Highligh in Physics 2005

1

• Congresso del Dipartimento di Fisica
• Highlights in Physics 2005
• 1114 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
  dellInsubria

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 ?, 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, 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 inter-atomic
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 O. 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.