Localization Study of a Cold Atom BEC in Two-Dimensional Bessel Optical Lattices

Abstract:

In order to investigate the stability and dynamics properties of a cold atom Bose-Einstein Condensate (BEC) in two-dimensional Bessel optical lattices, the stability condition of the system is analyzed and the corresponding Gross-pitaevskii equation (GPE) is solved in this paper by time-dependent variational method and numerical simulation. Firstly, the Euler-Lagrange equation containing the parameters describing the system stability and the effective potential energy needed by the variational analysis method to analyze the system stability is obtained by using the adjustable exponent Gaussian trial wave function. Secondly, according to the analytical solution of Euler-Lagrange equation and the local minimum value of potential energy, the stability condition of the system is further illuminated. Finally, the influence mechanism of these parameters on the local dynamics is revealed by solving the corresponding GPE with numerical method.

• Periodical: Key Engineering Materials (Volume 787)
• Pages: 105-112
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.787.105
• Online since: November 2018
• Authors: Guo Zhi Tang, Yuan Ren*, Zhou Wang
• Keywords: Bessel Optical Lattice, Cold Atoms BEC, Localization, Numerical Simulation, Variational Method

References

[1] Fetter A L. Bose-Einstein Condensates in Dilute Trapped Atomic Gases, J. Journal of Low Temperature Physics. 129(5-6) (2002)263-321.

[2] Anderson M H. Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, M. // Collected Papers Of Carl Wieman. (2015)453-456.

DOI: 10.1142/9789812813787_0062

[3] Davis K B, Mewes M, Andrews M R, et al. Bose-Einstein condensation in a gas of sodium atoms, J. Physical Review Letters. 75(22) (1995)3969-3973.

DOI: 10.1103/physrevlett.75.3969

[4] Bradley C C, Sackett C A, Tollett J J, et al. Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions, J. Physical Review Letters. 75(9) (1995)1687.

DOI: 10.1103/physrevlett.75.1687

[5] Fallani L, De S L, Lye J E, et al. Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice, J. Physical Review Letters. 93(14) (2004)140406.

DOI: 10.1103/physrevlett.93.140406

[6] Kartashov Y V, Carretero-Gonzalez R, Malomed B A, et al. Multipole-mode solitons in Bessel optical lattices, J. Optics Express. 13(26) (2005)10703-10710.

DOI: 10.1364/opex.13.010703

[7] Mihalache D, Mazilu D, Lederer F, et al. Stable spatiotemporal solitons in bessel optical lattices, J. Physical Review Letters. 95(2) (2005)023902.

DOI: 10.1103/physrevlett.95.023902

[8] Zhang F. Numerical simulation of nonlinear Schro¨dinger systems: a new conservative scheme, M. Elsevier Science Inc. (1995).

[9] Muruganandam P, Adhikari S K. Fortran programs for the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap, J. Computer Physics Communications. 180(10) (2009)1888-(1912).

DOI: 10.1016/j.cpc.2009.04.015

[10] Kartashov Y V, Vysloukh V A, Torner L. Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices, J. Physical Review Letters. 94(4) (2005)043902.

DOI: 10.1103/physrevlett.94.043902

[11] Kartashov Y V, Egorov A A, Vysloukh V A, et al. Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices, J. Physical Review E Statistical Nonlinear & Soft Matter Physics. 70(6 Pt 2)(2004)065602.

DOI: 10.1103/physreve.70.065602

[12] Dong L, Wang J, Wang H, et al. Bessel lattice solitons in competing cubic-quintic nonlinear media, J. Physical Review A. 79(79) (2009)11662-11662.

DOI: 10.1103/physreva.79.013807

[13] B. B. Baizakov, A. Bouketir, A. Messikh, et al. Variational analysis of flat-top solitons in Bose-Einstein condensates, J. International Journal of Modern Physics B. 25(18) (2011)2427-2440.

DOI: 10.1142/s0217979211101521