Congresso del Dipartimento di Fisica Highlights in Physics –14 October 2005, Dipartimento di Fisica, Università di Milano Solitons in attractive BECs L. Salasnich *, A. Parola †, and L. Reatto * * CNR-INFM, UdR Milano Università and Dipartimento di Fisica, Università di Milano † Dipartimento di Fisica e Matematica, Università dell’Insubria John Scott Russell and the solitary wave Over one hundred and fifty years ago, while conducting experiments to determine the most efficient design for canal boats, a young Scottish engineer named John Scott Russell ( ) made a remarkable scientific discovery. ``I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped - not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed”. A soliton is a shape invariant solitary wave. It propagates without deformations due to the interplay between the dispersive term and the nonlinear term of the equations of motion It was not until the mid 1960's when applied scientists began to use modern digital computers to study nonlinear wave propagation that the soundness of Russell's early ideas began to be appreciated. It is now clear that solitons can be found in many fields of research: hydrodynamics, light pulses in optical fibers, plasma physics, elementary particles of matter, and many others. Soliton Train. On the right there is a 3D rendering of an image of a matter wave soliton train. Each peak in the train is a Bose-Einstein condensate, a collection of atoms cooled to nearly absolute zero temperature. [K.E. Strecker, et al., Nature 471, 150 (2002)]. Solitons in attractive Bose-Einstein condensates (BECs) A Bose-Einstein condensate (BEC) is a macroscopic quantum matter wave. A BEC is made of large number of bosons, which are all in the same quantum state. In 2002, for the first time, single and multiple bright solitons have been produced with Bose-Einstein condensates made of 7 Li atoms We have investigated the formation of this soliton train by analyzing the fluctuations of the phase of the complex BEC macroscopic wave function Ψ, described by the time-dependent Gross-Pitaevskii equation: We have reproduced the experimental data and simulated the dynamics of the soliton train in a external harmonic potential U, as shown in the figure below [L. Salasnich, A. Parola, L. Reatto, Phys. Rev. Lett. 91, (2003)]. In the Gross-Pitaevskii equation the kinetic term is dispersive but its effect can be balanced by a self focusing attractive nonlinear term. This is the case of 7 Li atoms where the inter- atomic scattering length is negative. Attractive BEC in a ring of radius R, rotating with frequency Ω. On the right there is the energetic-stability diagram in the plane (R, g). The uniform solution is the ground state only in the green region. The localized solitonic solution is the ground-state in the yellow region. Above the blue dashed line no stable solution exists [A. Parola, L. Salasnich, R. Rota and L. Reatto, preprint 2005]. The atom wave solitons shown in the figure may be useful as the atom laser input to an atom interferometer. We are now investigating static and dynamical properties of single and multiple BEC brigh solitons in a quasi-1D ring. Quasi 1D-ring for cold atoms have been recently produced by using magneto-optical techniques.