xie and A. H. MacDonald, Nature of the correlated insulator states in twisted bilayer graphene, Phys. Rev. Lett. 124, 097601 (2020).
  10. Y. Choi, J. Kemmer, Y. Peng, A. Thomson, H. Arora, R. Polski, Y. Zhang, H. Ren, J. Alicea, G. Refael et al., Electronic correlations in twisted bilayer graphene near the magic angle, Nat. Phys. 15, 1174 (2019).
  11. J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Graphene bilayer with a twist: Electronic structure, Phys. Rev. Lett. 99, 256802 (2007).
  12. J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Continuum model of the twisted graphene bilayer, Phys. Rev. B 86, 155449 (2012).
  13. L. Zou, H. C. Po, A. Vishwanath, and T. Senthil, Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions, Phys. Rev. B 98, 085435 (2018).
  14. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53, 1951 (1984).
  15. W. Steurer, Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals, Z. Kristallogr. Cryst. Mater. 219, 391 (2004).
  16. W. Steurer, Quasicrystals: what do we know? what do we want to know? what can we know?, Acta Cryst. A 74, 1 (2018).
  17. K. Kamiya, T. Takeuchi, N. Kabeya, N. Wada, T. Ishimasa, A. Ochiai, K. Deguchi, K. Imura, and N. Sato, Discovery of superconductivity in quasicrystal, Nat. Commun. 9, 1 (2018).
  18. S. J. Ahn, P. Moon, T.-H. Kim, H.-W. Kim, H.-C. Shin, E. H. Kim, H. W. Cha, S.-J. Kahng, P. Kim, M. Koshino, Y.-W. Son, C.-W. Yang, and J. R. Ahn, Dirac electrons in a dodecagonal graphene quasicrystal, Science 361, 782 (2018).
  19. W. Yao, E. Wang, C. Bao, Y. Zhang, K. Zhang, K. Bao, C. K. Chan, C. Chen, J. Avila, M. C. Asensio, J. Zhu, and S. Zhou, Quasicrystalline 30∘ twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling, Proc. Natl. Acad. Sci. USA 115, 6928 (2018).
  20. J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, Why multilayer graphene on 4h−SiC(0001¯) behaves like a single sheet of graphene, Phys. Rev. Lett. 100, 125504 (2008).
  21. Y. Kim, H. Yun, S.-G. Nam, M. Son, D. S. Lee, D. C. Kim, S. Seo, H. C. Choi, H.-J. Lee, S. W. Lee, and J. S. Kim, Breakdown of the interlayer coherence in twisted bilayer graphene, Phys. Rev. Lett. 110, 096602 (2013).
  22. A. Majumdar, A. Rundquist, M. Bajcsy, V. D. Daisika, S. R. Bank, and J. Vuckovic, Design and analysis of photonic crystal coupled cavity arrays for quantum simulation, Phys. Rev. B 86, 195312 (2012).
  23. N. C. Harris, M. Prabhu, G. R. Steinbrecher, Y. Lahini, J. Mower, D. Bunandar, C. Chen, F. N. C. Wong, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, Quantum transport simulations in a programmable nanophotonic processor, Nat. Photonics 11, 447 (2017).
  24. I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013).
  25. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), and U. Sen, Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond, Adv. Phys. 56, 243 (2007).
  26. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  27. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  28. O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D.-S. Lühmann, B. A. Malomed, T. Sowiński, and J. Zakrzewski, Non-standard Hubbard models in optical lattices: A review, Rep. Prog. Phys. 78, 066001 (2015).
  29. T. Esslinger, Fermi-Hubbard physics with atoms in an optical lattice, Annu. Rev. Condens. Matter Phys. 1, 129 (2010).
  30. L. Tarruell and L. Sanchez-Palencia, Quantum simulation of the Hubbard model with ultracold fermions in optical lattices, C. R. Phys. 19, 365 (2018).
  31. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold bosonic atoms in optical lattices, Phys. Rev. Lett. 81, 3108 (1998).
  32. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature (London) 415, 39 (2002).
  33. T. Giamarchi and H. J. Schulz, Localization and interactions in one-dimensional quantum fluids, Europhys. Lett. 3, 1287 (1987).
  34. T. Giamarchi and H. J. Schulz, Anderson localization and interactions in one-dimensional metals, Phys. Rev. B 37, 325 (1988).
  35. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B 40, 546 (1989).
  36. J. Kisker and H. Rieger, Bose-glass and Mott-insulator phase in the disordered boson Hubbard model, Phys. Rev. B 55, R11981(R) (1997).
  37. B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, Atomic Bose and Anderson glasses in optical lattices, Phys. Rev. Lett. 91, 080403 (2003).
  38. P. Lugan, D. Clément, P. Bouyer, A. Aspect, M. Lewenstein, and L. Sanchez-Palencia, Ultracold Bose gases in 1D disorder: From Lifshits glass to Bose-Einstein condensate, Phys. Rev. Lett. 98, 170403 (2007).
  39. P. Lugan, D. Clément, P. Bouyer, A. Aspect, and L. Sanchez-Palencia, Anderson localization of Bogolyubov quasiparticles in interacting Bose-Einstein condensates, Phys. Rev. Lett. 99, 180402 (2007).
  40. V. Gurarie, L. Pollet, N. V. Prokof'ev, B. V. Svistunov, and M. Troyer, Phase diagram of the disordered Bose-Hubbard model, Phys. Rev. B 80, 214519 (2009).
  41. S. G. Söyler, M. Kiselev, N. V. Prokof'ev, and B. V. Svistunov, Phase diagram of the commensurate two-dimensional disordered Bose-Hubbard model, Phys. Rev. Lett. 107, 185301 (2011).
  42. G. Carleo, G. Boéris, M. Holzmann, and L. Sanchez-Palencia, Universal superfluid transition and transport properties of two-dimensional dirty bosons, Phys. Rev. Lett. 111, 050406 (2013).
  43. L. Sanchez-Palencia and M. Lewenstein, Disordered quantum gases under control, Nat. Phys. 6, 87 (2010).
  44. 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).
  45. K. Viebahn, M. Sbroscia, E. Carter, J.-C. Yu, and U. Schneider, Matter-wave diffraction from a quasicrystalline optical lattice, Phys. Rev. Lett. 122, 110404 (2019).
  46. 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).
  47. H. Yao, T. Giamarchi, and L. Sanchez-Palencia, Lieb-Liniger bosons in a shallow quasiperiodic potential: Bose glass phase and fractal Mott lobes, Phys. Rev. Lett. 125, 060401 (2020).
  48. R. Gautier, H. Yao, and L. Sanchez-Palencia, Strongly interacting bosons in a two-dimensional quasicrystal lattice, Phys. Rev. Lett. 126, 110401 (2021).
  49. D. Johnstone, P. Öhberg, and C. W. Duncan, Barriers to macroscopic superfluidity and insulation in a 2D Aubry–André model, J. Phys. B: At. Mol. Opt. Phys. 55, 125302 (2022).
  50. D. Johnstone, P. Öhberg, and C. W. Duncan, The mean-field Bose glass in quasicrystalline systems, J. Phys. A: Math. Theor. 54, 395001 (2021).
  51. 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).
  52. J.-C. Yu, S. Bhave, L. Reeve, B. Song, and U. Schneider, Observing the two-dimensional Bose glass in an optical quasicrystal, Nature 633, 338 (2024).
  53. A. González-Tudela and J. I. Cirac, Cold atoms in twisted-bilayer optical potentials, Phys. Rev. A 100, 053604 (2019).
  54. T. Salamon, A. Celi, R. W. Chhajlany, I. Frérot, M. Lewenstein, L. Tarruell, and D. Rakshit, Simulating twistronics without a twist, Phys. Rev. Lett. 125, 030504 (2020).
  55. X.-W. Luo and C. Zhang, Spin-twisted optical lattices: Tunable flat bands and Larkin-Ovchinnikov superfluids, Phys. Rev. Lett. 126, 103201 (2021).
  56. Z. Meng, L. Wang, W. Han, F. Liu, K. Wen, C. Gao, P. Wang, C. Chin, and J. Zhang, Atomic Bose–Einstein condensate in twisted-bilayer optical lattices, Nature (London) 615, 231 (2023).
  57. J. Lee and J. H. Pixley, Emulating twisted double bilayer graphene with a multiorbital optical lattice, SciPost Phys. 13, 033 (2022).
  58. G. C. Paul, P. Recher, and L. Santos, Particle dynamics and ergodicity-breaking in twisted-bilayer optical lattices, Phys. Rev. A 108, 053305 (2023).
  59. H. Yao, L. Tanzi, L. Sanchez-Palencia, T. Giamarchi, G. Modugno, and C. D'Errico, Mott transition for a Lieb-Liniger gas in a shallow quasiperiodic potential: Delocalization induced by disorder, Phys. Rev. Lett. 133, 123401 (2024).
  60. D. S. Petrov, M. Holzmann, and G. V. Shlyapnikov, Bose-einstein condensation in quasi-2d trapped gases, Phys. Rev. Lett. 84, 2551 (2000).
  61. D. S. Petrov and G. V. Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Phys. Rev. A 64, 012706 (2001).
  62. L. Pricoupenko and M. Olshanii, Stability of two-dimensional Bose gases in the resonant regime, J. Phys. B: At. Mol. Opt. Phys. 40, 2065 (2007).
  63. L.-C. Ha, C.-L. Hung, X. Zhang, U. Eismann, S.-K. Tung, and C. Chin, Strongly interacting two-dimensional Bose gases, Phys. Rev. Lett. 110, 145302 (2013).
  64. Further calculations for the unbalanced case, V1≠V2, not shown in this work, yield the same phases as discussed here and qualitatively similar phase diagrams.
  65. M. Boninsegni, N. Prokof'ev, and B. Svistunov, Worm algorithm for continuous-space path integral Monte Carlo simulations, Phys. Rev. Lett. 96, 070601 (2006).
  66. M. Boninsegni, N. V. Prokof'ev, and B. V. Svistunov, Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations, Phys. Rev. E 74, 036701 (2006).
  67. D. M. Ceperley, Path integrals in the theory of condensed helium, Rev. Mod. Phys. 67, 279 (1995).
  68. E. Gottlob and U. Schneider, Hubbard models for quasicrystalline potentials, Phys. Rev. B 107, 144202 (2023).
  69. C. Li, T. Zhou, I. Mazets, H.-P. Stimming, F. S. Møller, Z. Zhu, Y. Zhai, W. Xiong, X. Zhou, X. Chen, and J. Schmiedmayer, Relaxation of bosons in one dimension and the onset of dimensional crossover, SciPost Phys. 9, 058 (2020).
  70. N. Fabbri, D. Clément, L. Fallani, C. Fort, and M. Inguscio, Momentum-resolved study of an array of one-dimensional strongly phase-fluctuating Bose gases, Phys. Rev. A 83, 031604(R) (2011).
  71. N. Fabbri, M. Panfil, D. Clément, L. Fallani, M. Inguscio, C. Fort, and J.-S. Caux, Dynamical structure factor of one-dimensional Bose gases: Experimental signatures of beyond-luttinger-liquid physics, Phys. Rev. A 91, 043617 (2015).
  72. V. G. Rousseau, D. P. Arovas, M. Rigol, F. Hébert, G. G. Batrouni, and R. T. Scalettar, Exact study of the one-dimensional boson Hubbard model with a superlattice potential, Phys. Rev. B 73, 174516 (2006).
  73. B.-L. Chen, S.-P. Kou, Y. Zhang, and S. Chen, Quantum phases of the Bose-Hubbard model in optical superlattices, Phys. Rev. A 81, 053608 (2010).
  74. G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollwöck, and T. Giamarchi, Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases, Phys. Rev. A 78, 023628 (2008).
  75. Z. Zhu, S. Yu, D. Johnstone, and L. Sanchez-Palencia, Localization and spectral structure in two-dimensional quasicrystal potentials, Phys. Rev. A 109, 013314 (2024).
  76. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042066 for a discussion on the extraction of tunnelling rates from effective tight-binding models, the finite-temperature, and finite-size behavior or convergence of the SF domains.
  77. D. Johnstone, S. Mishra, Z. Zhu, and L. Sanchez-Palencia, Effective tight-binding models in optical moiré potentials, arXiv:2410.21371.
  78. Note that the global four-fold rotation symmetry is, however, preserved since Jb;xβ=Jc;yβ and Jb;yβ=Jc;xβ.
  79. F. Gerbier, Boson Mott insulators at finite temperatures, Phys. Rev. Lett. 99, 120405 (2007).
  80. M. Troyer, B. Ammon, and E. Heeb, Parallel object oriented Monte Carlo simulations, Lect. Notes Comput. Sci. 1505, 191 (1998).
  81. B. Bauer, L. D. Carr, H. Evertz, A. Feiguin, J. Freire, S. Fuchs, L. Gamper, J. Gukelberger, E. Gull, S. Guertler, A. Hehn, R. Igarashi, S. Isakov, D. Koop, P. Ma, P. Mates, H. Matsuo, O. Parcollet, G. Pawlowski, J. Picon, L. Pollet, E. Santos, V. Scarola, U. Schollwöck, C. Silva, B. Surer, S. Todo, S. Trebst, M. Troyer, M. Wall, P. Werner, and S. Wessel, The ALPS project release 2.0: Open source software for strongly correlated systems, J. Stat. Mech.: Th. Exp. (2011) P05001.

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Phys. Rev. Research 6, L042066– Published 23 December, 2024
  • Received 18 June 2024
  • Revised 9 October 2024
  • Accepted 28 November 2024
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