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Artificial Gauge Fields with Laser-Assisted Tunneling

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Abstract

In ultracold-atom setups the physics of charged particles in magnetic fields cannot be simulated directly because of the charge neutrality of the atoms. Therefore new experimental methods had to be developed to circumvent this limitation by designing effective systems whose dynamics are governed by a Hamiltonian analog to the one of a charged particle in a magnetic field. Many realizations are based on periodically driven systems that can be mapped onto effective time-independent Hamiltonians which exhibit the desired physical properties. The general formalism is summarized in this chapter. In the end it focuses on the laser-assisted tunneling technique, which is used for the experimental results described in the context of this thesis.

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References

  1. J. Dalibard, F. Gerbier, G. Juzeli\(\bar{\text{ u }}\)nas, P. Öhberg, Colloquium: Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011)

    Google Scholar 

  2. N. Goldman, G. Juzeli\(\bar{\text{ u }}\)nas, P. Öhberg, I.B. Spielman, Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014)

    Google Scholar 

  3. N.R. Cooper, Rapidly rotating atomic gases. Adv. Phys. 57, 539–616 (2008)

    Article  ADS  Google Scholar 

  4. A.L. Fetter, Rotating trapped Bose-Einstein condensates. Rev. Mod. Phys. 81, 647–691 (2009)

    Article  ADS  Google Scholar 

  5. M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell, Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999)

    Article  ADS  Google Scholar 

  6. K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Vortex formation in a Stirred Bose-Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000)

    Article  ADS  Google Scholar 

  7. J.R. Abo-Shaeer, C. Raman, J.M. Vogels, W. Ketterle, Observation of vortex lattices in Bose-Einstein condensates. Science 292, 476–479 (2001)

    Article  ADS  Google Scholar 

  8. Y.-J. Lin, R.L. Compton, A.R. Perry, W.D. Phillips, J.V. Porto, I.B. Spielman, Bose-Einstein condensate in a uniform light-induced vector potential. Phys. Rev. Lett. 102, 130401 (2009)

    Article  ADS  Google Scholar 

  9. Y.J. Lin, R.L. Compton, K. Jimenez-Garcia, J.V. Porto, I.B. Spielman, Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009)

    Article  ADS  Google Scholar 

  10. M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. D. Xiao, M.-C. Chang, Q. Niu, Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Y. Aharonov, D. Bohm, Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. D. Jaksch, P. Zoller, Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms. New J. Phys. 5, 56 (2003)

    Article  ADS  Google Scholar 

  14. F. Gerbier, J. Dalibard, Gauge fields for ultracold atoms in optical superlattices. New J. Phys. 12, 033007 (2010)

    Article  ADS  Google Scholar 

  15. N.R. Cooper, Optical flux lattices for ultracold atomic gases. Phys. Rev. Lett. 106, 175301 (2011)

    Article  ADS  Google Scholar 

  16. N.R. Cooper, J. Dalibard, Optical flux lattices for two-photon dressed states. Europhys. Lett. 95, 66004 (2011)

    Article  ADS  Google Scholar 

  17. K. Jiménez-García, L.J. LeBlanc, R.A. Williams, M.C. Beeler, A.R. Perry, I.B. Spielman, Peierls substitution in an engineered lattice potential. Phys. Rev. Lett. 108, 225303 (2012)

    Article  ADS  Google Scholar 

  18. J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, P. Windpassinger, Tunable gauge potential for neutral and spinless particles in driven optical lattices. Phys. Rev. Lett. 108, 225304 (2012)

    Google Scholar 

  19. J. Struck, C. Ölschläger, R. Le Targat, P. Soltan-Panahi, A. Eckardt, M. Lewenstein, P. Windpassinger, K. Sengstock, Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996–999 (2011)

    Article  ADS  Google Scholar 

  20. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, I. Bloch, Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011)

    Article  ADS  Google Scholar 

  21. W. Magnus, On the exponential solution of differential equations for a linear operator. Comm. Pure and Appl. Math. 7, 649–673 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  22. M.M. Maricq, Application of average Hamiltonian theory to the NMR of solids. Phys. Rev. B 25, 6622–6632 (1982)

    Article  ADS  Google Scholar 

  23. S. Rahav, I. Gilary, S. Fishman, Effective Hamiltonians for periodically driven systems. Phys. Rev. A 68, 013820 (2003)

    Article  ADS  Google Scholar 

  24. J.H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979–B987 (1965)

    Article  ADS  Google Scholar 

  25. T. Fromherz, Floquet states and intersubband absorption in strongly driven double quantum wells. Phys. Rev. B 56, 4772–4777 (1997)

    Article  ADS  Google Scholar 

  26. M. Grifoni, P. Hänggi, Driven quantum tunneling. Phys. Rep. 304, 229–354 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  27. T. Bilitewski, N.R. Cooper, Scattering theory for floquet-bloch states. Phys. Rev. A 91, 033601 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  28. W.R. Salzman, Quantum mechanics of systems periodic in time. Phys. Rev. A 10, 461–465 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  29. Y.B. Zel’dovich, The quasienergy of a quantum-mechanical system subjected to a periodic action. Sov. Phys. JETP 24, 1006 (1967)

    ADS  Google Scholar 

  30. H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field. Phys. Rev. A 7, 2203–2213 (1973)

    Article  ADS  Google Scholar 

  31. F. Gesztesy, H. Mitter, A note on quasi-periodic states. J. Phys. A: Math. Gen. 14, L79–L85 (1981)

    Article  ADS  Google Scholar 

  32. N. Goldman, J. Dalibard, Periodically-driven quantum systems: effective hamiltonians and engineered gauge fields. Phys. Rev. X 4, 031027 (2014)

    Google Scholar 

  33. M. Bukov, A. Polkovnikov, Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian. Phys. Rev. A 90, 043613 (2014)

    Article  ADS  Google Scholar 

  34. N. Goldman, J. Dalibard, M. Aidelsburger, N.R. Cooper, Periodically-driven quantum matter: the case of resonant modulations. Phys. Rev. A 91, 033632 (2015)

    Article  ADS  Google Scholar 

  35. S.R. Barone, M.A. Narcowich, F.J. Narcowich, Floquet theory and applications. Phys. Rev. A 15, 1109–1125 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  36. H. Lignier, C. Sias, D. Ciampini, Y. Singh, A. Zenesini, O. Morsch, E. Arimondo, Dynamical control of matter-wave tunneling in periodic potentials. Phys. Rev. Lett. 99, 220403 (2007)

    Article  ADS  Google Scholar 

  37. J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckhardt, M. Lewenstein, L. Mathey, Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields. Nature Phys. 9, 738–743 (2013)

    Article  ADS  Google Scholar 

  38. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, T. Esslinger, Experimental realisation of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014)

    Article  ADS  Google Scholar 

  39. Y.-A. Chen, S. Nascimbène, M. Aidelsburger, M. Atala, S. Trotzky, I. Bloch, Controlling correlated tunneling and superexchange interactions with AC-driven optical lattices. Phys. Rev. Lett. 107, 210405 (2011)

    Article  ADS  Google Scholar 

  40. M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, I. Bloch, Experimental realization of strong effective magnetic fields in optical superlattice potentials. Appl. Phys. B 113, 1–11 (2013)

    Article  ADS  Google Scholar 

  41. M. Aidelsburger, M. Atala, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch, Realization of the hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013)

    Article  ADS  Google Scholar 

  42. H. Miyake, G.A. Siviloglou, C.J. Kennedy, W.C. Burton, W. Ketterle, Realizing the harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett. 111, 185302 (2013)

    Article  ADS  Google Scholar 

  43. M. Atala, M. Aidelsburger, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch, Observation of chiral currents with ultracold atoms in bosonic ladders. Nature Phys. 10, 588–593 (2014)

    Article  ADS  Google Scholar 

  44. M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J.T. Barreiro, S. Nascimbène, N.R. Cooper, I. Bloch, N. Goldman, Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nature Phys. 11, 162–166 (2015)

    Article  ADS  Google Scholar 

  45. M. Bukov, L. D’Alessio, and A. Polkovnikov. Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering. arXiv:1407.4803 (2014)

  46. P. Hauke, O. Tieleman, A. Celi, C. Olschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, A. Eckardt, Non-abelian gauge fields and topological insulators in shaken optical lattices. Phys. Rev. Lett. 109, 145301 (2012)

    Article  ADS  Google Scholar 

  47. W.R. Salzman, An alternative to the magnus expansion in time-dependent perturbation theory. J. Chem. Phys. 82, 822–826 (1985)

    Article  ADS  Google Scholar 

  48. A. Eckardt, T. Jinasundera, C. Weiss, M. Holthaus, Analog of photon-assisted tunneling in a bose-einstein condensate. Phys. Rev. Lett. 95, 200401 (2005)

    Article  ADS  Google Scholar 

  49. N. Teichmann, M. Esmann, C. Weiss, Fractional photon-assisted tunneling for Bose-Einstein condensates in a double well. Phys. Rev. A 79, 063620 (2009)

    Article  ADS  Google Scholar 

  50. I. Bloch, J. Dalibard, W. Zwerger, Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

    Article  ADS  Google Scholar 

  51. M.C. Rechtsman, J.M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, Photonic floquet topological insulators. Nature 496, 196–200 (2013)

    Google Scholar 

  52. A. Bermudez, T. Schaetz, D. Porras, Synthetic gauge fields for vibrational excitations of trapped ions. Phys. Rev. Lett. 107, 150501 (2011)

    Article  ADS  Google Scholar 

  53. A. Bermudez, T. Schaetz, D. Porras, Photon-assisted-tunneling toolbox for quantum simulations in ion traps. New J. Phys. 14, 053049 (2012)

    Article  ADS  Google Scholar 

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Correspondence to Monika Aidelsburger .

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Aidelsburger, M. (2016). Artificial Gauge Fields with Laser-Assisted Tunneling. In: Artificial Gauge Fields with Ultracold Atoms in Optical Lattices. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-25829-4_3

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