Research PaperNo Access

Exact breather solutions of repulsive Bose atoms in a one-dimensional harmonic trap

Ze Cheng

School of Physics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

https://doi.org/10.1142/S0129183118501000Cited by:0 (Source: Crossref)

Abstract

Bose–Einstein condensates of repulsive Bose atoms in a one-dimensional harmonic trap are investigated within the framework of a mean field theory. We solve the one-dimensional nonlinear Gross–Pitaevskii (GP) equation that describes atomic Bose–Einstein condensates. As a result, we acquire a family of exact breather solutions of the GP equation. We numerically calculate the number density $n (z, t, N)$ of atoms that is associated with these solutions. The first discovery of the calculation is that at the instant of the saddle point, the density profile exhibits a sharp peak with extremely narrow width. The second discovery of the calculation is that in the center of the trap ( $z = 0$ m), the number density is a U-shaped function of the time $t$ . The third discovery of the calculation is that the surface plot of the density $n (z, t)$ likes a saddle surface. The fourth discovery of the calculation is that as the number $N$ of atoms increases, the Bose–Einstein condensate in a one-dimensional harmonic trap becomes stabler and stabler.

Keywords:

PACS: 03.75.Hh, 05.30.Jp, 64.60.−i, 67.85.−d

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References

1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman and E. A. Cornell , Science 269, 198 (1995). Web of Science, ADS, Google Scholar
2. K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn and W. Ketterle , Phys. Rev. Lett. 75, 3969 (1995). Web of Science, ADS, Google Scholar
3. C. C. Bradley, C. A. Sackett, J. J. Tollett and R. G. Hulet , Phys. Rev. Lett. 75, 1687 (1995). Web of Science, ADS, Google Scholar
4. Y. Li, G. I. Martone, L. P. Pitaevskii and S. Stringari , Phys. Rev. Lett. 110, 235302 (2013). Web of Science, ADS, Google Scholar
5. W. Han, G. Juzeliunas, W. Zhang and W. M. Liu , Phys. Rev. A 91, 013607 (2015). Web of Science, ADS, Google Scholar
6. J. R. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F. C. Top, A. O. Jamison and W. Ketterle , Nature (London) 543, 91 (2017). Web of Science, ADS, Google Scholar
7. J. Léonard, A. Morales, P. Zupancic, T. Esslinger and T. Donner , Nature (London) 543, 87 (2017). Web of Science, ADS, Google Scholar
8. T. Giamarchi , Quantum Physics in One Dimension (Clarendon Press, Oxford, 2003). Google Scholar
9. Ze Cheng , J. Stat. Mech., Theor. Exp. 2015, P09011 (2015). Web of Science, Google Scholar
10. D. S. Petrov, G. V. Shlyapnikov and J. T. M. Walraven , Phys. Rev. Lett. 85, 3745 (2000). Web of Science, ADS, Google Scholar
11. Z. X. Liang, Z. D. Zhang and W. M. Liu , Phys. Rev. Lett. 94, 050402 (2005). Web of Science, ADS, Google Scholar
12. R. Atre, P. K. Panigrahi and G. S. Agarwal , Phys. Rev. E 73, 056611 (2006). Web of Science, ADS, Google Scholar
13. U. AlKhawaja , Phys. Rev. E 75, 066607 (2007). Web of Science, Google Scholar
14. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik and V. V. Konotop , Phys. Rev. Lett. 100, 164102 (2008). Web of Science, ADS, Google Scholar
15. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno and M. Inguscio , Nature (London) 453, 895 (2008). Web of Science, ADS, Google Scholar
16. F. Dalfovo, S. Giorgini, L. P. Pitaevskii and S. Stringari , Rev. Mod. Phys. 71, 463 (1999). Web of Science, ADS, Google Scholar
17. C. J. Pethick and H. Smith , Bose–Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2008). Google Scholar
18. Lev Pitaevskii and Sandro Stringari , Bose–Einstein Condensation (Oxford University Press, Oxford, 2003). Google Scholar
19. D. Zwillinger , Standard Mathematical Tables and Formulae, 30th edn. (CRC Press, Boca Raton, 1996), p. 522. Google Scholar