Transcript Highligh in Physics 2005

Congresso del Dipartimento di Fisica
Highlights in Physics 2005
11–14 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
(1808-1882) 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.
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 7Li atoms
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)].
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:


2
2
i   
   U  g |  | 
t
2m
2
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, 080405 (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 7Li atoms where the interatomic scattering length is negative.
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.
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].