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Many-body physics with individually controlled Rydberg atoms

Nature Physics volume 16, pages 132–142 (2020)Cite this article

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Abstract

Recent decades have witnessed great developments in the field of quantum simulation—where synthetic systems are built and studied to gain insight into complicated, many-body real-world problems. Systems of individually controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for this task, particularly for the simulation of spin systems. Here, we review the techniques necessary for the manipulation of neutral atoms for the purpose of quantum simulation—such as quantum gas microscopes and arrays of optical tweezers—and explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models. We discuss recent achievements in the study of quantum many-body physics in this platform, and some current research directions beyond that.

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Fig. 1: Experimental platforms for realizing arrays of individually controlled neutral atoms.
Fig. 2: Quantum quench experiments for the Ising model.
Fig. 3: Quasi-adiabatic sweeps experiments for the Ising model.
Fig. 4: Quantum simulation of the XY model.

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References

  1. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    Article  MathSciNet  Google Scholar 

  2. Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).

    ADS  MathSciNet  MATH  Google Scholar 

  3. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    ADS  Google Scholar 

  4. Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).

    ADS  Google Scholar 

  5. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2010).

  6. Preskill, J. Quantum computing and the entanglement frontier. Preprint at https://arxiv.org/abs/1203.5813 (2012).

  7. Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014).

    Google Scholar 

  8. Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).

    Google Scholar 

  9. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Google Scholar 

  10. Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012).

    Google Scholar 

  11. Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

    Google Scholar 

  12. Chang, D. E., Vuletić, V. & Lukin, M. D. Quantum nonlinear optics — photon by photon. Nat. Photon. 8, 685–694 (2014).

    ADS  Google Scholar 

  13. Gallagher, T. F. Rydberg Atoms (Cambridge Univ. Press, 1994).

  14. Sibalić, N. & Adams, C. S. Rydberg Physics (IOP, 2018); https://iopscience.iop.org/book/978-0-7503-1635-4.

  15. Haroche, S. Controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85, 1083–1102 (2013).

    ADS  Google Scholar 

  16. Raimond, J.-M., Vitrant, G. & Haroche, S. Spectral line broadening due to the interaction between very excited atoms: ‘the dense Rydberg gas’. J. Phys. B 14, L655–L660 (1981).

    ADS  Google Scholar 

  17. Anderson, W. R., Veale, J. R. & Gallagher, T. F. Resonant dipole-dipole energy transfer in a nearly frozen Rydberg gas. Phys. Rev. Lett. 80, 249–252 (1998).

    ADS  Google Scholar 

  18. Mourachko, I. et al. Many-body effects in a frozen Rydberg gas. Phys. Rev. Lett. 80, 253–256 (1998).

    ADS  Google Scholar 

  19. Jaksch, D., Cirac, J. I., Zoller, P., Côté, R. & Lukin, M. D. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208–2211 (2000).

    ADS  Google Scholar 

  20. Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).

    ADS  Google Scholar 

  21. Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).

    ADS  Google Scholar 

  22. Schlosser, N., Reymond, G., Protsenko, I. & Grangier, P. Sub-poissonian loading of single atoms in a microscopic dipole trap. Nature 411, 1024–1027 (2001).

    ADS  Google Scholar 

  23. Urban, E. et al. Observation of Rydberg blockade between two atoms. Nat. Phys. 5, 110–114 (2009).

    Google Scholar 

  24. Gaëtan, A. et al. Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nat. Phys. 5, 115–118 (2009).

    Google Scholar 

  25. Wilk, T. et al. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104, 010502 (2010).

    ADS  Google Scholar 

  26. Isenhower, L. et al. Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104, 010503 (2010).

    ADS  Google Scholar 

  27. Comparat, D. & Pillet, P. Dipole blockade in a cold Rydberg atomic sample. J. Opt. Soc. Am. B 27, A208–A232 (2010).

    ADS  Google Scholar 

  28. Robicheaux, F. & Hernández, J. V. Many-body wave function in a dipole blockade configuration. Phys. Rev. A 72, 063403 (2005).

    ADS  Google Scholar 

  29. Weimer, H., Löw, R., Pfau, T. & Büchler, H. P. Quantum critical behavior in strongly interacting Rydberg gases. Phys. Rev. Lett. 101, 250601 (2010).

    Google Scholar 

  30. Weimer, H., Müller, M., Lesanovsky, I., Zoller, P. & Büchler, H. P. A Rydberg quantum simulator. Nat. Phys. 6, 382–388 (2010).

    Google Scholar 

  31. Olmos, B., González-Férez, R. & Lesanovsky, I. Collective Rydberg excitations of an atomic gas confined in a ring lattice. Phys. Rev. A 79, 043419 (2009).

    ADS  Google Scholar 

  32. Lesanovsky, I. Many-body spin interactions and the ground state of a dense Rydberg lattice gas. Phys. Rev. Lett. 106, 025301 (2011).

    ADS  Google Scholar 

  33. Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547–550 (2010).

    ADS  Google Scholar 

  34. Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).

    ADS  Google Scholar 

  35. Nogrette, F. et al. Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries. Phys. Rev. X 4, 021034 (2014).

    Google Scholar 

  36. Lee, W., Kim, H. & Ahn, J. Three-dimensional rearrangement of single atoms using actively controlled optical microtraps. Opt. Express 24, 9816–9825 (2016).

    ADS  Google Scholar 

  37. Barredo, D., de Léséleuc, S., Lienhard, V., Lahaye, T. & Browaeys, A. An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays. Science 354, 1021–1023 (2016).

    ADS  Google Scholar 

  38. Endres, M. et al. Atom-by-atom assembly of defect-free one-dimensional cold atom arrays. Science 354, 1024–1027 (2016).

    ADS  Google Scholar 

  39. Gross, C. & Bloch, I. Quantum simulation with ultra-cold atoms in optical lattices. Science 357, 995–1001 (2017).

    ADS  Google Scholar 

  40. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    ADS  Google Scholar 

  41. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).

    ADS  Google Scholar 

  42. Bergamini, S. et al. Holographic generation of micro-trap arrays for single atoms. J. Opt. Soc. Am. B 21, 1889–1894 (2004).

    ADS  MathSciNet  Google Scholar 

  43. Dumke, R. et al. Micro-optical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits. Phys. Rev. Lett. 89, 097903 (2002).

    ADS  Google Scholar 

  44. Schlosser, M. et al. Fast transport, atom sample splitting, and single-atom qubit supply in two-dimensional arrays of optical microtraps. New J. Phys. 14, 123034 (2012).

    ADS  Google Scholar 

  45. Piotrowicz, M. J. et al. Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array. Phys. Rev. A 88, 013420 (2013).

    ADS  Google Scholar 

  46. Grünzweig, T., Hilliard, A., McGovern, M. & Andersen, M. F. Near-deterministic preparation of a single atom in an optical microtrap. Nat. Phys. 6, 951–954 (2010).

    Google Scholar 

  47. Lester, B. J., Luick, N., Kaufman, A. M., Reynolds, C. M. & Regal, C. A. Rapid production of uniformly filled arrays of neutral atoms. Phys. Rev. Lett. 115, 073003 (2015).

    ADS  Google Scholar 

  48. Miroshnychenko, Y. et al. An atom sorting machine. Nature 442, 151 (2007).

    ADS  Google Scholar 

  49. Kim, H. et al. In situ single-atom array synthesis using dynamic holographic optical tweezers. Nat. Commun. 7, 13317 (2016).

    ADS  Google Scholar 

  50. Ohl de Mello, D. et al. Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems. Phys. Rev. Lett. 122, 203601 (2019).

    ADS  Google Scholar 

  51. Barredo, D., Lienhard, V., de Léséleuc, S., Lahaye, T. & Browaeys, A. Synthetic three-dimensional atomic structures assembled atom by atom. Nature 561, 79–82 (2018).

    ADS  Google Scholar 

  52. Nelson, K. D., Xiao, L. & David, S. Weiss. Imaging single atoms in a three-dimensional array. Nat. Phys. 3, 556–560 (2007).

    Google Scholar 

  53. Kumar, A., Wu, T.-Y., Giraldo, F. & Weiss, D. S. Sorting ultracold atoms in a 3D optical lattice in a realization of Maxwell’s demon. Nature 561, 83–87 (2018).

    ADS  Google Scholar 

  54. Browaeys, A., Barredo, D. & Lahaye, T. Experimental investigations of the dipolar interactions between a few individual Rydberg atoms. J. Phys. B 49, 152001 (2016).

    ADS  Google Scholar 

  55. Sibalic, N., Pritchard, J. D., Adams, C. S. & Weatherill, K. J. ARC: an open-source library for calculating properties of alkali Rydberg atoms. Comput. Phys. Commun. 220, 319–331 (2017).

    ADS  MATH  Google Scholar 

  56. Weber, S. et al. Calculation of Rydberg interaction potentials. J. Phys. B 50, 133001 (2017).

    ADS  Google Scholar 

  57. Johnson, T. A. et al. Rabi oscillations between ground and Rydberg states with dipole–dipole atomic interactions. Phys. Rev. Lett. 100, 113003 (2008).

    ADS  Google Scholar 

  58. Miroshnychenko, Y. et al. Coherent excitation of a single atom to a Rydberg state. Phys. Rev. A 82, 013405 (2010).

    ADS  Google Scholar 

  59. Labuhn, H. et al. Single-atom addressing in microtraps for quantum-state engineering using Rydberg atoms. Phys. Rev. A 90, 023415 (2014).

    ADS  Google Scholar 

  60. Jau, Y.-Y., Hankin, A. M., Keating, T., Deutsch, I. H. & Biedermann, G. W. Entangling atomic spins with a Rydberg-dressed spin-flip blockade. Nat. Phys. 12, 71–74 (2016).

    Google Scholar 

  61. Schauss, P. et al. Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491, 87–91 (2012).

    ADS  Google Scholar 

  62. Zeiher, J. et al. Microscopic characterization of scalable coherent Rydberg superatoms. Phys. Rev. X 5, 031015 (2015).

    Google Scholar 

  63. Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016).

    ADS  Google Scholar 

  64. de Léséleuc, S. et al. Accurate mapping of multilevel Rydberg atoms on interacting spin-1/2 particles for the quantum simulation of Ising models. Phys. Rev. Lett. 120, 113602 (2018).

    ADS  Google Scholar 

  65. Kim, H., Park, Y. J., Kim, K., Sim, H.-S. & Ahn, J. Detailed balance of thermalization dynamics in Rydberg-atom quantum simulators. Phys. Rev. Lett. 120, 180502 (2018).

    ADS  Google Scholar 

  66. Lee, W., Kim, M., Jo, H., Song, Y. & Ahn, J. Coherent and dissipative dynamics of entangled few-body systems of Rydberg atoms. Phys. Rev. A 99, 043404 (2019).

    ADS  Google Scholar 

  67. Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    ADS  Google Scholar 

  68. Pohl, T., Demler, E. & Lukin, M. D. Dynamical crystallization in the dipole blockade of ultracold atoms. Phys. Rev. Lett. 104, 043002 (2010).

    ADS  Google Scholar 

  69. Schauss, P. et al. Crystallization in Ising quantum magnets. Science 347, 1455–1458 (2015).

    ADS  Google Scholar 

  70. Lienhard, V. et al. Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic Ising antiferromagnets. Phys. Rev. X 8, 021070 (2018).

    Google Scholar 

  71. Guardado-Sanchez, E. et al. Probing the quench dynamics of antiferromagnetic correlations in a 2D quantum Ising spin system. Phys. Rev. X 8, 021069 (2018).

    Google Scholar 

  72. Keesling, A. et al. Probing quantum critical dynamics on a programmable Rydberg simulator. Nature 568, 207–211 (2019).

    ADS  Google Scholar 

  73. Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. A 9, 1387–1398 (1976).

    ADS  MATH  Google Scholar 

  74. Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985).

    ADS  Google Scholar 

  75. Bouchoule, I. & Mølmer, K. Spin squeezing of atoms by the dipole interaction in virtually excited Rydberg states. Phys. Rev. A 65, 041803(R) (2002).

    ADS  Google Scholar 

  76. Pupillo, G., Micheli, A., Boninsegni, M., Lesanovsky, I. & Zoller, P. Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics. Phys. Rev. Lett. 104, 223002 (2010).

    ADS  Google Scholar 

  77. Johnson, J. E. & Rolston, S. L. Interactions between Rydberg-dressed atoms. Phys. Rev. A 82, 033412 (2010).

    ADS  Google Scholar 

  78. Balewski, J. B. et al. Rydberg dressing: understanding of collective many-body effects and implications for experiments. New J. Phys. 16, 063012 (2014).

    ADS  Google Scholar 

  79. Glaetzle, A. W. et al. Quantum spin-ice and dimer models with Rydberg atoms. Phys. Rev. X 4, 041037 (2014).

    Google Scholar 

  80. Zeiher, J. et al. Coherent many-body spin dynamics in a long-range interacting Ising chain. Phys. Rev. X 7, 041063 (2017).

    Google Scholar 

  81. Zeiher, J. et al. Many-body interferometry of a Rydberg-dressed spin lattice. Nat. Phys. 12, 1095–1099 (2016).

    Google Scholar 

  82. Goldschmidt, E. A. et al. Anomalous broadening in driven dissipative Rydberg systems. Phys. Rev. Lett. 116, 113001 (2016).

    ADS  Google Scholar 

  83. Boulier, T. et al. Spontaneous avalanche dephasing in large Rydberg ensembles. Phys. Rev. A 120, 180502 (2018).

    Google Scholar 

  84. Clegg, R. M. The history of FRET. Rev. Fluoresc. 2006, 1–45 (2006).

    Google Scholar 

  85. Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2004).

  86. Günter, G. et al. Observing the dynamics of dipole-mediated energy transport by interaction-enhanced imaging. Science 342, 954–956 (2013).

    ADS  Google Scholar 

  87. Maxwell, D. et al. Storage and control of optical photons using Rydberg polaritons. Phys. Rev. Lett. 110, 103001 (2013).

    ADS  Google Scholar 

  88. Barredo, D. et al. Coherent excitation transfer in a “spin chain” of three Rydberg atoms. Phys. Rev. Lett. 114, 113002 (2015).

    ADS  Google Scholar 

  89. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).

    ADS  Google Scholar 

  90. Heeger, A. J., Kivelson, S., Schrieffer, J. R. & Su, W.-P. Solitons in conducting polymers. Rev. Mod. Phys. 60, 781–850 (1988).

    ADS  Google Scholar 

  91. Asbóth, J. K., Oroszlány, L. & Pályi, A. A short course on topological insulators: band-structure topology and edge states in one and two dimensions. Preprint at https://arxiv.org/abs/1509.02295 (2015).

  92. de Léséleuc, S. et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775–780 (2019).

    ADS  MathSciNet  Google Scholar 

  93. Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604–1606 (2012).

    ADS  MathSciNet  MATH  Google Scholar 

  94. de Léséleuc, S., Barredo, D., Lienhard, V., Browaeys, A. & Lahaye, T. Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states. Phys. Rev. A 97, 053803 (2018).

    ADS  Google Scholar 

  95. Levine, H. et al. High-fidelity control and entanglement of Rydberg atom qubits. Phys. Rev. Lett. 121, 123603 (2018).

    ADS  Google Scholar 

  96. Brown, M. O., Thiele, T., Kiehl, C., Hsu, T.-W. & Regal, C. A. Gray-molasses optical-tweezer loading: controlling collisions for scaling atom-array assembly. Phys. Rev. X 9, 011057 (2019).

    Google Scholar 

  97. Pagano, G. et al. Cryogenic trapped-ion system for large scale quantum simulation. Quantum Sci. Technol. 4, 014004 (2019).

    ADS  Google Scholar 

  98. Norcia, M. A., Young, A. W. & Kaufman, A. M. Microscopic control and detection of ultracold strontium in optical-tweezer arrays. Phys. Rev. X 8, 041054 (2018).

    Google Scholar 

  99. Cooper, A. et al. Alkaline-earth atoms in optical tweezers. Phys. Rev. X 8, 041055 (2018).

    Google Scholar 

  100. Jackson, N. C., Hanley, R. K., Hill, M., Adams, C. S. & Jones, M. P. A. Number-resolved imaging of 88Sr atoms in a long working distance optical tweezer. Preprint at https://arxiv.org/abs/1904.03233 (2019).

  101. Saskin, S., Wilson, J. T., Grinkenmeyer, B. & Thomson, J. D. Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array. Phys. Rev. Lett. 122, 143002 (2019).

    ADS  Google Scholar 

  102. Mukherjee, R., Millen, J., Nath, R., Jones, M. P. A. & Pohl, T. Many-body physics with alkaline-earth Rydberg lattices. J. Phys. B 44, 184010 (2011).

    ADS  Google Scholar 

  103. Dunning, F. B., Killian, T. C., Yoshida, S. & Burgdörfer, J. Recent advances in Rydberg physics using alkaline-earth atoms. J. Phys. B 49, 112003 (2016).

    ADS  Google Scholar 

  104. Nguyen, T. L. et al. Towards quantum simulation with circular Rydberg atoms. Phys. Rev. X 11, 011032 (2017).

    Google Scholar 

  105. Lechner, W., Hauke, P. & Zoller, P. A quantum annealing architecture with all-to-all connectivity from local interactions. Sci. Adv. 1, e1500838 (2015).

    ADS  Google Scholar 

  106. Glaetzle, A. W., van Bijnen, R. M. W., Zoller, P. & Lechner, W. A coherent quantum annealer with Rydberg atoms. Nat. Commun. 8, 15813 (2017).

    ADS  Google Scholar 

  107. Pichler, H., Wang, S.-T., Zhou, L., Choi, S. & Lukin, M. D. Quantum optimization for maximum independent set using Rydberg atom arrays. Preprint at https://arxiv.org/abs/1808.10816 (2018).

  108. Kokail, C. et al. Self-verifying variational quantum simulation of lattice models. Nature 569, 355–360 (2019).

    ADS  Google Scholar 

  109. Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79–99 (2018).

    Google Scholar 

  110. Saffman, M. Quantum computing with atomic qubits and Rydberg interactions: progress and challenges. J. Phys. B 49, 202001 (2016).

    ADS  Google Scholar 

  111. Weiss, D. S. & Saffman, M. Quantum computing with neutral atoms. Phys. Today 70, 44–50 (2017).

    Google Scholar 

  112. Reinhard, A., Cubel Liebisch, T., Knuffman, B. & Raithel, G. Level shifts of rubidium Rydberg states due to binary interactions. Phys. Rev. A 75, 032712 (2007).

    ADS  Google Scholar 

  113. Béguin, L., Vernier, A., Chicireanu, R., Lahaye, T. & Browaeys, A. Direct measurement of the van der Waals interaction between two Rydberg atoms. Phys. Rev. Lett. 110, 263201 (2013).

    ADS  Google Scholar 

  114. Barredo, D. et al. Demonstration of a strong Rydberg blockade in three-atom systems with anisotropic interactions. Phys. Rev. Lett. 112, 183002 (2014).

    ADS  Google Scholar 

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Acknowledgements

We thank the members of our group at Institut d’Optique, as well as all our colleagues of the Rydberg community, and in particular M. Lukin, M. Saffman, G. Biederman, C. Gross and I. Bloch, for many inspiring discussions over the years. This work benefited from financial support by the EU (FET-Flag 817482, PASQUANS), by ‘Investissements d’Avenir’ LabEx PALM (ANR-10-LABX-0039-PALM, projects QUANTICA and XYLOS), and by the Région Île-de-France in the framework of DIM SIRTEQ (project CARAQUES).

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  1. Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, Université Paris-Saclay, Palaiseau, France

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Correspondence to Antoine Browaeys.

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Browaeys, A., Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132–142 (2020). https://doi.org/10.1038/s41567-019-0733-z

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