DYNAMICS OF BOSE EINSTEIN CONDENSATE IN FOURIER SYNTESIZED OPTICAL LATTICE POTENTIAL

In this study, we examine the dynamics of Bose Einstein condensate trapped by Fourier synthesized optical lattice potential. We use time-dependent variational approach to find the ordinary differential equations of motion. We also solve directly Gross Pitaevskii equation numerically using split step Fourier method to verify our findings. Good agreement is achieved between analytical and numerical results.

___

  • REFERENCES[1] Bose S N. Plancks Gesetz und Lichtquantenhypothese. Zeitschrift für Physik 1924; 26: 178-181.
  • [2] Pethick C J, Smith H. Bose-Einstein Condensation in Dilute Gases. United Kingdom: Cambridge University Press, 2002.
  • [3] Anderson M H, Ensher J R, Matthews M R, Wiemann C E, Cornell E A. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 1995; 269: 198-201.
  • [4] Perez-Garcia V M, Michinel H, Cirac J I, Lewenstein M, Zoller P. Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations. Phys. Rev. A 1997; 56: 1424-1432.
  • [5] Perez-Garcia V M, Michinel H, Cirac J I, Lewenstein M, Zoller P. Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational Analysis. Phys. Rev. Lett. 1996; 77: 5320-5323.
  • [6]Abdullaev F K, Gammal A, Tomio L, Frederico T. Stability of trapped Bose-Einstein condensates. Phys. Rev. A 2001; 63: 043604-15.
  • [7] Wamba E, Sabari S, Porsezian K, Mohamadou A, Kofane T C. Dynamical instability of a Bose-Einstein condensate with higher-order interactions in an optical potential through a variational approach. Phys. Rev. E 2014; 89: 052917-13.
  • [8] Burlak G, Malomed B A. Dynamics of matter-wave solitons in a time-modulated two-dimensional optical lattice. Phys. Rev. A 2008; 77: 053606-22.
  • [9] Cheng Y, Adhikari S K. Spatially antisymmetric localization of matter wave in a bichromatic optical lattice. Laser Phys. Lett. 2010; 7: 824-830.
  • [10] Sakhel A R. Long-time averaged dynamics of a Bose-Einstein condensate in a bichromatic optical lattice with external harmonic confinement. Physica B: Condensed Matter 2016; 493: 72-80.
  • [11] Wamba E, Sabari S, Porsezian K, Mohamadou A, Kofane T C. A variational approach to the modulational-oscillatory instability of Bose Einstein condensate in an optical potential. Phys. Lett. A 2013; 377:2408-2415.
  • [12] Umarovi B A, Messikh A, Regaai N, Baizakov B B. Variational analysis of soliton scattering by external potentials. Journal of Physics: Conference Series 2013; 435: 012024-9.
  • [13] Castro C J, Urzagasti D. Seesaw drift of bright solitons of the nonlinear Schrödinger equation with a periodic potential. Journal of Nonlinear Optical Physics & Materials 2016; 25: 1650038-8.
  • [14] Cheng Y. Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity. J. Phys. B: At. Mol. Opt. Phys. 2009; 42: 205005-8.[15] Abdullaev F K,Gammal A,Tomio L. Dynamics of bright matter-wave solitons in a Bose–Einstein condensate with inhomogeneous scattering length. J. Phys. B: At. Mol. Opt. Phys. 2004; 37: 635–651.
  • [15] Abdullaev F K,Gammal A,Tomio L. Dynamics of bright matter-wave solitons in a Bose–Einstein condensate with inhomogeneous scattering length. J. Phys. B: At. Mol. Opt. Phys. 2004; 37: 635–651.
  • [16] Falco G M. Variational approach for Bose–Einstein condensates in strongly disordered traps. J. Phys. B: At. Mol. Opt. Phys. 2009; 42: 215303-8.
  • [17] Cheng Y, Adhikari S K. Matter-wave localization in a random potential. Phys. Rev. A 2010; 82: 013631-6.
  • [18] Ritt G, Geckeler C, Salger T, Cennini G, Weitz M. Fourier synthesis of optical potentials for atomic quantum gases. Phys. Rev. A 2006; 74: 063622-11.
  • [19] Salger T, Geckeler C, Kling S, Weitz M. Atomic Landau-Zener Tunneling in Fourier-Synthesized Optical Lattices. Phys. Rev. Lett. 2007; 99: 190405-4.
  • [20] He J R, Li H M. Nonautonomous bright matter-wave solitons and soliton collisions in Fourier-synthesized optical lattices. Optics Commun. 2011; 284:3084-3089.
  • [21] Ali S K, Pal D, Roy S K, Talukdar B. Application of variational calculus to propagation of coupled pulses in optical fibers. Czechoslovak Journal of Physics 2006; 6: 217-228.
  • [22] Javanainen J, Ruostekoski J. Symbolic calculation in development of algorithms: split-step methods for the Gross–Pitaevskii equation. Journal of Physics A: Mathematical and General 2006; 39: L179–L184.