Matter-wave solitons of collisionally inhomogeneous condensates

We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity is found to lead to a gravitational potential, as well as to a renormalization of the parabolic potential coefficient. This feature allows one to influence the motion of fundamental as well as higher-order solitons.

[1]  Yuri S. Kivshar,et al.  Dark optical solitons: physics and applications , 1998 .

[2]  B. A. Malomed,et al.  Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length , 2003 .

[3]  Jakob Reichel,et al.  Microchip traps and Bose–Einstein condensation , 2002 .

[4]  J. Schmiedmayer,et al.  Microscopic atom optics: from wires to an atom chip , 2008, 0805.2613.

[5]  Valeri A. Makarov,et al.  Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap , 2003 .

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

[7]  F. Keck,et al.  Dynamics of Bloch oscillations , 2004 .

[8]  Hiroki Saito,et al.  Dynamically stabilized bright solitons in a two-dimensional bose-einstein condensate. , 2003, Physical review letters.

[9]  S. Jochim,et al.  Collective excitations of a degenerate gas at the BEC-BCS crossover. , 2004, Physical review letters.

[10]  Averaging for solitons with nonlinearity management. , 2003, Physical review letters.

[11]  Cheng Chin,et al.  Preparation of a Pure Molecular Quantum Gas , 2003, Science.

[12]  D. Frantzeskakis,et al.  Hamiltonian averaging for solitons with nonlinearity management. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  M. Hellwig,et al.  Tuning the scattering length with an optically induced Feshbach resonance. , 2004, Physical review letters.

[14]  Walter Kohn,et al.  Cyclotron Resonance and de Haas-van Alphen Oscillations of an Interacting Electron Gas , 1961 .

[15]  P. Kevrekidis,et al.  Oscillations of dark solitons in trapped Bose-Einstein condensates. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Zachary Dutton,et al.  Observation of Quantum Shock Waves Created with Ultra- Compressed Slow Light Pulses in a Bose-Einstein Condensate , 2001, Science.

[17]  Víctor M. Pérez-García,et al.  Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers , 2003, nlin/0305030.

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

[19]  A M Kamchatnov,et al.  Adiabatic dynamics of periodic waves in Bose-Einstein condensates with time dependent atomic scattering length. , 2003, Physical review letters.

[20]  Yi Tang,et al.  DIRECT APPROACH TO THE STUDY OF SOLITON PERTURBATIONS OF THE NONLINEAR SCHRODINGER EQUATION AND THE SINE-GORDON EQUATION , 1998 .

[21]  Vladimir V. Konotop,et al.  Evolution of a dark soliton in a parabolic potential: Application to Bose-Einstein condensates , 2003 .

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

[23]  Cornish,et al.  Stable 85Rb bose-einstein condensates with widely tunable interactions , 2000, Physical review letters.

[24]  Yang,et al.  Perturbation-induced dynamics of dark solitons. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  B Eiermann,et al.  Bright Bose-Einstein gap solitons of atoms with repulsive interaction. , 2004, Physical review letters.

[26]  Dmitry V. Skryabin,et al.  Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications , 2002 .

[27]  J. Weiner.  Cold and Ultracold Collisions in Quantum Microscopic and Mesoscopic Systems , 2004 .

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

[29]  W M Liu,et al.  Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential. , 2005, Physical review letters.

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

[31]  C. Adams,et al.  Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates. , 2002, Physical review letters.

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

[33]  V. A. Makarov,et al.  Dark solitons and their head-on collisions in Bose-Einstein condensates , 2001 .

[34]  Maxim Olshanii.  Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons , 1998 .

[35]  D. J. Frantzeskakis,et al.  Analogies between dark solitons in atomic Bose-Einstein condensates and optical systems , 2004 .

[36]  B. Malomed,et al.  Modulational Instability in Bose–Einstein Condensates under Feshbach Resonance Management , 2004, cond-mat/0404664.

[37]  J. Satsuma,et al.  B Initial Value Problems of One-Dimensional self-Modulation of Nonlinear Waves in Dispersive Media (Part V. Initial Value Problems) , 1975 .

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

[39]  B. Malomed,et al.  Feshbach resonance management for Bose-Einstein condensates. , 2003, Physical review letters.

[40]  Shanhua Zhu,et al.  Dynamics of dark solitons in quasi-one-dimensional Bose-Einstein condensates , 2002 .

[41]  C. E. Wieman,et al.  RESONANT MAGNETIC FIELD CONTROL OF ELASTIC SCATTERING IN COLD 85RB , 1998 .

[42]  Atom-Atom Scattering under Cylindrical Harmonic Confinement: Numerical and Analytic Studies of the Confinement Induced Resonance. , 2002, Physical review letters.

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

[44]  Yuri S. Kivshar,et al.  Interaction of dark solitons with localized impurities in Bose-Einstein condensates , 2002 .

[45]  Anglin,et al.  Motion of dark solitons in trapped bose-einstein condensates , 2000, Physical review letters.

[46]  Yuri S. Kivshar,et al.  Dynamics of Solitons in Nearly Integrable Systems , 1989 .

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

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

[49]  U Al Khawaja,et al.  Bright soliton trains of trapped Bose-Einstein condensates. , 2002, Physical review letters.