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Prediction of exotic ion-crystal structures in a Paul trap

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Abstract

Trapped Coulomb crystals are of prime importance for the fields of one-component plasmas, quantum computing, quantum simulations, artificial atoms, nonlinear spectroscopy, and structural phase transitions. In all these applications it is essential to be able to accurately predict the structure of the crystals given the trapping parameters. For the Paul trap, one of the most promising platforms for quantum computing, this is nontrivial, since the confining radio-frequency fields are time-dependent. The pseudopotential approach eliminates this time-dependence. However, the standard pseudopotential, commonly used in atomic physics and quantum computing applications, is not even powerful enough to predict all stable two-ion crystal configurations. In this paper, we develop an improved pseudopotential, applicable to few-ion Coulomb crystals. Our potential is vastly more accurate than the standard version, and is powerful enough to predict analytically the existence and structural phase boundaries of new three- and four-ion configurations that are completely missed by the standard pseudopotential. In particular, we make quantitative predictions of the border lines between different crystal configurations in the Paul trap’s (q, a) stability diagram, which can be used to accurately switch between configurations. In addition, our improved pseudopotential accurately predicts the tilt angles of two-ion crystals. We also delineate the regions in (q, a) control parameter space where no two-, three-, and four-ion crystals exist. While this region is known for two-ion crystals, the regions for three- and four-ion crystals are new.

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References

  1. F. Diedrich, E. Peik, J.M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987)

    Article  ADS  Google Scholar 

  2. D.J. Wineland, J.C. Bergquist, W.M. Itano, J.J. Bollinger, C.H. Manney, Phys. Rev. Lett. 59, 2935 (1987)

    Article  ADS  Google Scholar 

  3. C.R. Monroe, R.J. Schoelkopf, M.D. Lukin, Sci. Am. 314, 50 (2016)

    Article  Google Scholar 

  4. S. Debnath, N.M. Linke, C. Figgatt, K.A. Landsman, K. Wright, C. Monroe, Nature 536, 63 (2016)

    Article  ADS  Google Scholar 

  5. D. Hucul, I.V. Inlek, G. Vittorini, C. Crocker, S. Debnath, S.M. Clark, C. Monroe, Nat. Phys. (Lond.) 11, 37 (2015)

    Article  Google Scholar 

  6. C. Monroe, R. Raussendorf, A. Ruthven, K.R. Brown, P. Maunz, L.-M. Duan, J. Kim, Phys. Rev. A 89, 022317 (2014)

    Article  ADS  Google Scholar 

  7. J.M. Taylor, T. Calarco, Phys. Rev. A 78, 062331 (2008)

    Article  ADS  Google Scholar 

  8. I.M. Buluta, M. Kitaoka, S. Georgescu, S. Hasegawa, Phys. Rev. A 77, 062320 (2008)

    Article  ADS  Google Scholar 

  9. C. Shen, L.-M. Duan, Phys. Rev. A 90, 022332 (2014)

    Article  ADS  Google Scholar 

  10. S.-T. Wang, C. Shen, L.-M. Duan, Sci. Rep. 5, 8555 (2015)

    Article  Google Scholar 

  11. P. Richerme, Phys. Rev. A 94, 032320 (2016)

    Article  ADS  Google Scholar 

  12. R. Blatt, C.F. Roos, Nat. Phys. 8, 277 (2012)

    Article  Google Scholar 

  13. M. Johanning, A.F. Varón, C. Wunderlich, J. Phys. B: At. Mol. Opt. Phys. 42, 154009 (2009)

    Article  ADS  Google Scholar 

  14. K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E.E. Edwards, J.K. Freericks, G.-D. Lin, L.-M. Duan, C. Monroe, Nature 465, 590 (2010)

    Article  ADS  Google Scholar 

  15. J.G. Bohnet, B.C. Sawyer, J.W. Britton, M.L. Wall, A.M. Rey, M. Foss-Feig, J.J. Bollinger, Science 352, 1297 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  16. D.G. Enzer, M.M. Schauer, J.J. Gomez, M.S. Gulley, M.H. Holzscheiter, P.G. Kwiat, S.K. Lamoreaux, C.G. Peterson, V.D. Sandberg, D. Tupa, A.G. White, R.J. Hughes, D.F.V. James, Phys. Rev. Lett. 85, 2466 (2000)

    Article  ADS  Google Scholar 

  17. P. Horak, A. Dantan, M. Drewsen, Phys. Rev. A 86, 043435 (2012)

    Article  ADS  Google Scholar 

  18. L.L. Yan, W. Wan, L. Chen, F. Zhou, S.J. Gong, X. Tong, M. Feng, Sci. Rep. 6, 21547 (2016)

    Article  ADS  Google Scholar 

  19. F. Calvo, C. Champenois, E. Yurtsever, Phys. Rev. A 80, 063401 (2009)

    Article  ADS  Google Scholar 

  20. E. Shimshoni, G. Morigi, S. Fishman, Phys. Rev. Lett. 106, 010401 (2011)

    Article  ADS  Google Scholar 

  21. S. Fishman, G. De Chiara, T. Calarco, G. Morigi, Phys. Rev. B 77, 064111 (2008)

    Article  ADS  Google Scholar 

  22. Z.-X. Gong, G.-D. Lin, L.-M. Duan, Phys. Rev. Lett. 105, 265703 (2010)

    Article  ADS  Google Scholar 

  23. A. Lemmer, C. Cormick, C.T. Schmiegelow, F. Schmidt-Kaler, M.B. Plenio, Phys. Rev. Lett. 114, 073001 (2015)

    Article  ADS  Google Scholar 

  24. W.W. Smith, O.P. Marakov, J. Lin, J. Mod. Opt. 52, 2253 (2005)

    Article  ADS  Google Scholar 

  25. S. Lee, K. Ravi, and S. A. Rangwala, Phys. Rev. A 87, 052701 (2013)

    Article  ADS  Google Scholar 

  26. J.E. Wells, R. Blümel, J.M. Kwolek, D.S. Goodman, W.W. Smith, Phys. Rev. A 95, 053416 (2017)

    Article  ADS  Google Scholar 

  27. J.M. Kwolek, D.S. Goodman, S.A. Entner, J.E. Wells, F.A. Narducci, W.W. Smith, Phys. Rev. A 97, 053420 (2018)

    Article  ADS  Google Scholar 

  28. M.A. Kastner, Phys. Today 46, 24 (1993)

    Article  ADS  Google Scholar 

  29. A. Tartakovskii (Ed.), Quantum Dots – Optics, Electron Transport and Future Applications (Cambridge University Press, Cambridge, 2012)

  30. N.M. Freitag, L.A. Chizhova, P. Nemes-Incze, C.R. Woods, R.V. Gorbachev, Y. Cao, A.K. Geim, K.S. Novoselov, J. Burgdörfer, F. Libisch, M. Morgenstern, Nano Lett. 16, 5798 (2016)

    Article  ADS  Google Scholar 

  31. H. Thomas, G.E. Morfill, V. Demmel, J. Goree, B. Feuerbacher, D. Möhlmann, Phys. Rev. Lett. 73, 652 (1994)

    Article  ADS  Google Scholar 

  32. T.E. Sheridan, Phys. Plasmas 12, 080701 (2005)

    Article  ADS  Google Scholar 

  33. E.Y. Andrei (Ed.), Two-Dimensional Electron Systems (Kluwer Academic, Dordrecht, 1997)

  34. E.R. Russell, F. Spaepen, D.A. Weitz, Phys. Rev. E 91, 032310 (2015)

    Article  ADS  Google Scholar 

  35. E. Tjhung, L. Berthier, Phys. Rev. Lett. 114, 148301 (2015)

    Article  ADS  Google Scholar 

  36. J.P. Schiffer, P. Kienle, Z. Phys. A 321, 181 (1985)

    Article  ADS  Google Scholar 

  37. Y. Yuri, H. Okamoto, Phys. Rev. ST Accel. Beams 8, 114201 (2005)

    Article  ADS  Google Scholar 

  38. U. Schramm, T. Schätz, D. Habs, Phys. Rev. Lett. 87, 184801 (2001)

    Article  ADS  Google Scholar 

  39. U. Schramm, T. Schätz, D. Habs, Phys. Rev. E 66, 036501 (2002)

    Article  ADS  Google Scholar 

  40. W. Paul, Rev. Mod. Phys. 62, 531 (1990)

    Article  ADS  Google Scholar 

  41. P.K. Ghosh, Ion Traps (Clarendon Press, Oxford, 1995)

  42. M.G. Moore, R. Blümel, Phys. Rev. A 50, R4453 (1994)

    Article  ADS  Google Scholar 

  43. J.A. Hoffnagle, R.G. Brewer, Appl. Phys. B 60, 113 (1995)

    Article  ADS  Google Scholar 

  44. M.G. Moore, R. Blümel, Phys. Scr. T 59, 429 (1995)

    Article  ADS  Google Scholar 

  45. M.G. Raizen, J.M. Gilligan, J.C. Bergquist, W.M. Itano, D.J. Wineland, Phys. Rev. A 45, 6493 (1992)

    Article  ADS  Google Scholar 

  46. M. Drewsen, C. Brodersen, L. Hornekær, J.S. Hangst, J.P. Schifffer, Phys. Rev. Lett. 81, 2878 (1998)

    Article  ADS  Google Scholar 

  47. V. Ursekar, Y.S. Nam, R. Blümel, in preparation

  48. R. Blümel, J.M. Chen, E. Peik, W. Quint, W. Schleich, Y.R. Shen, H. Walther, Nature 334, 309 (1988)

    Article  ADS  Google Scholar 

  49. R. Blatt, G. Werth, Phys. Rev. A 25, 1476 (1982)

    Article  ADS  Google Scholar 

  50. R.F. Wuerker, H. Shelton, R.V. Langmuir, J. Appl. Phys. 30, 342 (1959)

    Google Scholar 

  51. W. Paul, O. Osberghaus, E. Fischer Ein Ionenkäfig, Forschungsberichte des Wirtschafts und Verkehrsministeriums Nordrhein-Westfalen 415 (1958)

  52. W. Paul, H.P. Reinhard, U. von Zahn, Z. f. Phys. 152, 143 (1958)

    Article  ADS  Google Scholar 

  53. M. Abramowitz, I. A. Stegun (eds.), Handbook of Mathematical Functions, (National Bureau of Standards, Gaithersburg, MD, 1964)

  54. R. Blümel, C. Kappler, W. Quint, H. Walther, Phys. Rev. A 40, 808 (1989)

    Article  ADS  Google Scholar 

  55. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes, 2nd edn. (Cambridge University Press, Cambridge, 1992)

  56. H.G. Dehmelt, Adv. At. Mol. Phys. 3, 53 (1967)

    Article  ADS  Google Scholar 

  57. L.D. Landau, E.M. Lifshits, Mechanics, 2nd edn. (Pergamon Press, Oxford, 1976)

  58. J.O. Carrico, in Dynamical Mass Spectrometry, edited by D. Price (Heyden, London, 1972), Vol. 3

  59. J.P. Schiffer, M. Drewsen, J.S. Hangst, L. Hornekaer, Proc. Natl. Acad. Sci. USA 97, 10697 (2000)

    Article  ADS  Google Scholar 

  60. D.C. Rapaport, The Art of Molecular Dynamics Simulations, 2nd edn. (Cambridge University Press, Cambridge, 2004)

  61. Y.S. Nam, E.B. Jones, R. Blümel, Phys. Rev. A 90, 013402 (2014)

    Article  ADS  Google Scholar 

  62. H. Landa, M. Drewsen, B. Reznik1, A. Retzker, New J. Phys. 14, 093023 (2012)

    Article  ADS  Google Scholar 

  63. D.K. Weiss, Y.S. Nam, R. Blümel, Phys. Rev. A 93, 043424 (2016)

    Article  ADS  Google Scholar 

  64. H. Walther, Adv. At. Mol. Opt. Phys. 31, 137 (1993)

    Article  ADS  Google Scholar 

  65. J. D. Tarnas, Y. S. Nam, R. Blümel, Phys. Rev. A 88, 041401 (2013)

    Article  ADS  Google Scholar 

  66. S.T. Thornton, J.B. Marion, Classical Dynamics of Particles and Systems (Brooks/Cole, Belmont, CA, 2004)

  67. J.W. Emmert, M. Moore, R. Blümel, Phys. Rev. A 48, R1757 (1993)

    Article  ADS  Google Scholar 

  68. I.S. Gradshteyn, I.M. Ryzhik, in Table of Integrals, Series, and Products, 5th edn., edited by A. Jeffrey (Academic Press, Boston, 1994), Vol. 14, p. 1145

  69. L. Föppl, J. Reine Angew. Math. 141, 251 (1912)

    MathSciNet  Google Scholar 

  70. D.C. Giancoli, Physics – Principles with Applications, 7th edn. (Pearson, Boston, 2014)

  71. A.G. Fainshtein, N.L. Manakov, L.P. Rapoport, J. Phys. B: Atom. Molec. Phys. 11, 2561 (1978)

    Article  ADS  Google Scholar 

  72. R. Lechner, Ch. Maier, C. Hempel, P. Jurcevic, B.P. Lanyon, Th. Monz, M. Brownnutt, R. Blatt, Ch.F. Roos, Phys. Rev. A 93, 053401 (2016)

    Article  ADS  Google Scholar 

  73. F. Diedrich, J.C. Bergquist, W.M. Itano, D.J. Wineland, Phys. Rev. Lett. 62, 403 (1989)

    Article  ADS  Google Scholar 

  74. C. Monroe, D.M. Meekhof, B.E. King, S.R. Jefferts, W.M. Itano, D.J. Wineland, Phys. Rev. Lett. 75, 4011 (1995)

    Article  ADS  Google Scholar 

  75. A.J. Lichtenberg, M.A. Lieberman, in Regular and Stochastic Motion of Applied Mathematical Sciences (Springer, New York, 1983), Vol. 38

  76. H. Friedrich, Theoretical Atomic Physics, 3rd edn. (Springer, Berlin, 2006)

  77. A. Retzker, R.C. Thompson, D.M. Segal, M.B. Plenio, Phys. Rev. Lett. 101, 260504 (2008)

    Article  ADS  Google Scholar 

  78. E. Shimshoni, G. Morigi, S. Fishman, Phys. Rev. A 83, 032308 (2011)

    Article  ADS  Google Scholar 

  79. J.D. Baltrusch, C. Cormick, G. De Chiara, T. Calarco, G. Morigi, Phys. Rev. A 84, 063821 (2011)

    Article  ADS  Google Scholar 

  80. J.D. Baltrusch, C. Cormick, G. Morigi, Phys. Rev. A 86, 032104 (2012)

    Article  ADS  Google Scholar 

  81. M. Mielenz et al., Nat. Commun. 7, 11839 (2016)

    Article  ADS  Google Scholar 

  82. H. Landa, M. Drewsen, B. Reznik, A. Retzker, J. Phys. A: Math. Theor. 45, 455305 (2012)

    Google Scholar 

  83. D.C. Lay, Linear Algebra and Its Applications (Addison-Wesley, New York, 2003)

  84. N. Jacobson, Basic Algebra I (Dover, Mineola, NY, 2009)

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Authors and Affiliations

  1. Department of Physics, Boston University, Boston, MA, 02215, USA

    Varun Ursekar

  2. Department of Physics, Wesleyan University, Middletown, CT, 06459-0155, USA

    Joseph M. Silvester & Reinhold Blümel

  3. Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20740, USA

    Yun Seong Nam

  4. Joint Center for Quantum Information and Computer Science, Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    Yun Seong Nam

  5. IonQ Inc., College Park, MD, 20740, USA

    Yun Seong Nam

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  1. Varun Ursekar
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  4. Reinhold Blümel
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Correspondence to Varun Ursekar.

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Ursekar, V., Silvester, J.M., Nam, Y.S. et al. Prediction of exotic ion-crystal structures in a Paul trap. Eur. Phys. J. D 72, 165 (2018). https://doi.org/10.1140/epjd/e2018-80728-4

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