Digital quantum simulation with Rydberg atoms

  • H. Weimer
  • M. Müller
  • H. P. Büchler
  • I. Lesanovsky
Article

Abstract

We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involving many-body interactions and constraints. The central building block of the simulation scheme is constituted by a mesoscopic Rydberg gate that permits the entanglement of several atoms in an efficient, robust and quick protocol. In addition, optical pumping on ancillary atoms provides the dissipative ingredient for engineering the coupling between the system and a tailored environment. As an illustration, we discuss how the simulator enables the simulation of coherent evolution of quantum spin models such as the two-dimensional Heisenberg model and Kitaev’s toric code, which involves four-body spin interactions. We moreover show that in principle also the simulation of lattice fermions can be achieved. As an example for zcontrolled dissipative dynamics, we discuss ground state cooling of frustration-free spin Hamiltonians.

Keywords

Quantum simulator Digital quantum simulation Rydberg atoms Dissipative dynamics 

References

  1. 1.
    Abrams D.S., Lloyd S.: Simulation of many-body Fermi systems on a universal quantum computer. Phys. Rev. Lett. 79(13), 2586 (1997)ADSCrossRefGoogle Scholar
  2. 2.
    Aguado M., Brennen G.K., Verstraete F., Cirac J.I.: Creation, manipulation, and detection of abelian and non-abelian anyons in optical lattices. Phys. Rev. Lett. 101(26), 260501 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    Albuquerque A.F., Katzgraber H.G., Troyer M., Blatter G.: Engineering exotic phases for topologically protected quantum computation by emulating quantum dimer models. Phys. Rev. B 78(1), 014503 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    Bacon D., Childs A.M., Chuang I.L., Kempe J., Leung D.W., Zhou X.: Universal simulation of markovian quantum dynamics. Phys. Rev. A 64(6), 062302 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    Bakr W.S., Peng A., Tai M.E., Ma R., Simon J., Gillen J.I., Fölling S., Pollet L., Greiner M.: Probing the Superfluid to Mott Insulator transition at the single-atom level. Science 329(5991), 547–550 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    Barreiro J.T., Müller M., Schindler P., Nigg D., Monz T., Chwalla M., Hennrich M., Roos C.F., Zoller P., Blatt R.: An open-system quantum simulator with trapped ions. Nature 470, 486 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Bartenstein M., Altmeyer A., Riedl S., Jochim S., Chin C., Denschlag J.H., Grimm R.: Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas. Phys. Rev. Lett. 92(12), 120401 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Bernstein E., Vazirani U.: Quantum complexity theory. SIAM J. Comput. 26, 1411–1473 (1997)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Bloch I., Dalibard J., Zwerger W.: Many-body physics with ultracold gases. Rev. Mod. Phys. 80(3), 885–964 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Bombin H., Martin-Delgado M.A.: Topological quantum distillation. Phys. Rev. Lett. 97(18), 180501 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    Brion E., Mølmer K., Saffman M.: Quantum computing with collective ensembles of multilevel systems. Phys. Rev. Lett. 99(26), 260501 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Brown K.R., Clark R.J., Chuang I.L.: Limitations of quantum simulation examined by simulating a pairing hamiltonian using nuclear magnetic resonance. Phys. Rev. Lett. 97(5), 050504 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    Buluta I., Nori F.: Quantum simulators. Science 326(5949), 108–111 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    Diehl S., Micheli A., Kantian A., Kraus B., Büchler H.P., Zoller P.: Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008)CrossRefGoogle Scholar
  15. 15.
    Feynman R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fleischhauer M., Imamoglu A., Marangos J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77(2), 633–673 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Friedenauer A., Schmitz H., Glueckert J.T., Porras D., Schaetz T.: Simulating a quantum magnet with trapped ions. Nat. Phys. 4, 757–761 (2008)CrossRefGoogle Scholar
  18. 18.
    Gottesman D.: Class of quantum error-correcting codes saturating the quantum hamming bound. Phys. Rev. A 54(3), 1862–1868 (1996)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Greiner M., Mandel O., Esslinger T.W., Hänsch T., Bloch I.: Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms. Nature 415, 39 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    Herdman C.M., Young K.C., Scarola V.W., Sarovar M., Whaley K.B.: Stroboscopic generation of topological protection. Phys. Rev. Lett. 104(23), 230501 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Hubbard J.: Electron correlations in narrow energy bands. Proc. R. Soc. A 276(1365), 238–257 (1963)ADSCrossRefGoogle Scholar
  22. 22.
    Isenhower L., Urban E., Zhang X.L., Gill A.T., Henage T., Johnson T.A., Walker T.G., Saffman M.: Demonstration of a neutral atom controlled-not quantum gate. Phys. Rev. Lett. 104(1), 010503 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    Jaksch D., Bruder C., Cirac J.I., Gardiner C.W., Zoller P.: Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81(15), 3108–3111 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    Jaksch D., Cirac J.I., Zoller P., Rolston S.L., Côté R., Lukin M.D.: Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85(10), 2208–2211 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    Jané E., Vidal G., Dür W., Zoller P., Cirac J.I.: Simulation of quantum dynamics with quantum optical systems. Quantum Int. Comput. 3, 15–37 (2003)MATHGoogle Scholar
  26. 26.
    Jördens R., Strohmaier N., Günter K., Moritz H., Esslinger T.: A Mott insulator of Fermionic atoms in an optical lattice. Nature 455, 204–207 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    Kaltenbaek R., Lavoie J., Zeng B., Bartlett S.D., Resch K.J.: Optical one-way quantum computing with a simulated valence-bond solid. Nat. Phys. 6, 850–856 (2010)CrossRefGoogle Scholar
  28. 28.
    Kim K., Chang M.S., Korenblit S., Islam R., Edwards E.E., Freericks J.K., Lin G.D., Duan L.M., Monroe C.: Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    Kitaev A.Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    Kraus B., Büchler H.P., Diehl S., Kantian A., Micheli A., Zoller P.: Preparation of entangled states by quantum markov processes. Phys. Rev. A 78, 042307 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    Lanyon B.P., Whitfield J.D., Gillett G.G., Goggin M.E., Almeida M.P., Kassal I., Biamonte J.D., Mohseni M., Powell B.J., Barbieri M., Aspuru-Guzik A., White A.G.: Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010)CrossRefGoogle Scholar
  32. 32.
    Levin M.A., Wen X.-G.: String-net conden sation: a physical mechanism for topological phases. Phys. Rev. B 71(4), 045110 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Lloyd S.: Universal Quantum Simulators. Science 273(5278), 1073–1078 (1996)MathSciNetADSCrossRefMATHGoogle Scholar
  34. 34.
    Lloyd S., Viola L.: Engineering quantum dynamics. Phys. Rev. A 65(1), 010101 (2001)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Lukin M.D., Fleischhauer M., Côté R., Duan L.M., Jaksch D., Cirac J.I., Zoller P.: Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87(3), 037901 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    Ma X.S., Dakic B., Naylor W., Zeilinger A., Walther P.: Quantum simulation of a frustrated Heisenberg spin system. Nat. Phys. 7, 399 (2011)CrossRefGoogle Scholar
  37. 37.
    Müller M., Hammerer K., Zhou Y., Roos C.F., Zoller P.: Simulating open quantum systems: from many-body interactions to stabilizer pumping. New J. Phys. 13, 085007 (2011)CrossRefGoogle Scholar
  38. 38.
    Müller M., Lesanovsky I., Weimer H., Büchler H.P., Zoller P.: Mesoscopic Rydberg gate based on electromagnetically induced transparency. Phys. Rev. Lett. 102, 170502 (2009)CrossRefGoogle Scholar
  39. 39.
    Müller M., Liang L., Lesanovsky I., Zoller P.: Trapped Rydberg ions: from spin chains to fast quantum gates. New J. Phys. 10(9), 093009 (2008)CrossRefGoogle Scholar
  40. 40.
    Nelson K.D., Li X., Weiss D.S.: Imaging single atoms in a three dimensional array. Nat. Phys. 3, 556–560 (2007)CrossRefGoogle Scholar
  41. 41.
    Nielsen A.E.B., Mølmer K.: Topological matter with collective encoding and Rydberg blockade. Phys. Rev. A 82(5), 052326 (2010)ADSCrossRefGoogle Scholar
  42. 42.
    Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  43. 43.
    Olmos, B., Li, W., Hofferberth, S., Lesanovsky, I.: Amplifying single impurities immersed in a gas of ultra cold atoms (2011). arXiv:1106.4444Google Scholar
  44. 44.
    Pachos J.K., Wieczorek W., Schmid C., Kiesel N., Pohlner R., Weinfurter H.: Revealing anyonic features in a toric code quantum simulation. New J. Phys. 11(8), 083010 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    Porras D., Cirac J.I.: Effective quantum spin systems with trapped ions. Phys. Rev. Lett. 92(20), 207901 (2004)ADSCrossRefGoogle Scholar
  46. 46.
    Santos L., Baranov M.A., Cirac J.I., Everts H.-U., Fehrmann H., Lewenstein M.: Atomic quantum gases in Kagomé lattices. Phys. Rev. Lett. 93(3), 030601 (2004)ADSCrossRefGoogle Scholar
  47. 47.
    Schneider U., Hackermüller L., Will S., Best T., Bloch I., Costi T.A., Helmes R.W., Rasch D., Rosch A.: Metallic and insulating phases of repulsively interacting Fermions in a 3d optical lattice. Science 322(5907), 1520–1525 (2008)ADSCrossRefGoogle Scholar
  48. 48.
    Somaroo S., Tseng C.H., Havel T.F., Laflamme R., Cory D.G.: Quantum simulations on a quantum computer. Phys. Rev. Lett. 82(26), 5381–5384 (1999)ADSCrossRefGoogle Scholar
  49. 49.
    Verstraete F., Cirac J.I.: Mapping local hamiltonians of Fermions to local hamiltonians of spins. J. Stat. Mech. 2005(09), P09012 (2005)MathSciNetCrossRefGoogle Scholar
  50. 50.
    Verstraete F., Wolf M.M., Ignacio Cirac J.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5(9), 633–636 (2009)CrossRefGoogle Scholar
  51. 51.
    Weimer H., Müller M., Lesanovsky I., Zoller P., Büchler H.P.: A Rydberg quantum simulator. Nat. Phys. 6, 382–388 (2010)CrossRefGoogle Scholar
  52. 52.
    Weimer, H.: Quantum many-body physics with strongly interacting Rydberg atoms. PhD thesis, University of Stuttgart (2010)Google Scholar
  53. 53.
    Weitenberg C., Endres M., Sherson J.F., Cheneau M., Schauß P., Fukuhara T., Bloch I., Kuhr S.: Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011)ADSCrossRefGoogle Scholar
  54. 54.
    Whitlock S., Gerritsma R., Fernholz T., Spreeuw R.J.C.: Two-dimensional array of microtraps with atomic shift register on a chip. New J. Phys. 11(2), 023021 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    Wilk T., Gaëtan A., Evellin C., Wolters J., Miroshnychenko Y., Grangier P., Browaeys A.: Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104, 010502 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • H. Weimer
    • 1
    • 2
  • M. Müller
    • 3
    • 4
  • H. P. Büchler
    • 5
  • I. Lesanovsky
    • 6
  1. 1.Department of PhysicsHarvard UniversityCambridgeUSA
  2. 2.ITAMP, Harvard-Smithsonian Center for AstrophysicsCambridgeUSA
  3. 3.Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der WissenschaftenInstitut für Theoretische Physik der Universität InnsbruckInnsbruckAustria
  4. 4.Departamento de Física Teórica IUniversidad ComplutenseMadridSpain
  5. 5.Institute for Theoretical Physics IIIUniversity of StuttgartStuttgartGermany
  6. 6.Midlands Ultracold Atom Research Centre (MUARC), School of Physics and AstronomyThe University of NottinghamNottinghamUK

Personalised recommendations