Dark-in-bright solitons in Bose-Einstein condensates with attractive interactions

We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an optical lattice (OL) and/or a parabolic magnetic trap. We connect such structures with twisted localized modes (TLMs) that were previously found in the discrete nonlinear Schrodinger equation. Families of these structures are found as functions of the OL strength, tightness of the magnetic trap and chemical potential, and their stability regions are identified. Stable bound states of two TLMs are also found. In the case when the TLMs are unstable, their evolution is investigated by means of direct simulations, demonstrating that they transform into large-amplitude fundamental solitons. An analytical approach is also developed, showing that two or several fundamental solitons, with the phase shift π between adjacent ones, may form stable bound states, with parameters quite close to those of the TLMs revealed by simulations. TLM structures are also found numerically and explained analytically in the case when the OL is absent, the condensate being confined only by the magnetic trap.

[1]  Hulet,et al.  Negative scattering length of ultracold 7Li gas. , 1994, Physical Review Letters.

[2]  P C Haljan,et al.  Watching dark solitons decay into vortex rings in a Bose-Einstein condensate. , 2001, Physical review letters.

[3]  J. C. van der Meer,et al.  Hamiltonian Hopf bifurcation with symmetry , 1990 .

[4]  E. V. Zemlyanaya,et al.  Vibrations and Oscillatory Instabilities of Gap Solitons , 1998 .

[5]  L. Salasnich,et al.  Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates , 2002 .

[6]  A Smerzi,et al.  Discrete solitons and breathers with dilute Bose-Einstein condensates. , 2001, Physical review letters.

[7]  C. E. Wieman,et al.  Vortices in a Bose Einstein condensate , 1999, QELS 2000.

[8]  C. Salomon,et al.  Formation of a Matter-Wave Bright Soliton , 2002, Science.

[9]  B. Malomed,et al.  Unified semiclassical approximation for Bose-Einstein condensates: Application to a BEC in an optical potential , 2002, cond-mat/0207739.

[10]  Yuri S Kivshar,et al.  Ring dark solitons and vortex necklaces in Bose-Einstein condensates. , 2003, Physical review letters.

[11]  Andrey Kobyakov,et al.  Stability of strongly localized excitations in discrete media with cubic nonlinearity , 1998 .

[12]  J. Nathan Kutz,et al.  Bose-Einstein Condensates in Standing Waves , 2001 .

[13]  W. Ketterle,et al.  Observation of Feshbach resonances in a Bose–Einstein condensate , 1998, Nature.

[14]  A R Bishop,et al.  Dynamical superfluid-insulator transition in a chain of weakly coupled bose-Einstein condensates. , 2002, Physical review letters.

[15]  Chris H. Greene,et al.  Prospects for Mixed-Isotope Bose-Einstein Condensates in Rubidium , 1998 .

[16]  Phillips,et al.  Generating solitons by phase engineering of a bose-einstein condensate , 2000, Science.

[17]  Aubry,et al.  Growth and decay of discrete nonlinear Schrodinger breathers interacting with internal modes or standing-wave phonons , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Holland,et al.  Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[19]  F Minardi,et al.  Josephson Junction Arrays with Bose-Einstein Condensates , 2001, Science.

[20]  A R Bishop,et al.  Twisted localized modes. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[22]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.

[23]  Randall G. Hulet,et al.  Formation and propagation of matter-wave soliton trains , 2002, Nature.

[24]  T. Hänsch,et al.  Bose–Einstein condensates in 1D- and 2D optical lattices , 2001 .

[25]  P. Maddaloni,et al.  A Novel Mechanism for Superfluidity Breakdown in Weakly Coupled Bose-Einstein Condensates , 2002, cond-mat/0207139.

[26]  M. Salerno,et al.  Regular spatial structures in arrays of Bose?Einstein condensates induced by modulational instability , 2002 .

[27]  B. Malomed,et al.  Discrete vortex solitons. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Carl E. Wieman,et al.  Dynamics of collapsing and exploding Bose–Einstein condensates , 2001, Nature.

[29]  M. Oberthaler,et al.  Stability of gap solitons in a Bose-Einstein condensate , 2002, cond-mat/0208136.

[30]  Dalibard,et al.  Vortex formation in a stirred bose-einstein condensate , 1999, Physical review letters.

[31]  Stefano Trillo,et al.  Stability, Multistability, and Wobbling of Optical Gap Solitons , 1998 .

[32]  B A Malomed,et al.  Stability of multiple pulses in discrete systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  J C Bronski,et al.  Bose-Einstein condensates in standing waves: the cubic nonlinear Schrödinger equation with a periodic potential. , 2001, Physical review letters.

[34]  S. Burger,et al.  Dark solitons in Bose-Einstein condensates , 1999, QELS 2000.

[35]  Yuri S. Kivshar,et al.  Discreteness-induced oscillatory instabilities of dark solitons , 1998, patt-sol/9811002.

[36]  H. Herrero,et al.  Bose-Einstein solitons in highly asymmetric traps , 1998 .

[37]  Boris A. Malomed,et al.  Chapter 2 - Variational methods in nonlinear fiber optics and related fields , 2002 .

[38]  Yuri S. Kivshar,et al.  Bose-Einstein condensates in optical lattices: Band-gap structure and solitons , 2003 .

[39]  Kim Ø. Rasmussen,et al.  THE DISCRETE NONLINEAR SCHRÖDINGER EQUATION: A SURVEY OF RECENT RESULTS , 2001 .

[40]  Kestutis Staliunas,et al.  Faraday patterns in bose-Einstein condensates. , 2002, Physical review letters.

[41]  V. Konotop,et al.  Nonlinear excitations in arrays of Bose-Einstein condensates , 2001, cond-mat/0106042.