Prsentation PowerPoint

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Rubidium II 1) The point on our experiment 2)
Constriction of a magnetic guide and related
topics
Thierry Lahaye, PhD Student Johannes Vogels, Post
Doc Philippe Cren, PhD Student Christian Roos,
Post Doc David Guéry-Odelin and Jean Dalibard
Innsbruck
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1) The point on our experiment
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Loading from a vapor pressure
INJECTOR MAGNETIC GUIDE
Flux
In our first experimental setup, the MOT is
loaded from the vapor cell
To increase the flux one can increase the pressure
However, doing so one increases the loss of atoms
due to background pressure in the output beam
F3.109 atoms/s for P2.10-8 mbar
(Best compromise)
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Loading from a pre-cooled beam
150 mW per beam b15 G/cm d-3G
Plt10-9 mbar
P10-7 mbar
gt1010 atoms/s
Capture velocity of the injector MOT
Low velocity atoms are filtered by
the differential vacuum tube
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Results obtained with this setup (May 2002)
2D MOT as a source of atoms.
Beams of the injector are spatially filtered by
pinholes (10 mW per arm)
INJECTOR 4 beams configuration
a
a
a
We have seen atoms with velocities in the range
of 50 to 80 cm/s instead of 2 m/s.
Conclusion as the intensities of the beams are
to be well superimposed even in their wings, it
is very important to spatial filtered the beams.
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Is it a reliable source ?
The mean velocity has increased from 30 m/s up
to 45 m/s ???
The flux has decreased by 2 orders of magnitude
???!!!
The width has also increased
20 40 60 (m/s)
Flux of atoms per class of velocity
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Pushing beam
INJECTOR
2D MOT
Plt10-9 mbar
P10-7 mbar
We obtain a flux of 2 or 3 109 atoms/s after
optimization It is very sensitive to the
position of the pushing beam, we want to avoid a
beam in the axis (small angle)
Open questions How the distribution in velocity
is affected by the pushing beam ? What is the
part of the distribution that can be captured ?
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New setup
MOPA Fibers instead of slave pinhole
wdw
MOPA1
SLAVE1
100 mW
fiber 1
2 mW
30 mW
100 mW
fiber 2
MASTER
100 mW
MOPA2
SLAVE2
fiber 3
2 mW
30 mW
w-dw
100 mW
fiber 4
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Intrinsic instability of the 4 beams
configuration (explanation for 2 beams)
Expelling term due to local imbalance for an
off-axis atom
Divergence of the beam at the exit
Probably a limitation for low velocity coupling
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What about a 6 beams configuration ?
l/4 Mirror
Under investigation ...
Perhaps a 8 beams configuration ... later
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In the near future
1 _ Try to understand what happens with first
trap (2D MOT) 2 _ Take images of the exit of the
launching trap (INJECTOR) 3_ Investigate
different trap geometries for the injector 4 _
Consider to install a Zeeman slower
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2) Constriction of a magnetic guide and related
topics
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A single particle in a compressed guide (1)
w(z) radial angular frequency depends on z
z
Break the longitudinal invariance coupling
between transverse and longitudinal degree of
freedom.
The coupling is all the more important than the
particle is off-axis.
This problem can be solved exactly under the
adiabatic approximation
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A single particle in a compressed guide (2)
and
only kinetic energy
Particles are reflected if
For a given longitudinal velocity, this ratio
depends on the transverse amplitude.
N.B. reminiscent of the physics of charged
particles trapped in the earth magnetic field
(Von Allen).
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Hydrodynamic flux in a compressed guide (1)
Boltzmann equation ansatz (local equilibrium)
permits to derive effective 1D equations mainly
valid in the hydrodynamic regime.
In the stationary regime
conservation of the flux
equation for the force
coupling between long. and transv. degree of
freedom
conservation of the enthalpy
As a consequence conservation of the phase
space density
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Hydrodynamic flux in a compressed guide (2)
The beam is less and less monokinetic for a
compression
If w then T and u
Strictly speaking valid only for an initially
monokinetic beam otherwise there is a
correction that can be calculated.
beam
3D isotropic and harmonic trap
N.B. we obtain the same power for a gas confined
in a box longitudinally and by an as the guide
transversally.
A very general law valid for a beam, for 3D
isotropic trap (linear or harmonic), for a 2D1D
trap, ...
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Another way to increase to tilt the guide
Following the same approach, we derive this set
of equations
This set of equation conserves the phase space
density
Still valid
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Tilt the guide results
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Propagation of a quantum beam through a
constriction
we define
We solve the stationary solution of the
Schrödinger equation, we expand the solution on
the adiabatic basis
We find the following infinite set of equations
with
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Propagation of a quantum beam through a
constriction adiabatic approximation
We restrict to the transverse ground
state Adiabaticity means that the propagation
through the constriction does not affect the
transverse degree of freedom
or equivalently
Compression leads to an increase of the
zero-point energy which acts as a longitudinal
potential hill.
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What happens for interacting particles ? (1)
Effective 1D equation (
)
Starting point is the action
with
Search for a solution of the form
n is a local density of particles per unit length
We obtain a set of 1D hydrodynamic equations
This set of equations has been used for the study
of sound propagation, solitons, ...
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What happens for interacting particles ? (2)
weak interaction limit
Chemical potential
Thomas Fermi regime
In the stationary regime and TF regime
with
f108 atoms/s v05 cm/s na10 500Hz à 10kHz en 5
cm
Physical picture the radial size increases so
the effect of compression is all the more
important.
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A Bose beam in the degenerate regime through a
constriction
Bose beam thermal beam condensed beam
They are not affected in the same way by the
constriction
They acquire a non zero relative velocity
Their mutual friction tends to destroy the
condensed phase
To investigate quantitatively this problem, one
could use the ZGN equations which means in
practice perform a numerical simulation that
takes into account the exchange of particles and
energy between the thermal and the condensed beam
Question for a given compression, what is the
fraction of thermal beam one can tolerate ?
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A situation where those kinds of effects may have
to be taken into account
For trapped-atom interferometer in a magnetic
microtrap