Modulational instability conditions for the generation of localized structures in the context of matter waves in Bose-Einstein condensates are investigated analytically and numerically. The model is based on a modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude. It is shown that the modified term due to the quantum fluctuations modify significantly the modulational instability gain. Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations.
References
[1]
C. Pethick and H. Smith, “Bose-Einstein Condensation in Dilute Gases,” Cambridge University Press, Cambridge, 2003.
[2]
L. Pitaevskii and S. Stringari, “Bose-Einstein Condensation in Dilute Gases,” Oxford University Press, New Yrk, 2003.
[3]
J. M. Gerton, D. Strekalov, I. Prodan and R. G. Hulet, “Direct Observation of Growth and Collapse of a Bose-Einstein Condensate with Attractive Interaction,” Nature, Vol. 408, 2000, pp. 692-695. doi:10.1038/35047030B
[4]
T. S. Raju, P. K. Panigrahi and K. Porsezian, “Modulational Instability of Two-Component Bose-Einstein Condensates in a Quasi-One Dimensional Geometry,” Physics Review A, Vol. 71, No. 3, 2005, Article ID: 035601.
doi:10.1103/PhysRevA.71.035601
[5]
A. Hasegawa and F. Tappert, “Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers,” Applied Physics Letter, Vol. 23, No. 3, 1973, pp. 142-144.
doi:10.1063/1.1654836
[6]
C. Tabi, A. Mohamadou and T. C. Kofane, “Modulated Wave Packets in DNA and Impact of Viscosity,” Chinese Physics Letter, Vol. 26, No. 6, 2009, Article ID: 068703.
doi:10.1088/0256-307X/26/6/068703
[7]
S. Cowell, H. Heiselberg, I. E. Mazets, J. Morales, V. R. Pandhari-pande and C. J. Pethick, “Cold Bose Gases with Large Scattering Lengths,” Physics Review Letter, Vol. 88, 2002, pp. 210403-210406.
doi:10.1103/PhysRevLett.88.210403
[8]
E. Tiesinga, C. J. Williams, F. H. Mies and P. S. Julienne, “Interacting Atoms under Strong Quantum Confinement,” Physics Review A, Vol. 61, No. 6, 2000, Article ID: 063416. doi:10.1103/PhysRevA.61.063416
[9]
H. Fu, Y. Wang and B. Gao, “Beyond the Fermi Pseudopotential: A Modified Gross-Pitaevskii Equation,” Physics Review A, Vol. 67, No. 5, 2003, Article ID: 053612.
doi:10.1103/PhysRevA.67.053612
[10]
G. Theocharis, Z. Rapti, P. G. Kevrekidis, D. J. Frantzeskakis and V. V. Konotop, “Modulational Instability of Gross-Pitaevskii-Type Equations in 1+1 Dimensions,” Physics Review A, Vol. 67, No. 6, 2003, Article ID: 063610. doi:10.1103/PhysRevA.67.063610
[11]
P. Muruganandam and S. Adhikari, “Fortran Programs for the Time-Dependent Gross-Pitaevskii Equation in a Fully Anisotropic Trap,” Computer Physics Communication, Vol. 180, No. 10, 2009, pp. 1888-1912.
doi:10.1016/j.cpc.2009.04.015
[12]
L.Wu and J. F. Zhang, “Modulational Instability of (1+1)-Dimensional Bose-Einstein Condensate with Three-Body Interatomic Interaction,” Chinese Physics Letter, Vol. 24, No. 6, 2007, pp. 1471-1474.
doi:10.1088/0256-307X/24/6/012
[13]
E. Wamba, A. Mohamadou and T. C. Kofane, “Modulational Instability of a Trapped Bose-Einstein Condensate with Two-and Three-Body Interactions,” Physics Review E, Vol. 77, No. 4, 2008, Article ID: 046216.
doi:10.1103/PhysRevE.77.046216
[14]
J. K. Xu, “Modulational Instability of the Trapped Bose-Einstein Condensates,” Physics Letter A, Vol. 341, No. 5-6, 2005, pp. 527-531.
doi:10.1016/j.physleta.2005.05.018
