Spontaneous Symmetry Breaking of Solitons Trapped in a Double-Gauss Potentials

Cuong Duy Nguyen, Khoa Xuan Dinh, Van Long Cao, Trippenbach M., Thuan Dinh Bui, Thuy Thanh Do

Abstract


We consider an extended model of the model considered before with double-square potential, namely one-dimensional (1D) nonlinear Schrödinger equation (NLSE) with self-focusing nonlinearity and a 1D double-gauss potential. Spontaneous symmetry breaking has been presented in terms of the control parameter which is propagation constant in the case of optics and chemical potential in the of Bose-Einstein Condensate (BEC), correspondingly. The numerical simulations predict a bifurcation breaking the symmetry of 1D trapped in the double-gauss potential of the supercritical type as in the case of double-square potential. Furthermore we have constructed bifurcation diagrams considering the stability of solitons with three methods: the method using Vakhitov–Kolokolov (V-K) Stability Criterion, Pseudospectral Method and Method for Linear-Stability Eigenvalues. It will be shown that for our model the results obtained are the same for these three methods but the third one is the fastest.

Keywords


Bose–Einstein condensate, nonlinear optical systems, double-square potential.

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References


E. B. Davies, Symmetry breaking for a non-linear Schrödinger equation, Commu. Math. Phys. (England). 64 (1979) 191-210.

B.A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, Symmetric and asymmetric solitons in twin-core nonlinear optical fibers, Physical Review E. 53 (1996) 4084-4091.

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Spontaneous symmetry breaking in a nonlinear double-well structure, Phys. Rev. A. 78 (2008) 053601.

M. Trippenbach, E. Infeld, J. Gocałek, M. Matuszewski, M. Oberthaler, and B. A. Malomed, Spontaneous symmetry breaking of gap solitons and phase transitions in double-well traps, Physical review A. 78 (2008) 013603.

Nguyen Viet Hung, Pawe l Zi´n, Marek Trippenbach, and Boris A. Malomed, Two - dimensional solitons in media with the stripe - shaped nonlinearity modulation, Phys. Rev. E. 82 (2010) 046602.

Nguyen Viet Hung, Marek Trippenbach, and Boris A. Malomed, Symmetric and asymmetric solitons trapped in H-shaped potentials, Phys. Rev. A. 84 (2011) 053618.

Lazar Gubeskys and Boris A. Malomed, Symmetric and asymmetric solitons in dual-core couplers with competing quadratic and cubic nonlinearities, Journal of the Optical Society of America B. Vol. 30 (2013) 1843-1852.

Nguyen Viet Hung, Marek Trippenbach, Eryk Infeld, and Boris A. Malomed, Spatial control of the competition between self-focusing and self-defocusing nonlinearities in one- and two-dimensional systems, Physical review A. 90 (2014) 023841.

Boris A. Malomed, Spontaneous Symmetry Breaking in Nonlinear Systems: an Overview and a Simple Model, Springer Proceedings in Physics. Vol. 173 (2015).

Elad Shamriz, Nir Dror, and Boris A. Malomed, Spontaneous symmetry breaking in a split potential box, Phys. Rev. E. 94 (2016) 022211.

Krzysztof B. Zegadlo, Nir Dror, Marek Trippenbach, Miroslaw A. Karpierz and Boris A. Malomed, Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well

potentials, Physical Review A. (2016).

Zhaopin Chen, Yongyao Li, Boris A. Malomed, and Luca Salasnich, Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in twoand one-dimensional linearly coupled traps with cubic self-attraction, Phys. Rev. A. 96 (2017) 033621.

Vitaly Lutsky and Boris A. Malomed, Solitons supported by singular modulation of the cubic nonlinearity, Optics Express, Vol. 25 (2017) 12967- 12983.

Krzysztof B. Zegadlo, Nguyen Viet Hung, Aleksandr Ramaniuk, Marek Trippenbach and Boris A. Malomed, Symmetry Breakings in Dual-Core Systems with Double-Spot Localization of Nonlinearity, Symmetry. 10 (2018) 156.

K. Hayata and M. Koshiba, Self-localization and spontaneous symmetry breaking of optical fields propagating in strongly nonlinear channel waveguides: limitations of the scalar field approximation, J. Opt. Soc. Am. B. 9 (1992) 1362.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, Symmetry-Breaking Instability of Multimode Vector Solitons, Phys. Rev. Lett. 89 (2002) 083901.

Y. J. Tsofe and B. A. Malomed, Quasi-symmetric and asymmetric gap solitons in linearly coupled Bragg gratings with a phase shift, Phys. Rev. E. 75 (2007) 056603.

W. C. K. Mak, B. A. Malomed, and P. L. Chu, Soliton coupling in waveguide with quadratic nonlinearity, Phys. Rev. E. 55 (1997) 6134.

L. Albuch and B. A. Malomed, Transitions between symmetric and asymmetric solitons in dual-core systems with cubic–quintic nonlinearity, Math. Comput. Simul. 74 (2007) 312.

Dalfovo, F., Giorgini, S., Pitaevskii, L. P. & Stringari, Theory of Bose-Einstein condensation in trapped gases, S. Rev. Mod. Phys. 71 (1999) 463–512.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential, Phys. Rev. A. 55 (1997) 4318-4324.

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum coherent atomic tunneling between two trapped BoseEinstein condensates, Phys. Rev. Lett. 79 (1997) 4950-4953.

M. Matuszewski, B. A. Malomed, and M.Trippenbach, Spontaneous symmetry breaking of solitons trapped in a double-channel potential, Phys. Rev. A. 75 (2007) 063621.

V. M. P´erez-García, H. Michinel, and H. Herrero, Bose-Einstein solitons in highly asymmetric traps, Phys. Rev. A. 57 (1998) 3837-3842.

C. Par´e and M. Florja´nczyk, Approximate model of soliton dynamics in all-optical couplers, Phys. Rev. A. 41 (1990) 6287-6295.

A. I. Maimistov, Propagation of a light pulse in nonlinear tunnel-coupled optical waveguides, Sov. J. Quantum Electron. 21 (1991) 687-690.

P. L. Chu, B. A. Malomed, and G. D. Peng, Soliton switching and propagation in nonlinear fiber couplers: analytical results, J. Opt. Soc. Am. B. 10 (1993) 1379-1385.

N. Akhmediev and A. Ankiewicz, Novel soliton states and bifurcation phenomena in nonlinear fiber couplers, Phys. Rev. Lett. 70 (1993) 2395-2398.

A. W. Snyder, D. J. Mitchell, L. Poladian, D. R. Rowland, and Y. Chen, Physics of nonlinear fiber couplers, J. Opt. Soc. Am. B 8 (1991) 2102-2118.

JianKe Yang, Nonlinear Waves in Integrable and Nonintegrable Systems, Monographs on Mathematical Modeling and Computation, (2010).

Nguyen Duy Cuong et al, in preparation.




DOI: https://doi.org/10.15625/0868-3166/28/4/13195 Display counter: Abstract : 170 views. PDF : 105 views.

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