Abstract.
The low-energy-level macroscopic wave functions of the Bose-Einstein condensate (BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel splitting is evaluated in terms of the even and odd wave functions corresponding to the global ground and excited states respectively. We show that the numerical result is in good agreement with the analytic level splitting obtained by means of the periodic instanton method.
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M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn, W. Ketterle, Science 275, 637 (1997)
E.A. Hinds, C.J. Vale, M.G. Boshier, Phys. Rev. Lett. 86, 1462 (2001)
T.G. Tiecke, M. Kemmann, Ch. Buggle, I. Shvarchuck, W. von Klitzing, J.T.M. Walraven, J. Opt. B: Quant. Semiclass. Opt. 5, S119 (2003)
Y. Shin, M. Saba, T.A. Pasquini, W. Ketterle, D.E. Pritchard, A.E. Leanhardt, Phys. Rev. Lett. 92, 050405 (2004)
Y. Shin, M. Saba, A. Schirotzek, T.A. Pasquini, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 92, 150401 (2004)
B.P. Anderson, M.A. Kasevich, Science 282, 1686 (1998)
F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science 293, 843 (2001)
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
M. Kramer, L. Pitaevskii, S. Stringari, Phys. Rev. Lett. 88, 180404 (2002)
B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004)
F. Dalfovo, L. Pitaevskii, S. Stringari, Phys. Rev. A 54, 4213 (1996)
A. Smerzi, S. Fantoni, S. Giovanazzi, S.R. Shenoy, Phys. Rev. Lett. 79, 4950 (1997)
S. Giovanazzi, A. Smerzi, S. Fantoni, Phys. Rev. Lett. 84, 4521 (2000)
L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 60, 4171 (1999)
D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)
W.-D. Li, Y.-B. Zhang, J.-Q. Liang, Phys. Rev. A 67, 065601 (2003)
W.-M. Liu, W.-B. Fan, W.-M. Zheng, J.-Q. Liang, S.T. Chui, Phys. Rev. Lett. 88, 170408 (2002)
Y. Zhang, H.J. W. Müller-Kirsten, Phys. Rev. A 64, 023608 (2001)
A. Gorlitz et al., Phys. Rev. Lett. 87, 130402 (2001)
D.S. Petrov, G.V. Shlyapnikov, J.T.M. Walraven, Phys. Rev. Lett. 85, 3745 (2000)
M. Olshanii, Phys. Rev. Lett. 81, 938 (1998)
J.-Q. Liang, H.J.W. Müller-Kirsten, Phys. Rev. D 46, 4685 (1992); J.-Q. Liang, H.J.W. Müller-Kirsten, Phys. Rev. D 51, 718 (1995)
L.S. Schulman, Techniques and Applications of Path Integration (Wiley-Interscience, New York, 1981)
C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, London, 2001); L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Oxford University Press, New York, 2003); A. Minguzzi, S. Succi, F. Toschi, M.P. Tosi, P. Vignolo, Phys. Rep. 395, 223 (2004)
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. (Cambridge University Press, London, 1992)
P.A. Ruprecht, M.J. Holland, K. Burnett, Phys. Rev. A 51, 4704 (1995)
S.K. Adhikari, Phys. Rev. E 62, 2937 (2000)
F. Dalfovo, S. Giorgini, L. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999); F. Dalfovo, S. Stringari, Phys. Rev. A 53, 2477 (1996)
J.R. Gardner, R.A. Cline, J.D. Miller, D.J. Heinzen, H.M.J.M. Boesten, B.J. Verhaar, Phys. Rev. Lett. 74, 3764 (1995)
L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 65, 043614 (2002)
M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, e-print arXiv:cond-mat/0411757
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Hao, Y., Liang, JQ. & Zhang, Y. Numerical simulation on tunnel splitting of Bose-Einstein condensate in multi-well potentials. Eur. Phys. J. D 36, 33–39 (2005). https://doi.org/10.1140/epjd/e2005-00090-0
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DOI: https://doi.org/10.1140/epjd/e2005-00090-0