Dark-Bright Discrete Solitons: A Numerical Study of Existence, Stability and Dynamics

In the present work, we numerically explore the existence and stability properties of dierent types of congurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We nd that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions between dark-bright solitons and between a dark-bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we nd a wide range of potential dynamical outcomes depending on the

[1]  Kivshar,et al.  Dark solitons in discrete lattices. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  R. Morandotti,et al.  Discrete vector solitons in Kerr nonlinear waveguide arrays , 2003, Postconference Digest Quantum Electronics and Laser Science, 2003. QELS..

[3]  Andrey V. Gorbach,et al.  Discrete breathers — Advances in theory and applications , 2008 .

[4]  Y. Kivshar,et al.  Symbiotic optical solitons and modulational instability , 1991 .

[5]  Yaron Silberberg,et al.  Discrete Solitons in Optics , 2008 .

[6]  Demetrios N. Christodoulides,et al.  Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices , 2003, Nature.

[7]  W. Ketterle,et al.  OPTICAL CONFINEMENT OF A BOSE-EINSTEIN CONDENSATE , 1998 .

[8]  D. J. Frantzeskakis,et al.  PATTERN FORMING DYNAMICAL INSTABILITIES OF BOSE–EINSTEIN CONDENSATES , 2004, cond-mat/0406657.

[9]  H. Susanto,et al.  Interlaced solitons and vortices in coupled DNLS lattices , 2008, 0812.1301.

[10]  M. Lakshmanan,et al.  Interaction of dark–bright solitons in two-component Bose–Einstein condensates , 2009, 0902.0934.

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

[12]  Panayotis G. Kevrekidis,et al.  The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives , 2009 .

[13]  B. A. Malomed,et al.  Discrete solitons in nonlinear Schrodinger lattices with a power-law nonlinearity , 2009 .

[14]  Robert S. MacKay,et al.  Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators , 1994 .

[15]  Tal Carmon,et al.  Observation of discrete solitons in optically induced real time waveguide arrays. , 2003, Physical review letters.

[16]  Carl E. Wieman,et al.  PRODUCTION OF TWO OVERLAPPING BOSE-EINSTEIN CONDENSATES BY SYMPATHETIC COOLING , 1997 .

[17]  A. R. Bishop,et al.  Bound states of two-dimensional solitons in the discrete nonlinear Schrödinger equation , 2001 .

[18]  C. Hamner,et al.  Dynamics of dark–bright solitons in cigar-shaped Bose–Einstein condensates , 2010, 1005.3789.

[19]  M. Oberthaler,et al.  Dynamics of Bose-Einstein condensates in optical lattices , 2006 .

[20]  V. A. Brazhnyi,et al.  THEORY OF NONLINEAR MATTER WAVES IN OPTICAL LATTICES , 2004 .

[21]  J R Anglin,et al.  Dark-bright solitons in inhomogeneous Bose-Einstein condensates. , 2001, Physical review letters.

[22]  M Segev,et al.  Interaction between vector solitons and solitonic gluons. , 1999, Optics letters.

[23]  Yaron Silberberg,et al.  Discretizing light behaviour in linear and nonlinear waveguide lattices , 2003, Nature.

[24]  K. Bongs,et al.  Oscillations and interactions of dark and dark bright solitons in Bose Einstein condensates , 2008 .

[25]  J. S. Aitchison,et al.  Discrete Spatial Optical Solitons in Waveguide Arrays , 1998 .

[26]  H. Susanto,et al.  High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  C. Hamner,et al.  Generation of dark-bright soliton trains in superfluid-superfluid counterflow. , 2010, Physical review letters.

[28]  Ricardo Carretero-González,et al.  Emergent Nonlinear Phenomena in Bose-Einstein Condensates , 2008 .

[29]  P. Kevrekidis,et al.  Vortex solutions of the discrete Gross-Pitaevskii equation , 2008, 0803.3379.

[30]  P. Kevrekidis,et al.  Stable vortex-bright-soliton structures in two-component Bose-Einstein condensates. , 2010, Physical review letters.

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

[32]  Mordechai Segev,et al.  Discrete solitons in photorefractive optically induced photonic lattices. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  V. M. P'erez-Garc'ia,et al.  Stable multidimensional soliton stripes in two-component Bose–Einstein condensates , 2010, 1004.3672.

[34]  N. Berloff,et al.  Coherent Atomic Soliton Molecules , 2010, 1003.4617.

[35]  M. Segev,et al.  Incoherently coupled dark-bright photorefractive solitons. , 1996, Optics letters.

[36]  B. Malomed,et al.  Bright-dark soliton complexes in spinor Bose-Einstein condensates , 2007, 0705.1324.

[37]  J. R. Ensher,et al.  Dynamics of component separation in a binary mixture of Bose-Einstein condensates , 1998 .

[38]  K Aravinthan,et al.  A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation , 2007 .

[39]  I. Bloch.  Ultracold quantum gases in optical lattices , 2005 .

[40]  Yuri S. Kivshar,et al.  Optical Solitons: From Fibers to Photonic Crystals , 2003 .

[41]  R. Morandotti,et al.  Self-focusing and defocusing in waveguide arrays. , 2001, Physical review letters.

[42]  R. N. Thurston,et al.  Collisions of dark solitons in optical fibers , 1991, Annual Meeting Optical Society of America.