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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Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).
Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).
Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2010).
Preskill, J. Quantum computing and the entanglement frontier. Preprint at https://arxiv.org/abs/1203.5813 (2012).
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014).
Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).
Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).
Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012).
Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).
Chang, D. E., Vuletić, V. & Lukin, M. D. Quantum nonlinear optics — photon by photon. Nat. Photon. 8, 685–694 (2014).
Gallagher, T. F. Rydberg Atoms (Cambridge Univ. Press, 1994).
Sibalić, N. & Adams, C. S. Rydberg Physics (IOP, 2018); https://iopscience.iop.org/book/978-0-7503-1635-4.
Haroche, S. Controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85, 1083–1102 (2013).
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).
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).
Mourachko, I. et al. Many-body effects in a frozen Rydberg gas. Phys. Rev. Lett. 80, 253–256 (1998).
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).
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).
Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).
Schlosser, N., Reymond, G., Protsenko, I. & Grangier, P. Sub-poissonian loading of single atoms in a microscopic dipole trap. Nature 411, 1024–1027 (2001).
Urban, E. et al. Observation of Rydberg blockade between two atoms. Nat. Phys. 5, 110–114 (2009).
Gaëtan, A. et al. Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nat. Phys. 5, 115–118 (2009).
Wilk, T. et al. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104, 010502 (2010).
Isenhower, L. et al. Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104, 010503 (2010).
Comparat, D. & Pillet, P. Dipole blockade in a cold Rydberg atomic sample. J. Opt. Soc. Am. B 27, A208–A232 (2010).
Robicheaux, F. & Hernández, J. V. Many-body wave function in a dipole blockade configuration. Phys. Rev. A 72, 063403 (2005).
Weimer, H., Löw, R., Pfau, T. & Büchler, H. P. Quantum critical behavior in strongly interacting Rydberg gases. Phys. Rev. Lett. 101, 250601 (2010).
Weimer, H., Müller, M., Lesanovsky, I., Zoller, P. & Büchler, H. P. A Rydberg quantum simulator. Nat. Phys. 6, 382–388 (2010).
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).
Lesanovsky, I. Many-body spin interactions and the ground state of a dense Rydberg lattice gas. Phys. Rev. Lett. 106, 025301 (2011).
Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547–550 (2010).
Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).
Nogrette, F. et al. Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries. Phys. Rev. X 4, 021034 (2014).
Lee, W., Kim, H. & Ahn, J. Three-dimensional rearrangement of single atoms using actively controlled optical microtraps. Opt. Express 24, 9816–9825 (2016).
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).
Endres, M. et al. Atom-by-atom assembly of defect-free one-dimensional cold atom arrays. Science 354, 1024–1027 (2016).
Gross, C. & Bloch, I. Quantum simulation with ultra-cold atoms in optical lattices. Science 357, 995–1001 (2017).
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).
Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011).
Bergamini, S. et al. Holographic generation of micro-trap arrays for single atoms. J. Opt. Soc. Am. B 21, 1889–1894 (2004).
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).
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).
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).
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).
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).
Miroshnychenko, Y. et al. An atom sorting machine. Nature 442, 151 (2007).
Kim, H. et al. In situ single-atom array synthesis using dynamic holographic optical tweezers. Nat. Commun. 7, 13317 (2016).
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).
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).
Nelson, K. D., Xiao, L. & David, S. Weiss. Imaging single atoms in a three-dimensional array. Nat. Phys. 3, 556–560 (2007).
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).
Browaeys, A., Barredo, D. & Lahaye, T. Experimental investigations of the dipolar interactions between a few individual Rydberg atoms. J. Phys. B 49, 152001 (2016).
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).
Weber, S. et al. Calculation of Rydberg interaction potentials. J. Phys. B 50, 133001 (2017).
Johnson, T. A. et al. Rabi oscillations between ground and Rydberg states with dipole–dipole atomic interactions. Phys. Rev. Lett. 100, 113003 (2008).
Miroshnychenko, Y. et al. Coherent excitation of a single atom to a Rydberg state. Phys. Rev. A 82, 013405 (2010).
Labuhn, H. et al. Single-atom addressing in microtraps for quantum-state engineering using Rydberg atoms. Phys. Rev. A 90, 023415 (2014).
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).
Schauss, P. et al. Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491, 87–91 (2012).
Zeiher, J. et al. Microscopic characterization of scalable coherent Rydberg superatoms. Phys. Rev. X 5, 031015 (2015).
Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016).
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).
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).
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).
Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).
Pohl, T., Demler, E. & Lukin, M. D. Dynamical crystallization in the dipole blockade of ultracold atoms. Phys. Rev. Lett. 104, 043002 (2010).
Schauss, P. et al. Crystallization in Ising quantum magnets. Science 347, 1455–1458 (2015).
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).
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).
Keesling, A. et al. Probing quantum critical dynamics on a programmable Rydberg simulator. Nature 568, 207–211 (2019).
Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. A 9, 1387–1398 (1976).
Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985).
Bouchoule, I. & Mølmer, K. Spin squeezing of atoms by the dipole interaction in virtually excited Rydberg states. Phys. Rev. A 65, 041803(R) (2002).
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).
Johnson, J. E. & Rolston, S. L. Interactions between Rydberg-dressed atoms. Phys. Rev. A 82, 033412 (2010).
Balewski, J. B. et al. Rydberg dressing: understanding of collective many-body effects and implications for experiments. New J. Phys. 16, 063012 (2014).
Glaetzle, A. W. et al. Quantum spin-ice and dimer models with Rydberg atoms. Phys. Rev. X 4, 041037 (2014).
Zeiher, J. et al. Coherent many-body spin dynamics in a long-range interacting Ising chain. Phys. Rev. X 7, 041063 (2017).
Zeiher, J. et al. Many-body interferometry of a Rydberg-dressed spin lattice. Nat. Phys. 12, 1095–1099 (2016).
Goldschmidt, E. A. et al. Anomalous broadening in driven dissipative Rydberg systems. Phys. Rev. Lett. 116, 113001 (2016).
Boulier, T. et al. Spontaneous avalanche dephasing in large Rydberg ensembles. Phys. Rev. A 120, 180502 (2018).
Clegg, R. M. The history of FRET. Rev. Fluoresc. 2006, 1–45 (2006).
Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2004).
Günter, G. et al. Observing the dynamics of dipole-mediated energy transport by interaction-enhanced imaging. Science 342, 954–956 (2013).
Maxwell, D. et al. Storage and control of optical photons using Rydberg polaritons. Phys. Rev. Lett. 110, 103001 (2013).
Barredo, D. et al. Coherent excitation transfer in a “spin chain” of three Rydberg atoms. Phys. Rev. Lett. 114, 113002 (2015).
Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).
Heeger, A. J., Kivelson, S., Schrieffer, J. R. & Su, W.-P. Solitons in conducting polymers. Rev. Mod. Phys. 60, 781–850 (1988).
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).
de Léséleuc, S. et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775–780 (2019).
Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604–1606 (2012).
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).
Levine, H. et al. High-fidelity control and entanglement of Rydberg atom qubits. Phys. Rev. Lett. 121, 123603 (2018).
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).
Pagano, G. et al. Cryogenic trapped-ion system for large scale quantum simulation. Quantum Sci. Technol. 4, 014004 (2019).
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).
Cooper, A. et al. Alkaline-earth atoms in optical tweezers. Phys. Rev. X 8, 041055 (2018).
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).
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).
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).
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).
Nguyen, T. L. et al. Towards quantum simulation with circular Rydberg atoms. Phys. Rev. X 11, 011032 (2017).
Lechner, W., Hauke, P. & Zoller, P. A quantum annealing architecture with all-to-all connectivity from local interactions. Sci. Adv. 1, e1500838 (2015).
Glaetzle, A. W., van Bijnen, R. M. W., Zoller, P. & Lechner, W. A coherent quantum annealer with Rydberg atoms. Nat. Commun. 8, 15813 (2017).
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).
Kokail, C. et al. Self-verifying variational quantum simulation of lattice models. Nature 569, 355–360 (2019).
Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79–99 (2018).
Saffman, M. Quantum computing with atomic qubits and Rydberg interactions: progress and challenges. J. Phys. B 49, 202001 (2016).
Weiss, D. S. & Saffman, M. Quantum computing with neutral atoms. Phys. Today 70, 44–50 (2017).
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).
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).
Barredo, D. et al. Demonstration of a strong Rydberg blockade in three-atom systems with anisotropic interactions. Phys. Rev. Lett. 112, 183002 (2014).
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).
The authors declare no competing interests.
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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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