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On
the
Track
of
Modern
Physics
http://www.physik.uni-mainz.de/quantum/bec/
The research team at the MPQ and University of Munich was the second group outside the USA to report BEC.
The evidence for condensation emerged from time of flight measurements. A sharp peak in the velocity
distribution was observed below a critical temperature.
(© Immanuel Bloch, Quantum, Mainz)
So called Gross-Pitaevskii equation is the basis for the practical description
of Bose-Einstein condensate in diluted gases. It resembles much the
“ordinary" Schrödinger equation, apart from an interaction term.
Atoms are individuals. Sometimes, they loose their
individuality and move together. This happens at low
temperatures (nK), when their de Broglie waves
overlap. The whole atomic cloud becomes a single
quantum object.
And this term makes the
difference: only including the
interaction between separated
particles (attracting, repulsing)
one gets a real, experimental
situation.
Each of the atoms in the condensate (in blue) has the same quantum
mechanical wave function, and so they all move as one. Atoms outside the
condensate move faster and in all directions.
(Science 22/12/2005, Illustration: Steve Keller, reproduced with permission)
Three steps of Bose – Einstein condensation
magnetic field
- Lev, the wavepacket describing an electron
diverges in time. Does it result from a special,
Gaussian form of the packet?
- No! Any packet diverges in time – this is a
superposition of waves with different lengths.
Only a plane wave does not diverge in time.
- Lev, tell me what idea
was behind Your famous
equation?
- So, quantum mechanics does not
describe electron as a stable object?
-Wrong! Electron is stable and
point-like! Schrödinger’s equation
does NOT describe the electron
itself but the probability of finding
the electron in a given point!
current
1. Atoms are trapped in
special configurations
of strong magnetic
fields
Trapped atoms are like
top-spins in the center
of a quite shallow plate.
trapped atoms
2. The atomic cloud is
cooled (atoms slow down)
by absorbing and emitting
photon quanta from counter
- propagating laser beams.
laser beam
- In 1956 H. Hall and W. Vined in UK
discovered a very interesting
phenomenon - quantum vortexes in superfluid
Helium. They were predicted by L. Onsager
and R. Feynman, but we had no good theory.
I thought on the subject for several years and
finally, in 1961, being on vacations,
I understood that the theory can be developed
for the Bose-condensed gases, which were
in fact created in 1975 only. I remember that
Landau agreed with my theory not immediately,
but after several discussions.
Cooling ,by collisions: a ruby
“atom” in "melassa" of photons
(here polystyrene balls).
3. The hottest atoms are
removed, by flipping
them with radio-frequency
to a non-trapped (another
Zeeman sublevel) state.
Photos are from professor Pitaevskii’s 70th birthday dinner. Thanks! Asking questions: GK
Cooling with evaporation,
even using a hot air stream,
is very effective
http://www.physik.uni-mainz.de/quantum/bec/introduction/evaporativecooling.html
This picture is a wonderful example of the Unity of
Physics. The free falling condensate covers
distances rising in time according to Galileo’s law
s=gt2 (and showing a parabolic trajectory here).
A magnetic trap, below a cubic glass cell for cooling atoms
(Dr Leonardo Ricci, Trento University
This picture is also a tribute to Werner Heisenberg.
Initially, the atomic cloud is more squeezed in the
vertical direction than in the horizontal one. But, the
better determination of the position in space requires
A worse determination of velocity. In fact, the velocity
distribution is wider in the vertical direction, so the
cloud diffuses more.
Studies of this new, exotic, supercool
form of matter allow to understand
numerous other phenomena, from
high temperature super-conductors,
to neutron stars or the quark-gluon
plasma of the early Universe.
The experimental set-up for Bose-Einstein condensation
The tower in front is the magneto-optical trap and the magnetic
trap, into which atoms pre-cooled in MOT are transferred.
(Prof. Ennio Arimondo, University of Pisa)
Possible applications range from
atomic lasers to precise measurements of the Casimir-Polder force.
Cortesy Prof. Massimo Inguscio, LENS, Firenze
Antezza, Mauro; Pitaevskii, Lev P; Stringari, Sandro
We calculate the effect of the interaction between
an optically active material and a Bose-Einstein
condensate on the collective oscillations of the
condensate. We provide explicit expressions for the
frequency shift of the center of mass oscillation
in terms of the potential generated by the
substrate and of the density profile of the gas.
The form of the potential is discussed in details
and various regimes (van der Waals-London, CasimirPolder and thermal regimes) are identified as a
function of the distance of atoms from the surface.
Submitted to PRA
Concise and exemplary description of BEC
http://physicsweb.org/articles/world/10/3/3/1