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Journal of Low Temperature Physics

, Volume 194, Issue 1–2, pp 106–135 | Cite as

On the Role of Trap Anharmonicity in the Dynamics of a One-Dimensional Bose Gas Suddenly Released from a Power-Law Trap into a Box Potential

  • Roger R. SakhelEmail author
  • Asaad R. Sakhel
Article
  • 68 Downloads

Abstract

The effects of trapping anharmonicity on the expansion of a Bose–Einstein condensate (BEC) that is suddenly released from a one-dimensional power-law trap into a hard wall box potential are presented. It is chiefly found that trapping anharmonicity, from a general point of view, has no influence on the qualitative behavior of the dynamics apart from the fact that a higher power-law exponent leads to a faster expansion of the BEC. The evolution of the density distributions, both spatial and momentum, the self-similarity of the spatial density at later times, and its connection to energy components and their dynamics, such as the zero-point, interaction, and kinetic energy are examined. By a decomposition of the wavefunction via modal coefficients, the basis being the harmonic oscillator states, the dynamics of these coefficients are determined. The latter shows that high states become occupied as a result of the BEC expansion. Moreover, the information entropy is evaluated from the latter coefficients that particularly displays a time behavior in the form of small oscillations at long times arising from the interaction with the walls. When the BEC collides with the hard walls of the box potential, it is found to be in a very highly excited state. As such, it is demonstrated that a future need for the practical recapture of an expanding BEC requires methods that suppress the resulting excitations if a reexamination of the ground-state in the “recapturing confinement” is needed. In passing, the important role played by the width of the wavefunction is once again revealed as in previous work (Sakhel and Sakhel in J Phys B 50:105301, 2017). We propose experiments for the measurement of kinetic energy as a function of time for this type of investigation. For example, an in situ measurement of the momentum distribution reveals information about the latter. The current results on the density dynamics can be also verified experimentally.

Keywords

Expansion of a Bose gas Low-dimensional Bose–Einstein condensates Quantum fluids Variational methods Crank–Nicolson method 

Notes

Acknowledgements

We would like to thank Petar Jovanovich at the Scientific Computing Laboratory, Institute of Physics in Belgrade, Serbia, for helping us with the parallelization of a code.

References

  1. 1.
    D. Jukic, R. Pezer, T. Gasenzer, H. Buljan, Phys. Rev. A 78, 053602 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    P. Pedri, L. Santos, P. Öhberg, S. Stringari, Phys. Rev. A 68, 043601 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    J.-S. Caux, R.M. Konik, Phys. Rev. Lett. 109, 175301 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    J.P. Ronzheimer, M. Schreiber, S. Braun, S.S. Hodgman, S. Langer, I.P. McCulloch, F. Heidrich-Meisner, I. Bloch, U. Schneider, Phys. Rev. Lett. 110, 205301 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    C.J. Bolech, F. Heidrich-Meisner, S. Langer, I.P. McCulloch, G. Orso, M. Rigol, Phys. Rev. Lett. 109, 110602 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    L. Vidmar, S. Langer, I.P. McCulloch, U. Schneider, U. Schollwöck, F. Heidrich-Meisner, Phys. Rev. B 88, 235117 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    P. Öhberg, L. Santos, Phys. Rev. Lett. 89, 240402 (2002)CrossRefGoogle Scholar
  9. 9.
    D.M. Gangardt, M. Pustilnik, Phys. Rev. A 110, 041604(R) (2008)ADSCrossRefGoogle Scholar
  10. 10.
    K. Gawryluk, M. Brewczyk, M. Gajda, K. Rzazewski, J. Phys. B At. Mol. Opt. Phys. 43, 105303 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    A.S. Campbell, D.M. Gangardt, K.V. Kheruntsyan, Phys. Rev. Lett. 114, 125302 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    M. Holland, J. Cooper, Phys. Rev. A 53, R1954 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    V.A. Brazhnyi, A.M. Kamchatnov, V.V. Konotop, Phys. Rev. A 68, 035603 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    J.A. Stickney, A.A. Zozulya, Phys. Rev. A 65, 053612 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    P. Pedri, L. Pitaevskii, S. Stringari, C. Fort, S. Burger, F.S. Cataliotti, P. Maddaloni, F. Minardi, M. Inguscio, Phys. Rev. Lett. 87, 220401 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)ADSCrossRefGoogle Scholar
  17. 17.
    K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. Van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    M.O. Mewes, M.R. Andrews, N.J. van Druten, D.M. Kurn, D.S. Durfee, W. Ketterle, Phys. Rev. Lett. 77, 416 (1996)ADSCrossRefGoogle Scholar
  19. 19.
    C.J. Myatt, E.A. Burt, R.W. Ghrist, E.A. Cornell, C.E. Wieman, Phys. Rev. Lett. 78, 586 (1997)ADSCrossRefGoogle Scholar
  20. 20.
    M.R. Andrews, M.-O. Mewes, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Science 273, 84 (1996)ADSCrossRefGoogle Scholar
  21. 21.
    S. Eckel, A. Kumar, T. Jacobson, I.B. Spielman, G.K. Campbell, Phys. Rev. X 8, 021021 (2018)Google Scholar
  22. 22.
  23. 23.
    M. Rigol, V. Dunjko, M. Olshanii, Nat. Lett. 452, 854 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    P. Calabrese, J. Cardy, J. Stat. Mech. 6, P06008 (2007)Google Scholar
  25. 25.
    J.-S. Caux, F.H.L. Essler, Phys. Rev. Lett. 110, 257203 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    S. Langer, M.J.A. Schuetz, I.P. McCulloch, U. Schollwöck, F. Heidrich-Meisner, Phys. Rev. A 85, 043618 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    Y. Castin, R. Dum, Phys. Rev. Lett. 77, 5315 (1996)ADSCrossRefGoogle Scholar
  28. 28.
    K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, K. Sengstock, Phys. Rev. Lett. 63, 031602(R) (2001)ADSGoogle Scholar
  29. 29.
    P. Massignan, M. Modugno, Phys. Rev. A 67, 023614 (2003)ADSCrossRefGoogle Scholar
  30. 30.
    T.M. Wright, M. Rigol, M.J. Davis, K.V. Kheruntsyan, Phys. Rev. Lett. 113, 050601 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    T.M. Cover, J.A. Thomas, Elements of Information Theory, 2nd edn. (Wiley, New York, 2005)CrossRefzbMATHGoogle Scholar
  32. 32.
    P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 180, 1888 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    R.R. Sakhel, A.R. Sakhel, H.B. Ghassib, J. Low. Temp. Phys. 173, 177 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    R.R. Sakhel, A.R. Sakhel, H.B. Ghassib, Phys. B 478, 68 (2015)ADSCrossRefGoogle Scholar
  35. 35.
    V.M. Perez-Garcia, H. Michinel, J.I. Cirac, M. Lewenstein, P. Zöller, Phys. Rev. Lett. 77, 5320 (1996)ADSCrossRefGoogle Scholar
  36. 36.
    V.M. Perez-Garcia, H. Michinel, J.I. Cirac, M. Lewenstein, P. Zöller, Phys. Rev. A 56, 1424 (1997)ADSCrossRefGoogle Scholar
  37. 37.
    R. Sakhel, A. Sakhel, J. Phys. B At. Mol. Opt. Phys. 50(10), 105301 (2017)ADSCrossRefGoogle Scholar
  38. 38.
    D. Vudragović, I. Vidanović, A. Balaž, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 183, 2021 (2012)ADSCrossRefGoogle Scholar
  39. 39.
    I. Vidanovic, A. Balaz, H. Al-Jibbouri, A. Pelster, Phys. Rev. A 84, 013618 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    H. Al-Jibbouri, I. Vidanovic, A. Balaz, A. Pelster, J. Phys. B At. Mol. Opt. Phys. 46(6), 065303 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    Y. Cheng, S.K. Adhikari, Phys. Rev. A 84, 053634 (2011)ADSCrossRefGoogle Scholar
  42. 42.
    Y. Cheng, S.K. Adhikari, Phys. Rev. A 84, 023632 (2011)ADSCrossRefGoogle Scholar
  43. 43.
    Y. Cheng, S.K. Adhikari, Phys. Rev. A 83, 023620 (2011)ADSCrossRefGoogle Scholar
  44. 44.
    A.R. Sakhel, R.R. Sakhel, J. Low. Temp. Phys. 190, 120 (2018)ADSCrossRefGoogle Scholar
  45. 45.
    R.R. Sakhel, A.R. Sakhel, H.B. Ghassib, Phys. Rev. A 84, 033634 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    R.R. Sakhel, A.R. Sakhel, H.B. Ghassib, A. Balaz, Eur. Phys. J. D 70, 66 (2016)ADSCrossRefGoogle Scholar
  47. 47.
    R. Kishor Kumar, L. Young-S, D. Vudragović, A. Balaz, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 195, 117 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    V. Loncar, A. Balaz, A. Bogojevic, S. Skrbic, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 200, 406 (2016)ADSCrossRefGoogle Scholar
  49. 49.
    L. Young-S, D. Vudragović, P. Muruganandam, S.K. Adhikari, A. Balaz, Comput. Phys. Commun. 204, 209 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    B. Sataric, V. Slavnic, A. Belic, A. Balaz, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 200, 411 (2016)ADSCrossRefGoogle Scholar
  51. 51.
    Z.-C. Wang, H.-W. Yang, S. Yin, Eur. Phys. J. D 20, 117 (2002)ADSCrossRefGoogle Scholar
  52. 52.
    L. Ermann, E. Vergini, D.L. Shepelyansky, Phys. Rev. A 94, 013618 (2016)ADSCrossRefGoogle Scholar
  53. 53.
    G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, 6th edn. (Elsevier, Amsterdam, 2005)zbMATHGoogle Scholar
  54. 54.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  55. 55.
    C.J. Pethick, H. Smith, Bose–Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2008)CrossRefGoogle Scholar
  56. 56.
    H. Moritz, T. Stöferle, M. Köhl, T. Esslinger, Phys. Rev. Lett. 91, 250402 (2003)ADSCrossRefGoogle Scholar
  57. 57.
    W. Rohringer, D. Fischer, F. Steiner, I.E. Mazets, J. Schmiedmayer, M. Trupke, Sci. Rep. 5, 9820 (2015)ADSCrossRefGoogle Scholar
  58. 58.
    B. Rauer, P. Grisins, I.E. Mazets, T. Schweigler, W. Rohringer, R. Geiger, T. Langen, J. Schmiedmayer, Phys. Rev. Lett. 116, 030402 (2016)ADSCrossRefGoogle Scholar
  59. 59.
    N.P. Proukakis, J. Schmiedmayer, H.T.C. Stoof, Phys. Rev. A 73, 053603 (2006)ADSCrossRefGoogle Scholar
  60. 60.
    S. Höfferberth, I. Lesanovsky, B. Fischer, T. Schumm, J. Schmiedmayer, Nature 449, 324 (2007)ADSCrossRefGoogle Scholar
  61. 61.
    B. Fang, G. Carleo, A. Johnson, I. Bouchoule, Phys. Rev. Lett. 113, 035301(R) (2014)ADSCrossRefGoogle Scholar
  62. 62.
    Y. Kagan, E.L. Surkov, G.V. Shlyapnikov, Phys. Rev. A 54, 1753(R) (1996)ADSCrossRefGoogle Scholar
  63. 63.
    S. Giovanazzi, P. Pedri, L. Santos, A. Griesmaier, M. Fattori, T. Koch, J. Stuhler, T. Pfau, Phys. Rev. A 74, 013621 (2006)ADSCrossRefGoogle Scholar
  64. 64.
    S. Giovanazzi, A. Görlitz, T. Pfau, J. Opt. B 5, S208 (2005)CrossRefGoogle Scholar
  65. 65.
    J. Stuhler, A. Griesmaier, T. Koch, M. Fattori, T. Pfau, S. Giovanazzi, P. Pedri, L. Santos, Phys. Rev. Lett. 95, 150406 (2005)ADSCrossRefGoogle Scholar
  66. 66.
    L. Pitaevskii, S. Stringari, Bose–Einstein Condensation (Oxford University Press, Oxford, 2003)zbMATHGoogle Scholar
  67. 67.
    F. Dalfovo, L. Pitaevskii, S. Stringari, Phys. Rev. A 54, 4213 (1996)ADSCrossRefGoogle Scholar
  68. 68.
    C. Emil Lundh, J. Pethick, H. Smith, Phys. Rev. A 55, 2126 (1997)ADSCrossRefGoogle Scholar
  69. 69.
    R.K. Bhaduri, Phys. Rev. Lett. 39, 329 (1977)ADSCrossRefGoogle Scholar
  70. 70.
    J.-D. Chai, J.D. Weeks, J. Phys. Chem. 108, 6780 (2004)Google Scholar
  71. 71.
    P. Bocchieri, A. Longer, Phys. Rev. 107, 337 (1957)ADSMathSciNetCrossRefGoogle Scholar
  72. 72.
    M.A. Doncheski, R.W. Robinett, Eur. J. Phys. 20, 29 (1999)CrossRefGoogle Scholar
  73. 73.
    G.D. Bruce, S.L. Bromley, G. Smirne, L. Torralbo-Campo, D. Cassettari, Phys. Rev. A 84, 053410 (2011)ADSCrossRefGoogle Scholar
  74. 74.
    T. Karzig, A. Levchenko, L.I. Glazman, F. von Oppen, New J. Phys. 14, 105009 (2012)ADSCrossRefGoogle Scholar
  75. 75.
    G.M. Schütz, S. Trimper, Europhys. Lett. 47, 164 (1999)ADSMathSciNetCrossRefGoogle Scholar
  76. 76.
    M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Ricco, S.R. Clark, D. Jaksch, A. Cavalleri, Nature 530, 461 (2016)ADSCrossRefGoogle Scholar
  77. 77.
    A. Kruchkov, Phys. Rev. A 93, 043817 (2016)ADSCrossRefGoogle Scholar

Copyright information

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Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceIsra UniversityAmmanJordan
  2. 2.Department of Physics and Basic Sciences, Faculty of Engineering TechnologyAl-Balqa Applied UniversityAmmanJordan
  3. 3.The Abdus-Salam International Center for Theoretical PhysicsTriesteItaly

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