Geodesic
Nonlinear dynamics in double square-well potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 292-303 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The first example of the coexistence of Josephson oscillations with a self-trapping regime is found in the context of the coherent nonlinear dynamics in a double square-well potential. We prove the simultaneous existence of symmetric, antisymmetric, and asymmetric stationary solutions of the associated Gross–Pitaevskii equation, which explains this macroscopic bistability. We illustrate and confirm the effect with numerical simulations. This property allows suggesting experiments with Bose–Einstein condensates in engineered optical lattices or with weakly coupled optical waveguide arrays.
Keywords: waveguide array, Bose–Einstein condensate. 
@article{TMF_2007_152_2_a6,
     author = {R. Khomeriki and J. Leon and S. Ruffo and S. Wimberger},
     title = {Nonlinear dynamics in double square-well potentials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {292--303},
     year = {2007},
     volume = {152},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a6/}
}
TY  - JOUR
AU  - R. Khomeriki
AU  - J. Leon
AU  - S. Ruffo
AU  - S. Wimberger
TI  - Nonlinear dynamics in double square-well potentials
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 292
EP  - 303
VL  - 152
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a6/
LA  - ru
ID  - TMF_2007_152_2_a6
ER  - 
%0 Journal Article
%A R. Khomeriki
%A J. Leon
%A S. Ruffo
%A S. Wimberger
%T Nonlinear dynamics in double square-well potentials
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 292-303
%V 152
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a6/
%G ru
%F TMF_2007_152_2_a6
R. Khomeriki; J. Leon; S. Ruffo; S. Wimberger. Nonlinear dynamics in double square-well potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 292-303. http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a6/

[1] S. M. Jensen, IEEE J. Quantum Electronics, 18 (1982), 1580 | DOI

[2] B. D. Josephson, Phys. Lett., 1 (1962), 251 | DOI | Zbl

[3] P. L. Anderson, J. W. Rowell, Phys. Rev. Lett., 10 (1963), 230 | DOI

[4] M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, M. K. Oberthaler, Phys. Rev. Lett., 95 (2005), 010402 | DOI

[5] A. Smerzi, S. Fantoni, S. Giovanazzi, S. R. Shenoy, Phys. Rev. Lett., 79 (1997), 4950 | DOI

[6] S. Raghavan, A. Smerzi, S. Fantoni, S. R. Shenoy, Phys. Rev. A, 59 (1999), 620 | DOI

[7] L. P. Pitaevskii, ZhETF, 40 (1961), 646; E. P. Gross, Nuovo Cimento, 20 (1961), 454 ; J. Math. Phys., 4 (1963), 195 | DOI | MR | Zbl | DOI

[8] E. A. Ostrovskaya, Yu. S. Kivshar, M. Lisak et al., Phys. Rev. A, 61 (2000), 031601 | DOI

[9] D. Ananikian, T. Bergeman, Phys. Rev. A, 73 (2006), 013604 | DOI

[10] A. Montina, F. T. Arecchi, Phys. Rev. A, 66 (2002), 013605 | DOI

[11] T. Kapitula, P. G. Kevrekidis, Nonlinearity, 18 (2005), 2491 | DOI | MR | Zbl

[12] H. S. Eisenberg, Y. Silberberg, R. Morandotti et al., Phys. Rev. Lett., 81 (1998), 3383 | DOI

[13] R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, J. S. Aitchison, Phys. Rev. Lett., 86 (2001), 3296 | DOI

[14] D. Mandelik, H. S. Eisenberg, Y. Silberberg et al., Phys. Rev. Lett., 90 (2003), 053902 ; D. Mandelik, R. Morandotti, J. S. Aitchison, Y. Silberberg, Phys. Rev. Lett., 92 (2004), 093904 | DOI | DOI

[15] A. A. Sukhorukov, D. Neshev, W. Krolikowski, Y. S. Kivshar, Phys. Rev. Lett., 92 (2004), 093901 | DOI

[16] J. W. Fleischer, T. Carmon, M. Segev et al., Phys. Rev. Lett., 90 (2003), 023902 | DOI

[17] J. W. Fleischer, M. Segev, N. K. Efremidis et al., Nature, 422 (2003), 147 | DOI

[18] A. Fratalocchi, G. Assanto, Phys. Rev. E, 73 (2006), 046603 ; A. Fratalocchi, G. Assanto, K. Brzdakiewicz, M. Karpierz, Opt. Express, 13 (2005), 1808 | DOI | DOI

[19] F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science, 293 (2001), 843 | DOI

[20] M. Anderlini, J. Sebby-Strabley, J. Kruse et al., J. Phys. B, 39 (2006), S199 | DOI

[21] P. F. Byrd, M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Springer, Berlin–Göttingen–Heidelberg, 1954 | MR | Zbl

[22] T. Bergeman, M. G. Moore, M. Olshanii, Phys. Rev. Lett., 91 (2003), 163201 | DOI

[23] I. Bloch, J. Phys. B, 38 (2005), S629 ; O. Morsch, M. Oberthaler, Rev. Mod. Phys., 78 (2006), 179 | DOI | DOI

[24] L. Carr, M. J. Holland, B. A. Malomed, J. Phys. B, 38 (2005), 3217 ; S. Wimberger, P. Schlagheck, R. Mannella, J. Phys. B, 39 (2006), 729 ; P. Schlagheck, T. Paul, Phys. Rev. A, 73 (2006), 023619 | DOI | DOI | DOI

[25] R. Khomeriki, S. Ruffo, S. Wimberger, Europhys. Lett., 77 (2007), 40005 ; cond-mat/0610014 | DOI

[26] A. Smerzi, A. Trombettoni, Phys. Rev. A, 68 (2003), 023613 | DOI

[27] M. J. Ablowitz, Z. H. Musslimani, Phys. Rev. Lett., 87 (2001), 254102 ; Phys. Rev. E, 65 (2002), 056618 | DOI | DOI | MR

[28] J. C. Slater, Phys. Rev., 87 (1952), 807 | DOI | Zbl

[29] R. Khomeriki, J. Leon, S. Ruffo, Phys. Rev. Lett., 97 (2006), 143902 | DOI

[30] D. N. Christodoulides, R. I. Joseph, Opt. Lett., 13 (1988), 794 | DOI