Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Solitons in Nonlinear Optical Lattices
Authors: Tapas Kumar Sinha, Joseph Mathew
Abstract:
Based on the Lagrangian for the Gross –Pitaevskii equation as derived by H. Sakaguchi and B.A Malomed [5] we have derived a double well model for the nonlinear optical lattice. This model explains the various features of nonlinear optical lattices. Further, from this model we obtain and simulate the probability for tunneling from one well to another which agrees with experimental results [4].Keywords: Double well model, nonlinear optical lattice, Solitons, tunneling.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060719
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[1] Klaus Kirsten And David J Toms ," Bose-Einstein Condensation Of Atomic Gases In A General Harmonic-Oscillator Confining Potential Trap" In Phys. Rev. A 54, 1996, 4188-4206
[2] P. O. Fedichev, Yu. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven," Influence of Nearly Resonant Light on the Scattering Length in Low- Temperature Atomic Gases"in Phys. Rev. Lett. 77, 1996, 2913-2916
[3] F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and Lauro Tomio "Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice" in Phys. Rev. A 76, 2007, 043611-043621.
[4] C. Sias, H. Lignier, Y. P. Singh, A. Zenesini, D. Ciampini, O. Morsch, and E. Arimondo "Observation of Photon-Assisted Tunneling in Optical Lattices" in Phys. Rev. Lett. 100, 2008, 040404 -040408.
[5] Hidetsugu Sakaguchi and Boris A. Malomed "Matter-wave solitons in nonlinear optical lattices" in Phys. Rev. E 72, 2005,046610 -1-
[6] J. A. Krumhansl and J. R. Schrieffer "Dynamics and Statistical Mechanics of a one-dimensional model Hamiltonian for structural phase transitions" in Physical Review B, Vol 11, 1975, pp 3535-3545.
[7] J. A. Krumhansl and J. R. Schrieffer "Dynamics and Statistical Mechanics of a one-dimensional model Hamiltonian Physical Review B, Vol 11, 1975, pp 3535-3545.
[8] Julio Sanchez-Curto, Pedro Chamotrro-Posada, and Graham S. McDonald "Dark Solitons at nonlinear interfaces" in Optics Letters Vol. 35, Issue 9, 2010, pp 1347-1349.
[9] J. Belmonte-Beitia and J. Cuevas "Existence of dark solitons in a class of stationary nonlinear Schrodinger equations with periodically modulated nonlinearity and periodic asymptotics" J. Mathematical Physics, 52, 2011, 032702-032711.
[10] H. L. F. da Luz, F. Kh. Abdullaev, A. Gammal, M. Salerno, and Lauro Tomio "Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices" Physical Review A 82, 2010, pp 043618-1- 043618-8.
[11] S. Pitois, G. Millot, and S. Wabnitz, Phys. Rev. Lett. 81, 1998, pp1409- 1412.
[12] S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K, Sengstock, A. Sanpera, G.V. Shlyapnikov, and M. Lewnstein " Dark Solitons in Bose Einstein Condensates" Phys. Rev. Lett, 83, 1999, pp 5198-5201.
[13] J. Denschlag et. al " Generating Solitons by phase engineering of a Bose-Einstein condensate" Science 287, 2000, pp 97-101.
[14] Michael Albiez, Rudolf Gati, Jonas Folling, Stefan Hunsmann, Matteo Cristiani, and Markus K. Oberthaler "Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction", Phys. Rev. Lett. 95, 2005, pp 010402-1-010402-4.
[15] Sk Golam Ali and B. Talukdar " Coupled matter-wave solitons in optical lattices" in Annals of Physics, Vo. 324, Issue 6, 2009, pp 1194-1210.
[16] A. Kobyakov, S. Darmanyan, T. Pertsch, and F. Lederer "Stable discrete domain walls and quasirectangular solitons in quadratically nonlinear waveguide arrays", JOSAB, Vol. 16, Issue 10, 1999, pp 1737-1742.
[17] Mason A. Porter, "Experimental Results Related to DNLS Equations" in Springer Tracts in Modern Physics, Vol. 232/2009, 2009, pp 175-189.