2015, 2015(special): 169-175. doi: 10.3934/proc.2015.0169

Matter-wave solitons with a minimal number of particles in a time-modulated quasi-periodic potential

1. 

CIICAp, Universidad Autónoma del Estado de Morelos, Cuernavaca, Mor., México, CP 62209, Mexico, Mexico

Received  September 2014 Revised  February 2015 Published  November 2015

The two-dimensional (2D) matter-wave soliton families supported by an external potential are systematically studied, in a vicinity of the junction between stable and unstable branches of the families. In this case the norm of the solution attains a minimum, facilitating the creation of such excitation. We study the dynamics and stability boundaries for fundamental solitons in a 2D self-attracting Bose-Einstein condensate (BEC), trapped in an quasiperiodic optical lattice (OL), with the amplitude subject to periodic time modulation.
Citation: Gennadiy Burlak, Salomon García-Paredes. Matter-wave solitons with a minimal number of particles in a time-modulated quasi-periodic potential. Conference Publications, 2015, 2015 (special) : 169-175. doi: 10.3934/proc.2015.0169
References:
[1]

B. A. Malomed, Soliton Management in Periodic Systems, (Springer: New York, (2006).   Google Scholar

[2]

A. Gaunt, R. Fletcher, R. Smith and Z. Hadzibabic, A superheated Bose-condensed gas,, Nature Physics, 9 (2013).   Google Scholar

[3]

G. Burlak and B. A. Malomed, Dynamics of matter-wave solitons in a time-modulated two-dimensional optical lattice,, Phys. Rev. A, 77 (2008).   Google Scholar

[4]

B. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett., 63, 642 (2003); J. Yang and Z. H. Musslimani, Opt. Lett., 28, 2094 (2003); Z. H. Musslimani, and J. Yang,, J. Opt. Soc. Am. B, 21 (2004).   Google Scholar

[5]

B. B. Baizakov, B. A. Malomed and M. Salerno, Phys. Rev. A, 70, 053613 (2004); Eur. Phys. J. D, 38, 367 (2006); T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno,, Physica D, 238 (2009).   Google Scholar

[6]

H. Sakaguchi and B. A. Malomed, Gap solitons in quasiperiodic optical lattices,, Phys. Rev. E, 74 (2006).   Google Scholar

[7]

N. G. Vakhitov, A. A. Kolokolov and Izv. Vys. Uch. Zaved., Radiofizika, 16, 1020 (1973) [in Russian; English translation:, Radiophys. Quant. Electr., 16 (1975).   Google Scholar

[8]

G. Kalosakas, K. . Rasmussen and A. R. Bishop, Delocalizing Transition of Bose-Einstein Condensates in Optical Lattices,, Phys. Rev. Lett., 89 (0304).   Google Scholar

[9]

B. B. Baizakov, B. A. Malomed and M. Salerno, in: Nonlinear Waves: Classical and Quantum Aspects, ed. by F. Kh. Abdullaev and V. V. Konotop, pp. 61-80 (Kluwer Academic Publishers: Dordrecht, 2004); also, available at: , ().   Google Scholar

[10]

B. B. Baizakov, B. A. Malomed and M. Salerno, in: Nonlinear Waves: Classical and Quantum Aspects,, ed. by F. Kh. Abdullaev, (2004).   Google Scholar

[11]

G. Burlak and A. Klimov, The solitons redistribution in Bose-Einstein condensate in quasiperiodic optical lattice,, Phys. Lett. A, 369 (2007).   Google Scholar

[12]

F. Dalfovo, S. Giorgini, and L. P. Pitaevskii, Theory of Bose-Einstein condensation in trapped gases,, Rev. Mod. Phys., 71 (1999).   Google Scholar

[13]

B. A. Malomed, D. Mihalache, F. Wise and L. Torner, J. Spatiotemporal optical solitons,, Optics B: Quant. Semics. Opt., 7 (2005).   Google Scholar

[14]

Y. V. Kartashov, B. A. Malomed and L. Torner, Solitons in nonlinear lattices,, Rev. Mod. Phys., 83 (2011).   Google Scholar

[15]

J. Yang and T. I. Lakoba, Accelerated imaginary-time evolution methods for the computation of solitary waves,, Stud. Appl. Math. 120, (2008).   Google Scholar

[16]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Discrete solitons in optics,, Phys. Rep. 463, (2008).   Google Scholar

[17]

J. Yang, Nonlinear waves in integrable and nonintegrable systems., (SIAM-USA, (2010).   Google Scholar

[18]

G. Burlak, B. A. Malomed, Matter-wave solitons with a minimal number of particles in two-dimensional quasiperiodic potentials., Phys. Rev. E, 85 (2012), 57601.   Google Scholar

show all references

References:
[1]

B. A. Malomed, Soliton Management in Periodic Systems, (Springer: New York, (2006).   Google Scholar

[2]

A. Gaunt, R. Fletcher, R. Smith and Z. Hadzibabic, A superheated Bose-condensed gas,, Nature Physics, 9 (2013).   Google Scholar

[3]

G. Burlak and B. A. Malomed, Dynamics of matter-wave solitons in a time-modulated two-dimensional optical lattice,, Phys. Rev. A, 77 (2008).   Google Scholar

[4]

B. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett., 63, 642 (2003); J. Yang and Z. H. Musslimani, Opt. Lett., 28, 2094 (2003); Z. H. Musslimani, and J. Yang,, J. Opt. Soc. Am. B, 21 (2004).   Google Scholar

[5]

B. B. Baizakov, B. A. Malomed and M. Salerno, Phys. Rev. A, 70, 053613 (2004); Eur. Phys. J. D, 38, 367 (2006); T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno,, Physica D, 238 (2009).   Google Scholar

[6]

H. Sakaguchi and B. A. Malomed, Gap solitons in quasiperiodic optical lattices,, Phys. Rev. E, 74 (2006).   Google Scholar

[7]

N. G. Vakhitov, A. A. Kolokolov and Izv. Vys. Uch. Zaved., Radiofizika, 16, 1020 (1973) [in Russian; English translation:, Radiophys. Quant. Electr., 16 (1975).   Google Scholar

[8]

G. Kalosakas, K. . Rasmussen and A. R. Bishop, Delocalizing Transition of Bose-Einstein Condensates in Optical Lattices,, Phys. Rev. Lett., 89 (0304).   Google Scholar

[9]

B. B. Baizakov, B. A. Malomed and M. Salerno, in: Nonlinear Waves: Classical and Quantum Aspects, ed. by F. Kh. Abdullaev and V. V. Konotop, pp. 61-80 (Kluwer Academic Publishers: Dordrecht, 2004); also, available at: , ().   Google Scholar

[10]

B. B. Baizakov, B. A. Malomed and M. Salerno, in: Nonlinear Waves: Classical and Quantum Aspects,, ed. by F. Kh. Abdullaev, (2004).   Google Scholar

[11]

G. Burlak and A. Klimov, The solitons redistribution in Bose-Einstein condensate in quasiperiodic optical lattice,, Phys. Lett. A, 369 (2007).   Google Scholar

[12]

F. Dalfovo, S. Giorgini, and L. P. Pitaevskii, Theory of Bose-Einstein condensation in trapped gases,, Rev. Mod. Phys., 71 (1999).   Google Scholar

[13]

B. A. Malomed, D. Mihalache, F. Wise and L. Torner, J. Spatiotemporal optical solitons,, Optics B: Quant. Semics. Opt., 7 (2005).   Google Scholar

[14]

Y. V. Kartashov, B. A. Malomed and L. Torner, Solitons in nonlinear lattices,, Rev. Mod. Phys., 83 (2011).   Google Scholar

[15]

J. Yang and T. I. Lakoba, Accelerated imaginary-time evolution methods for the computation of solitary waves,, Stud. Appl. Math. 120, (2008).   Google Scholar

[16]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Discrete solitons in optics,, Phys. Rep. 463, (2008).   Google Scholar

[17]

J. Yang, Nonlinear waves in integrable and nonintegrable systems., (SIAM-USA, (2010).   Google Scholar

[18]

G. Burlak, B. A. Malomed, Matter-wave solitons with a minimal number of particles in two-dimensional quasiperiodic potentials., Phys. Rev. E, 85 (2012), 57601.   Google Scholar

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