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  • Letter
  • Open Access

Floquet-Rydberg quantum simulator for confinement in Z2 gauge theories

Enrico C. Domanti1,2,3,*, Dario Zappalà3,4, Alejandro Bermudez5,†, and Luigi Amico1,2,3,6

  • *Enrico.Domanti@tii.ae
  • †On sabbatical at Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, UK.
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Phys. Rev. Research 6, L022059 – Published 11 June, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022059

Abstract

Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the nonperturbative mechanisms underlying the confinement of quarks. In this work, considering periodically driven arrays of Rydberg atoms in a tweezer ladder geometry, we devise a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a Z2 LGT, in which hardcore bosons/spinless fermions are coupled to dynamical gauge fields. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically modulated real-time dynamics.

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References (79)

  1. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, USA, 1995).
  2. C. N. Yang and R. L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96, 191 (1954).
  3. K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
  4. J. Greensite, Introduction to the Confinement Problem (Springer Nature, Switzerland, 2020).
  5. S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K. K. Szabo, and G. Vulvert, Ab initio determination of light hadron masses, Science 322, 1224 (2008).
  6. K. Nagata, Finite-density lattice QCD and sign problem: Current status and open problems, Prog. Part. Nucl. Phys. 127, 103991 (2022).
  7. R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
  8. J. I. Cirac and P. Zoller, Goals and opportunities in quantum simulation, Nat. Phys. 8, 264 (2012).
  9. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  10. U.-J. Wiese, Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories, Ann. Phys. 525, 777 (2013).
  11. E. Zohar, J. I. Cirac, and B. Reznik, Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices, Rep. Prog. Phys. 79, 014401 (2016).
  12. M. Dalmonte and S. Montangero, Lattice gauge theory simulations in the quantum information era, Contemp. Phys. 57, 388 (2016).
  13. M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  14. M. C. Bañuls and K. Cichy, Review on novel methods for lattice gauge theories, Rep. Prog. Phys. 83, 024401 (2020).
  15. M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra, P. R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliūnas, V. Kasper, A. Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T. V. Zache, J. Zakrzewski et al., Cold atoms meet lattice gauge theory, Philos. Trans. R. Soc. A 380, 20210064 (2022).
  16. N. Klco, A. Roggero, and M. J. Savage, Standard model physics and the digital quantum revolution: thoughts about the interface, Rep. Prog. Phys. 85, 064301 (2022).
  17. C. W. Bauer, Z. Davoudi, A. B. Balantekin, T. Bhattacharya, M. Carena, W. A. de Jong, P. Draper, A. El-Khadra, N. Gemelke, M. Hanada, D. Kharzeev, H. Lamm, Y.-Y. Li, J. Liu, M. Lukin, Y. Meurice, C. Monroe, B. Nachman, G. Pagano, J. Preskill et al., Quantum simulation for high-energy physics, PRX Quantum 4, 027001 (2023).
  18. S. Flannigan, N. Pearson, G. H. Low, A. Buyskikh, I. Bloch, P. Zoller, M. Troyer, and A. J. Daley, Propagation of errors and quantitative quantum simulation with quantum advantage, Quantum Sci. Technol. 7, 045025 (2022).
  19. R. Trivedi, A. F. Rubio, and J. I. Cirac, Quantum advantage and stability to errors in analogue quantum simulators, arXiv:2212.04924.
  20. J. Schwinger, Gauge invariance and mass. II, Phys. Rev. 128, 2425 (1962).
  21. S. Coleman, R. Jackiw, and L. Susskind, Charge shielding and quark confinement in the massive schwinger model, Ann. Phys. 93, 267 (1975).
  22. G. 't Hooft, A two-dimensional model for mesons, Nucl. Phys. B 75, 461 (1974).
  23. D. J. Gross and W. Taylor, Two-dimensional QCD is a string theory, Nucl. Phys. B 400, 181 (1993).
  24. F. J. Wegner, Duality in generalized ising models and phase transitions without local order parameters, J. Math. Phys. 12, 2259 (1971).
  25. U. Borla, R. Verresen, F. Grusdt, and S. Moroz, Confined phases of one-dimensional spinless fermions coupled to Z2 gauge theory, Phys. Rev. Lett. 124, 120503 (2020).
  26. M. c. v. Kebrič, L. Barbiero, C. Reinmoser, U. Schollwöck, and F. Grusdt, Confinement and mott transitions of dynamical charges in one-dimensional lattice gauge theories, Phys. Rev. Lett. 127, 167203 (2021).
  27. D. González-Cuadra, L. Tagliacozzo, M. Lewenstein, and A. Bermudez, Robust topological order in fermionic Z2 gauge theories: From Aharonov-Bohm instability to soliton-induced deconfinement, Phys. Rev. X 10, 041007 (2020).
  28. J. Nyhegn, C.-M. Chung, and M. Burrello, ZN lattice gauge theory in a ladder geometry, Phys. Rev. Res. 3, 013133 (2021).
  29. A. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
  30. X.-G. Wen, Topological order: From long-range entangled quantum matter to a unified origin of light and electrons, ISRN Condens. Matter Phys. 2013, 1 (2013).
  31. E. Fradkin and S. H. Shenker, Phase diagrams of lattice gauge theories with Higgs fields, Phys. Rev. D 19, 3682 (1979).
  32. I. S. Tupitsyn, A. Kitaev, N. V. Prokof'ev, and P. C. E. Stamp, Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model, Phys. Rev. B 82, 085114 (2010).
  33. S. Gazit, M. Randeria, and A. Vishwanath, Emergent dirac fermions and broken symmetries in confined and deconfined phases of Z2 gauge theories, Nat. Phys. 13, 484 (2017).
  34. S. Gazit, F. F. Assaad, S. Sachdev, A. Vishwanath, and C. Wang, Confinement transition of Z2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry, Proc. Natl. Acad. Sci. USA 115, E6987 (2018).
  35. C. Muschik, M. Heyl, E. Martinez, T. Monz, P. Schindler, B. Vogell, M. Dalmonte, P. Hauke, R. Blatt, and P. Zoller, U(1) Wilson lattice gauge theories in digital quantum simulators, New J. Phys. 19, 103020 (2017).
  36. Z. Davoudi, M. Hafezi, C. Monroe, G. Pagano, A. Seif, and A. Shaw, Towards analog quantum simulations of lattice gauge theories with trapped ions, Phys. Rev. Res. 2, 023015 (2020).
  37. G. Pardo, T. Greenberg, A. Fortinsky, N. Katz, and E. Zohar, Resource-efficient quantum simulation of lattice gauge theories in arbitrary dimensions: Solving for Gauss's law and fermion elimination, Phys. Rev. Res. 5, 023077 (2023).
  38. R. Irmejs, M.-C. Bañuls, and J. I. Cirac, Quantum simulation of Z2 lattice gauge theory with minimal resources, Phys. Rev. D 108, 074503 (2023).
  39. L. Barbiero, C. Schweizer, M. Aidelsburger, E. Demler, N. Goldman, and F. Grusdt, Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to Z2 lattice gauge theories, Sci. Adv. 5, eaav7444 (2019).
  40. O. Băzăvan, S. Saner, E. Tirrito, G. Araneda, R. Srinivas, and A. Bermudez, Synthetic Z2 gauge theories based on parametric excitations of trapped ions, arXiv:2305.08700.
  41. J. Zhang, J. Unmuth-Yockey, J. Zeiher, A. Bazavov, S.-W. Tsai, and Y. Meurice, Quantum simulation of the universal features of the polyakov loop, Phys. Rev. Lett. 121, 223201 (2018).
  42. S. Notarnicola, M. Collura, and S. Montangero, Real-time-dynamics quantum simulation of (1+1)-dimensional lattice qed with Rydberg atoms, Phys. Rev. Res. 2, 013288 (2020).
  43. A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Emerging two-dimensional gauge theories in Rydberg configurable arrays, Phys. Rev. X 10, 021057 (2020).
  44. D. González-Cuadra, T. V. Zache, J. Carrasco, B. Kraus, and P. Zoller, Hardware efficient quantum simulation of non-Abelian gauge theories with qudits on Rydberg platforms, Phys. Rev. Lett. 129, 160501 (2022).
  45. S. Ohler, M. Kiefer-Emmanouilidis, A. Browaeys, H. P. Büchler, and M. Fleischhauer, Self-generated quantum gauge fields in arrays of Rydberg atoms, New J. Phys. 24, 023017 (2022).
  46. J. Mildenberger, W. Mruczkiewicz, J. C. Halimeh, Z. Jiang, and P. Hauke, Probing confinement in a Z2 lattice gauge theory on a quantum computer, arXiv:2203.08905.
  47. L. Homeier, A. Bohrdt, S. Linsel, E. Demler, J. C. Halimeh, and F. Grusdt, Realistic scheme for quantum simulation of Z2 lattice gauge theories with dynamical matter in (2+1)d, Commun. Phys. 6, 127 (2023).
  48. D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, J. Ye, and P. Zoller, Fermionic quantum processing with programmable neutral atom arrays, Proc. Natl. Acad. Sci. USA 120, e2304294120 (2023).
  49. C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices, Nat. Phys. 15, 1168 (2019).
  50. H. C. J. Gan, G. Maslennikov, K.-W. Tseng, C. Nguyen, and D. Matsukevich, Hybrid quantum computing with conditional beam splitter gate in trapped ion system, Phys. Rev. Lett. 124, 170502 (2020).
  51. A. Browaeys, D. Barredo, and T. Lahaye, Experimental investigations of dipole–dipole interactions between a few Rydberg atoms, J. Phys. B: At., Mol. Opt. Phys. 49, 152001 (2016).
  52. M. Morgado and S. Whitlock, Quantum simulation and computing with Rydberg-interacting qubits, AVS Quantum Science 3, 023501 (2021).
  53. A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017).
  54. J. Kogut and L. Susskind, Hamiltonian formulation of Wilson's lattice gauge theories, Phys. Rev. D 11, 395 (1975).
  55. L. Susskind, Lattice fermions, Phys. Rev. D 16, 3031 (1977).
  56. E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16, 407 (1961).
  57. D. H. Dunlap and V. M. Kenkre, Dynamic localization of a charged particle moving under the influence of an electric field, Phys. Rev. B 34, 3625 (1986).
  58. H. Lignier, C. Sias, D. Ciampini, Y. Singh, A. Zenesini, O. Morsch, and E. Arimondo, Dynamical control of matter-wave tunneling in periodic potentials, Phys. Rev. Lett. 99, 220403 (2007).
  59. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022059 for the derivation of the target Z2 LGT at second order in the Floquet perturbative analysis. Key points for the experimental realization of the proposed Floquet scheme are also discussed and additional details are provided about the impact of gauge-violating processes.
  60. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for Tensor network calculations, SciPost Phys. Codebases, 4 (2022).
  61. M. Fishman, S. R. White, and E. M. Stoudenmire, Codebase release 0.3 for ITensor, SciPost Phys. Codebases, 4 (2022).
  62. D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quantum Information & Computation 7, 401 (2007).
  63. M. C. Bañuls, Tensor network algorithms: A route map, Annu. Rev. Condens. Matter Phys. 14, 173 (2023).
  64. F. M. Surace and A. Lerose, Scattering of mesons in quantum simulators, New J. Phys. 23, 062001 (2021).
  65. E. C. Domanti, P. Castorina, D. Zappalà, and L. Amico, Aharonov-bohm effect for confined matter in lattice gauge theories, Phys. Rev. Res. 6, 013268 (2024).
  66. M. R. Flannery, D. Vrinceanu, and V. N. Ostrovsky, Long-range interaction between polar Rydberg atoms, J. Phys. B: At., Mol. Opt. Phys. 38, S279 (2005).
  67. S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, Calculation of Rydberg interaction potentials, J. Phys. B: At., Mol. Opt. Phys. 50, 133001 (2017).
  68. S. Bettelli, D. Maxwell, T. Fernholz, C. S. Adams, I. Lesanovsky, and C. Ates, Exciton dynamics in emergent Rydberg lattices, Phys. Rev. A 88, 043436 (2013).
  69. D. Maxwell, D. J. Szwer, D. Paredes-Barato, H. Busche, J. D. Pritchard, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, Storage and control of optical photons using Rydberg polaritons, Phys. Rev. Lett. 110, 103001 (2013).
  70. D. Barredo, H. Labuhn, S. Ravets, T. Lahaye, A. Browaeys, and C. S. Adams, Coherent excitation transfer in a spin chain of three Rydberg atoms, Phys. Rev. Lett. 114, 113002 (2015).
  71. A. P. Orioli, A. Signoles, H. Wildhagen, G. Günter, J. Berges, S. Whitlock, and M. Weidemüller, Relaxation of an isolated dipolar-interacting Rydberg quantum spin system, Phys. Rev. Lett. 120, 063601 (2018).
  72. S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, Optical control of the resonant dipole-dipole interaction between rydberg atoms, Phys. Rev. Lett. 119, 053202 (2017).
  73. C. Chen, G. Emperauger, G. Bornet, F. Caleca, B. Gély, M. Bintz, S. Chatterjee, V. Liu, D. Barredo, N. Y. Yao, T. Lahaye, F. Mezzacapo, T. Roscilde, and A. Browaeys, Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator, arXiv:2311.11726.
  74. J. S. Frasier, Resonant processes in a frozen gas, arXiv:cond-mat/0104551.
  75. S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms, Science 365, 775 (2019).
  76. M. Saffman and T. G. Walker, Analysis of a quantum logic device based on dipole-dipole interactions of optically trapped Rydberg atoms, Phys. Rev. A 72, 022347 (2005).
  77. J. C. Halimeh, H. Lang, J. Mildenberger, Z. Jiang, and P. Hauke, Gauge-symmetry protection using single-body terms, PRX Quantum 2, 040311 (2021).
  78. J. C. Halimeh, L. Homeier, C. Schweizer, M. Aidelsburger, P. Hauke, and F. Grusdt, Stabilizing lattice gauge theories through simplified local pseudogenerators, Phys. Rev. Res. 4, 033120 (2022).
  79. T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array, Phys. Rev. Lett. 123, 230501 (2019).

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Phys. Rev. Research 6, L022059– Published 11 June, 2024
  • Received 29 December 2023
  • Accepted 5 April 2024
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