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Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap


Makarov, Valeri A. y Huang, Guoxiang y Velarde, Manuel G. (2003) Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap. Physical Review A , 67 (2). pp. 23604-1. ISSN 1050-2947

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We consider, both analytically and numerically, the evolution of two-dimensional (2D) nonlinear matter-wave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is c=(1/2 1/4)c 0, where c 0 is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.

Tipo de documento:Artículo
Palabras clave:Dark solitons; Matter waves; Water-waves; Gases; Propagation; Equation; Collisions; Scattering; Evolution; Creation
Materias:Ciencias > Matemáticas > Funciones (Matemáticas)
Código ID:16885

F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999), and references therein.

A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001).

M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, and E.A. Cornell, Phys. Rev. Lett. 83, 2498 (1999) ; ibid.K.W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, 84, 806 (2000) ; J.R. Abo-Shaeer, C. Raman, J.M. Vogels, and W. Ketterle, Science 292, 476 (2001) .

J. Denschlag, J.E. Simsarian, D.L. Feder, Ch.W. Clark, L.A. Collins, J. Cubizolles, L. Deng, E.W. Hagley, K. Helmerson, W.P. Reinhardt, S.L. Rolston, B.I. Schneider, and W.D. Phillips, Science 287, 97 (2000).

S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G.V. Shlyapnikov, and M. Lewenstein, Phys. Rev. Lett. 83, 5198 (1999).

Z. Dutton, M. Budde, C. Slowe, and L.V. Hau, Science 293, 663 (2001).

L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L.D. Carr, Y. Castin, and C. Salomon, Science 296, 1290 (2002).

K.E. Strecker, G.B. Partridge, A.G. Truscott, and R.G. Hulet, Nature (London) 417, 150 (2002) .

L. Deng, E.W. Hagley, J. Wen, M. Trippenbach, Y. Band, P.S. Julienne, J.E. Simsarian, K. Helmerson, S.L. Rolston, and W.D. Phillips, Nature (London) 398, 218 (1999).

E.V. Goldstein and P. Meystre, Phys. Rev. A 59, 1509 (1999) [CAS]; ibid.59, 3896 (1999) ; ibid.K. Rzazewski, M. Trippenbach, S.J. Singer, and Y.B. Band, 61, 013606 (1999);M.G. Moore and P. Meystre, Phys. Rev. Lett. 83, 5202 (1999) ; Y. Wu, X. Yang, C.P. Sun, X.J. Zhou, and Y.Q. Wang, Phys. Rev. A 61, 043604 (2000);ibid.J. Heurich, H. Pu, M.G. Moore, and P. Meystre, 63, 033605 (2000);ibid.M. Trippenbach, Y.B. Band, and P.S. Julienne, 62, 023608 (2000).

V.M. Perez-Garcia, H. Michinel, and H. Herrero, Phys. Rev. A 57, 3837 (1998);ibid.A.D. Jackson, G.M. Kavoulakis, and C.J. Pethick, 58, 2417 (1998) ; ibid.O. Zobay, S. Potting, P. Meystre, and E.M. Wright, 59, 643 (1999) ; ibid.A.E. Muryshev, H.B. van Linden van den Heuvell, and G.V. Shlyapnikov, 60, R2665 (1999) .

Th. Busch and J.R. Anglin, Phys. Rev. Lett. 84, 2298 (2000) ; ibid.M.D. Girardeau and E.M. Wright, 84, 5691 (2000) ; K.V. Kheruntsyan and P.D. Drummond, Phys. Rev. A 61, 063816 (2000);ibid.L.D. Carr, C.W. Clark, and W.P. Reinhardt, 62, 063610 (2000).

A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001) ; ibid.P. Ohberg and L. Santos, 86, 2918 (2001);ibid.Th. Busch and J.R. Anglin, 87, 010401 (2001) ; L.D. Carr, J. Brand, S. Burger, and A. Sanpera, Phys. Rev. A 63, 051601 (2001);ibid.P.D. Drummond, A. Eleftheriou, K. Huang, and K.V. Kheruntsyan, 63, 053602 (2001);ibid.V.S. Filho, F.K. Abdullaev, A. Gammal, and L. Tomio, 63, 053603 (2001);P.V. Elyutin, A.V. Buryak, V.V. Gubernov, R.A. Sammut, and I.N. Towers, Phys. Rev. E 64, 016607 (2001) ; Biao Wu, Jie Liu, and Qian Niu, Phys. Rev. Lett. 88, 034101 (2002);V.V. Konotop and M. Salerno, Phys. Rev. A 65, 021602 (2002).

B.P. Anderson, P.C. Haljan, C.A. Regal, D.L. Feder, L.A. Collins, C.W. Clark, and E.A. Cornell, Phys. Rev. Lett. 86, 2926 (2001) .

D.L. Feder, M.S. Pindzola, L.A. Collins, B.I. Schneider, and C.W. Clark, Phys. Rev. A 62, 053606 (2000).

T. Tsurumi and M. Wadati, J. Phys. Soc. Jpn. 67, 2294 (1998) .

G. Huang, Chin. Phys. Lett. 18, 628 (2001).

G. Huang, M.G. Velarde, and V.A. Makarov, Phys. Rev. A 64, 013617 (2001).

G. Huang, J. Szeftel, and S. Zhu, Phys. Rev. A 65, 053605 (2002).

M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, Science 269, 198 (1995) .

D.S. Jin, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, Phys. Rev. Lett. 77, 420 (1996) .

D.S. Petrov, M. Holzmann, and G.V. Shlyapnikov, Phys. Rev. Lett. 84, 2551 (2000) .

A. Görlitz, J.M. Vogels, A.E. Leanhardt, C. Raman, T.L. Gustavson, J.R. Abo-Shaeer, A.P. Chikkatur, S. Gupta, S. Inouye, T. Rosenband, and W. Ketterle, Phys. Rev. Lett. 87, 130402 (2001).

M.J. Ablowitz and H. Segur, J. Fluid Mech. 92, 691 (1979).

M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, PA, 1981), Chap. 4.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, England, 1995), Chap. 3.

E. Zaremba, Phys. Rev. A 57, 518 (1998) .

H. Michinel, V.M. Pérez-García, and R. de la Fuente, Phys. Rev. A 60, 1513 (1999) .

S. Pötting, P. Meystre, and E.M. Wright, e-print cond-mat/0009289.

D.S. Petrov, G.V. Shlyapnikov, and J.T.M. Walraven, Phys. Rev. Lett. 85, 3745 (2000) .

Y. Castin, in Coherent Atomic Matter Waves, edited by R. Kaiser, C. Westbrook, and F. David (EDP Sciences/Les Ulis, France, Springer-Verlag/Berlin, 2001), pp. 1–36;Y. Castine-print cond-mat/0105058.

L.D. Carr and Y. Castin, e-print cond-mat/0205624.

α(j) and β(j) in Eqs. (13) and (14) can be obtained from Eqs. (A9)–(A12) by setting ∂/∂x3=∂/∂y3=0.

E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos, 2nd ed. (Cambridge University Press, Cambridge, England, 2000).

M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, England, 1991).

E. Infeld, A. Senatorski, and A.A. Skorupski, Phys. Rev. E 51, 3183 (1995) ; ibid.D.E. Pelinovsky, Y.A. Stepanyants, and Y.S. Kivshar, 51, 5016 (1995) .

A.A. Nepomnyashchy, M.G. Velarde, and P. Colinet, Interfacial Phenomena and Convection (CRC-Chapman and Hall, 2002).

Y.S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).

L.M. Pismen, Vortices in Nonlinear Fields. From Liquid Crystals to Superfluids. From Non-Equilibrium Patterns to Cosmic Strings (Clarendon Press, Oxford, 1999).

M.J. Ablowitz and H. Segur, Solitons and Inverse Scattering Transform (SIAM, Philadelphia, 1981), Chap. 3.

Y. Matsuno, J. Phys. A 12, 619 (1979) ; ibid.13, 1519 (1980) ; D.W. Aossey, S.R. Skinner, J.L. Cooney, J.E. Williams, M.T. Gavin, D.R. Andersen, and K.E. Lonngren, Phys. Rev. A 45, 2606 (1992) ; Y. Matsuno, Phys. Rev. Lett. 69, 609 (1992);Phys. Rev. E 49, 2091 (1994), and references therein.

D. David, D. Levi, and P. Winternitz, Stud. Appl. Math. 76, 133 (1987).

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