Journal of Low Temperature Physics

, Volume 173, Issue 3–4, pp 177–206 | Cite as

Nonequilibrium Dynamics of a Bose-Einstein Condensate Excited by a Red Laser Inside a Power-Law Trap with Hard Walls

  • Roger R. Sakhel
  • Asaad R. Sakhel
  • Humam B. Ghassib
Article

Abstract

We explore the nonequilibrium dynamics of a two-dimensional trapped Bose-Einstein condensate excited by a moving red-detuned laser potential. The trap is a combination of a general power-law potential cutoff by a hard wall box potential. The red laser potential is allowed to exit the box potential, leaving the system in a highly nonequilibrium state. This is crucial since the red laser potential squeezes the BEC trapped inside it against the hard wall-boundary at this instant, paving the way for the creation of a shock wave. Once the red laser potential has left the box potential, the Hamiltonian of the system becomes time-independent and the total energy stabilizes. Our systems are simulated by the time-dependent Gross-Ptiaevskii Equation which is numerically solved by the split-step Crank-Nicolson method in real time. It is found that the value at which the total energy stabilizes in the transient stage of the simulation is largely controlled by the initialization process. Before the red laser potential leaves the trap, when the Hamiltonian of the system is still time-dependent, oscillations in the total energy occur if the system is initialized adiabatically by application of a gradually growing and moving red laser potential. If this laser potential is not moving, yet fully present in the initialization process, these oscillations are not observed in the transient stage of the simulation. In addition, the system displays oscillations in the root-mean-square radius of the trapped cloud. The amplitudes of these radial oscillations continue even after the red laser potential leaves the box potential and are used to explore the deviation of the nonstationary states from the corresponding ground states. It is demonstrated that the geometry of the power law potential influences the amplitude of these radial oscillations, reducing them and bringing the systems closer to an equilibrium state. We then argue that by going to tighter trapping geometries, it is not possible to achieve a completely stable system which has been earlier excited by a red laser potential. Most importantly, an increase in the curvature of the power law trap results in chaotic oscillations of the cloud. This work should stimulate further experiments exploring the extent of the nonequilibrium states by a measurement of the amplitude of the root-mean-square radial oscillations of the trapped cloud.

Keywords

Ultra cold trapped Bose gases Dynamics of a Bose-Einstein condensate Crank Nicolson method Excitations by a red detuned laser potential Time-dependent Gross Pitaevskii equation Chaos 

Supplementary material

10909_2013_894_MOESM1_ESM.mpg (7.9 mb)
(MPG 7.9 MB)

References

  1. 1.
    J.S. Stießberger, W. Zwerger, Phys. Rev. A 62, 061601(R) (2000) ADSCrossRefGoogle Scholar
  2. 2.
    K. Fujimoto, M. Tsubota, Phys. Rev. A 82, 043611 (2010) ADSCrossRefGoogle Scholar
  3. 3.
    K. Fujimoto, M. Tsubota, J. Low Temp. Phys. 162, 307 (2011) ADSCrossRefGoogle Scholar
  4. 4.
    B. Jackson, J.F. McCann, C.S. Adams, Phys. Rev. A 61, 051603R (2000) ADSCrossRefGoogle Scholar
  5. 5.
    A. Radouani, Phys. Rev. A 70, 013602 (2004) ADSCrossRefGoogle Scholar
  6. 6.
    B.M. Caradoc-Davies, R.J. Ballagh, K. Burnett, Phys. Rev. Lett. 83, 895 (1999) ADSCrossRefGoogle Scholar
  7. 7.
    B.M. Caradoc-Davies, R.J. Ballagh, P.B. Blakie, Phys. Rev. A 62, 011602(R) (2000) ADSCrossRefGoogle Scholar
  8. 8.
    T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, B.P. Anderson, Phys. Rev. Lett. 104, 160401 (2010) ADSCrossRefGoogle Scholar
  9. 9.
    P. Engels, C. Atherton, Phys. Rev. Lett. 99, 160405 (2007) ADSCrossRefGoogle Scholar
  10. 10.
    R. Onofrio, C. Raman, J.M. Vogels, J.R. Abo-Shaeer, A.P. Chikkatur, W. Ketterle, Phys. Rev. Lett. 85(11), 2228 (2000) ADSCrossRefGoogle Scholar
  11. 11.
    K.W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, Phys. Rev. Lett. 84, 806 (2000) ADSCrossRefGoogle Scholar
  12. 12.
    C. Raman, J.R. Abo-Shaeer, J.M. Vogels, K. Xu, W. Ketterle, Phys. Rev. Lett. 87, 210402 (2001) ADSCrossRefGoogle Scholar
  13. 13.
    C. Raman, M. Köhl, R. Onofrio, D.S. Durfee, C.E. Kuklewicz, Z. Hadzibabic, W. Ketterle, Phys. Rev. Lett. 83(13), 2502 (1999) ADSCrossRefGoogle Scholar
  14. 14.
    K.W. Madison, F. Chevy, V. Bretin, J. Dalibard, Phys. Rev. Lett. 86, 4443 (2001) ADSCrossRefGoogle Scholar
  15. 15.
    T.-L. Horng, S.-C. Gou, T.-C. Lin, G.A. El, A.P. Itin, A.M. Kamchatnov, Phys. Rev. A 79, 053619 (2009) ADSCrossRefGoogle Scholar
  16. 16.
    M. Hammes, D. Rychtarik, H.-C. Nägerl, R. Grimm, Phys. Rev. A 66, 051401(R) (2002) ADSCrossRefGoogle Scholar
  17. 17.
    M.C. Garrett, A. Ratnapala, E.D. van Ooijen, C.J. Vale, K. Weegink, S.K. Schnelle, O. Vainio, N.R. Heckenberg, H. Rubinsztein-Dunlop, M.J. Davis, Phys. Rev. A 83, 013630 (2011) ADSCrossRefGoogle Scholar
  18. 18.
    D.R. Scherer, C.N. Weiler, T.W. Neely, B.P. Anderson, Phys. Rev. Lett. 98, 110402 (2007) ADSCrossRefGoogle Scholar
  19. 19.
    C. Tuchendler, A.M. Lance, A. Browaeys, Y.R.P. Sortais, P. Grangier, Phys. Rev. A 78, 033425 (2008) ADSCrossRefGoogle Scholar
  20. 20.
    D.M. Stamper-Kurn, H.-J. Miesner, A.P. Chikkatur, S. Inouye, J. Stenger, W. Ketterle, Phys. Rev. Lett. 81, 2194 (1998) ADSCrossRefGoogle Scholar
  21. 21.
    D. Comparat, A. Fioretti, G. Stern, E. Dimova, B. Laburthe Tolra, P. Pillet, Phys. Rev. A 73, 043410 (2006) ADSCrossRefGoogle Scholar
  22. 22.
    D. Jacob, E. Mimoun, L. De Sarlo, M. Weitz, J. Dalibard, F. Gerbier, New J. Phys. 13, 065022 (2011) ADSCrossRefGoogle Scholar
  23. 23.
    T.L. Gustavson, A.P. Chikkatur, A.E. Leanhardt, A. Görlitz, S. Gupta, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 88, 020401 (2001) CrossRefGoogle Scholar
  24. 24.
    M.D. Barrett, J.A. Sauer, M.S. Chapman, Phys. Rev. Lett. 87, 010404 (2001) ADSCrossRefGoogle Scholar
  25. 25.
    M. Schulz, H. Crepaz, F. Schmidt-Kaler, J. Eschner, R. Blatt, J. Mod. Opt. 54, 1619 (2007) ADSCrossRefGoogle Scholar
  26. 26.
    N.P. Proukakis, J. Schmiedmayer, H.T.C. Stoof, Phys. Rev. A 73, 053603 (2006) ADSCrossRefGoogle Scholar
  27. 27.
    R.B. Diener, B. Wu, M.G. Raizen, Q. Niu, Phys. Rev. Lett. 89, 070401 (2002) ADSCrossRefGoogle Scholar
  28. 28.
    T. Aioi, T. Kadokura, T. Kishimoto, H. Saito, Phys. Rev. X 1, 021003 (2011) CrossRefGoogle Scholar
  29. 29.
    H. Uncu, D. Tarhan, E. Demiralp, O.E. Mustecaplioglu, Laser Phys. 18, 331 (2008) ADSCrossRefGoogle Scholar
  30. 30.
    C. Weitenberg, S. Kuhr, K. Mølmer, J.F. Sherson, Phys. Rev. A 84, 032322 (2011) ADSCrossRefGoogle Scholar
  31. 31.
    A.V. Carpentier, J. Belmonte-Beitia, H. Michinel, V.M. Perez-Garcia, J. Mod. Opt. 55, 2819 (2008) CrossRefMATHGoogle Scholar
  32. 32.
    A.M. Kaufman, B.J. Lester, C.A. Regal, Phys. Rev. X 2, 041014 (2012) CrossRefGoogle Scholar
  33. 33.
    N.G. Parker, N.P. Proukakis, M. Leadbeater, C.S. Adams, Phys. Rev. Lett. 90(22), 220401 (2003) ADSCrossRefGoogle Scholar
  34. 34.
    N.G. Parker, N.P. Proukakis, C.S. Adams, Phys. Rev. A 81, 033606 (2010) ADSCrossRefGoogle Scholar
  35. 35.
    R.R. Sakhel, A.R. Sakhel, H.B. Ghassib, Phys. Rev. A 84, 033634 (2011) ADSCrossRefGoogle Scholar
  36. 36.
    P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 180, 1888 (2009) ADSCrossRefGoogle Scholar
  37. 37.
    G.D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, D. Cassettari, Phys. Scr. T 143, 014008 (2011) ADSCrossRefGoogle Scholar
  38. 38.
    G.D. Bruce, S.L. Bromley, G. Smirne, L. Torralbo-Campo, D. Cassettari, Phys. Rev. A 84, 053410 (2011) ADSCrossRefGoogle Scholar
  39. 39.
    K. Merloti, R. Dubessy, L. Longchambon, A. Perrin, P.-E. Pottie, V. Lorent, H. Perrin, New J. Phys. 15, 033007 (2013) ADSCrossRefGoogle Scholar
  40. 40.
    K. Bongs, S. Burger, G. Birkl, K. Sengstock, W. Ertmer, K. Rzażewski, A. Sanpera, M. Lewenstein, Phys. Rev. Lett. 83, 3577 (1999) ADSCrossRefGoogle Scholar
  41. 41.
    J. Ruostekoski, B. Kneer, W.P. Schleich, G. Rempe, Phys. Rev. A 63, 043613 (2001) ADSCrossRefGoogle Scholar
  42. 42.
    M. Horikoshi, K. Nakagawa, Phys. Rev. A 74, 031602(R) (2006) ADSCrossRefGoogle Scholar
  43. 43.
    O. Garcia, B. Deissler, K.J. Hughes, J.M. Reeves, C.A. Sackett, Phys. Rev. A 74, 031601(R) (2006) ADSCrossRefGoogle Scholar
  44. 44.
    B.V. Hall, S. Whitlock, R. Anderson, P. Hannaford, A.I. Sidorov, Phys. Rev. Lett. 98, 030402 (2007) ADSCrossRefGoogle Scholar
  45. 45.
    D.K. Faust, W.P. Reinhardt, Phys. Rev. Lett. 105, 240404 (2010) ADSCrossRefGoogle Scholar
  46. 46.
    M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn, W. Ketterle, Science 275, 637 (1997) CrossRefGoogle Scholar
  47. 47.
    R. Carretero-González, B.P. Anderson, P.G. Kevrekidis, D.J. Frantzeskakis, C.N. Weiler, Phys. Rev. A 77, 033625 (2008) ADSCrossRefGoogle Scholar
  48. 48.
    R. Carretero-González, N. Whitaker, P.G. Kevrekidis, D.J. Frantzeskakis, Phys. Rev. A 77, 023605 (2008) ADSCrossRefGoogle Scholar
  49. 49.
    J.J. Chang, P. Engels, M.A. Hoefer, Phys. Rev. Lett. 101, 170404 (2008) ADSCrossRefGoogle Scholar
  50. 50.
    T. Yang, B. Xiong, K.A. Benedict, Phys. Rev. A 87, 023603 (2013) ADSCrossRefGoogle Scholar
  51. 51.
    F. Chevy, V. Bretin, P. Rosenbusch, K.W. Madison, J. Dalibard, Phys. Rev. Lett. 88, 250402 (2002) ADSCrossRefGoogle Scholar
  52. 52.
    Yu. Kagan, E.L. Surkov, G.V. Shlyapnikov, Phys. Rev. A 54, R1753 (1996) ADSCrossRefGoogle Scholar
  53. 53.
    L.P. Pitaevskii, Phys. Lett. A 221, 14 (1996) ADSCrossRefGoogle Scholar
  54. 54.
    L.P. Pitaevskii, A. Rosch, Phys. Rev. A 55, R853 (1997) ADSCrossRefGoogle Scholar
  55. 55.
    T.K. Ghosh, Phys. Lett. A 285, 222 (2001) ADSCrossRefMATHGoogle Scholar
  56. 56.
    P.K. Ghosh, Phys. Rev. A 65, 012103 (2001) ADSCrossRefGoogle Scholar
  57. 57.
    T. Kimura, Phys. Rev. A 66, 013608 (2002) ADSCrossRefGoogle Scholar
  58. 58.
    D. Juki’c, H. Buljan, New J. Phys. 12, 055010 (2010) ADSCrossRefGoogle Scholar
  59. 59.
    J. Kälbermann, J. Phys. A, Math. Theor. 37, 2871 (2004) Google Scholar
  60. 60.
    P. Muruganandam, S.K. Adhikari, Phys. Rev. A 65, 043608 (2002) ADSCrossRefGoogle Scholar
  61. 61.
    H. Ott, J. Fortágh, S. Kraft, A. Günther, D. Komma, C. Zimmermann, Phys. Rev. Lett. 91, 040402 (2003) ADSCrossRefGoogle Scholar
  62. 62.
    D. Vudragović, I. Vidanović, A. Balaž, P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 183, 2021 (2012) ADSCrossRefGoogle Scholar
  63. 63.
    Computer Physics Communication Library, Science Direct. http://www.cpc.cs.qub.ac.uk
  64. 64.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002) Google Scholar
  65. 65.
    D.J. Frantzeskakis, J. Phys. A, Math. Theor. 43, 213001 (2010) MathSciNetADSCrossRefGoogle Scholar
  66. 66.
    A. Weller, J.P. Ronzheimer, C. Gross, J. Esteve, M.K. Oberthaler, D.J. Frantzeskakis, G. Theocharis, P.G. Kevrekidis, Phys. Rev. Lett. 101, 130401 (2008) ADSCrossRefGoogle Scholar
  67. 67.
    C.K. Law, C.M. Chan, P.T. Leung, M.-C. Chu, Phys. Rev. Lett. 85, 1598 (2000) ADSCrossRefGoogle Scholar
  68. 68.
    H.B. Ghassib, S. Chatterjee, Z. Phys. B, Condens. Matter 51, 93 (1983) ADSCrossRefGoogle Scholar
  69. 69.
    V.M. Pérez-Garciá, V.V. Konotop, V.A. Brazhnyi, Phys. Rev. Lett. 92, 220403 (2004) CrossRefGoogle Scholar
  70. 70.
    W.P. Reinhardt, C.W. Clark, J. Phys. B, At. Mol. Opt. Phys. 30, L785 (1997) ADSCrossRefGoogle Scholar
  71. 71.
    T.F. Scott, R.J. Ballagh, K. Burnett, J. Phys. B, At. Mol. Opt. Phys. 31, L329 (1998) ADSCrossRefGoogle Scholar
  72. 72.
    C. Lee, E.A. Ostrovskaya, Y.S. Kivshar, J. Phys. B, At. Mol. Opt. Phys. 40, 4235 (2007) ADSCrossRefGoogle Scholar
  73. 73.
    S.K. Adhikari, Private communication, Sao Paulo State University Google Scholar
  74. 74.
    E. Lundh, cond-mat/0405316v1 (2004)

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Roger R. Sakhel
    • 1
  • Asaad R. Sakhel
    • 2
  • Humam B. Ghassib
    • 3
  1. 1.Department of Basic Sciences, Faculty of Information TechnologyIsra UniversityAmmanJordan
  2. 2.Department of Applied Sciences, Faculty of Engineering TechnologyAl-Balqa Applied UniversityAmmanJordan
  3. 3.Department of PhysicsThe University of JordanAmmanJordan

Personalised recommendations