Rubidium IIRubidium II
1) The point on our experiment1) The point on our experiment
2) Constriction of a magnetic guide2) Constriction of a magnetic guide
and related topicsand related topics
Thierry Lahaye, PhD StudentJohannes Vogels, Post Doc
Philippe Cren, PhD StudentChristian Roos, Post Doc
David Guéry-Odelin and Jean Dalibard
Innsbruck
1) The point on our experiment1) The point on our experiment
Loading from a vapor pressure
In our first experimental setup, the MOT is loaded from the vapor cell
However, doing so one increases the loss of atoms due to background pressure in the output beam
atoms/s for P=2.10-8 mbar
To increase the flux one can increase the pressure
(Best compromise)
Flux:
INJECTOR MAGNETIC GUIDE
Loading from a pre-cooled beam
2D MOT INJECTOR150 mW per beamb’=15 G/cm=-3
20 40 60 800
0.2
0.4
0.6
0.8
1
Flux(v<v0)/Flux total
v0 (m/s)
Low velocityatoms are filtered by thedifferential vacuum tube
atoms/s
P<10-9 mbar
Capturevelocity of the injector MOT
P=10-7 mbar
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)
We have seen atoms with velocities in the range of 50 to 80 cm/sinstead of 2 m/s.
Conclusion: as the intensities of the beams are to be well superimposedeven in their wings, it is very important to spatial filtered the beams.
Bv =
2k c o s (
’INJECTOR4 beamsconfiguration
Is it a reliable source ?
20 40 60 80
0.000
-0.005
0.005
0.010
v0 (m/s)
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
Pushing beam
INJECTORP<10-9 mbar
P=10-7 mbar
2D MOT
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 ?
New setup
MOPA & Fibers instead of slave + pinhole
MOPA1
MOPA2
MASTER
SLAVE1
SLAVE2
fiber 1
fiber 2
fiber 3
fiber 4
2 mW
2 mW 30 mW
30 mW
100 mW
100 mW
100 mW
100 mW
Intrinsic instability of the 4 beams configuration (explanation for 2 beams)
Probably a limitation for low velocity coupling
x
y
1
2
« classical » restoringforce for < 0
Expelling term dueto local imbalancefor an off-axis atom
Divergence of the beam at the exit
What about a 6 beams configuration ?
B
/4 + Mirror
Under investigation ...
Perhaps a 8 beams configuration ... later
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
2) Constriction of a magnetic 2) Constriction of a magnetic guide and related topicsguide and related topics
A single particle in a compressed guide (1)
z(z) radial angularfrequency depends on 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:
A single particle in a compressed guide (2)
and
only kinetic energy
Particles are reflected ifFor a given longitudinal velocity,this ratio depends on the transverseamplitude.
N.B. reminiscent of the physics of charged particles trapped in the earth magnetic field (Von Allen).
Hydrodynamic flux in a compressed guide (1)
Boltzmann equation + ansatz (local equilibrium) permits to deriveeffective 1D equations mainly valid in the hydrodynamic regime.
conservation of the flux
In the stationary regime:
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
Hydrodynamic flux in a compressed guide (2)
If then T and u The beam is less and lessmonokinetic for a compression
Strictly speaking valid only for an initially monokinetic beam otherwise there is a correctionthat can be calculated.
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 2D+1D trap, ...
beam
3D isotropic and harmonic trap
Another way to increase : to tilt the guide
Still valid
Following the same approach, we derive this set of equations
This set of equation conserves the phase space density
Tilt the guide: results
Propagation of a quantum beam through a constriction
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
we define
Propagation of a quantum beam through a constriction: adiabatic approximation
We restrict to the transverse ground state
Adiabaticity means that the propagation through the constrictiondoes not affect the transverse degree of freedom:
Compression leads to anincrease of the zero-pointenergy which acts as a longitudinal potential hill.
or equivalently
What happens for interacting particles ? (1)
Effective 1D equation ( )
Starting point is the action
with
Search for a solution of the formn is a local density of particlesper unit length
We obtain a set of 1D hydrodynamic equations
This set of equations has been used for the study of soundpropagation, solitons, ...
What happens for interacting particles ? (2)
Chemical potentialThomas Fermi regime
weak interaction limit
In the stationary regimeand TF regime
with
atoms/sv0=5 cm/sna=10500Hz à 10kHzen 5 cm
Physical picture : the radial size increases so the effect of compression is all the more important.
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 anumerical simulation that takes into account the exchange of particles and energy between the thermal and thecondensed beam
Question: for a given compression, what is the fraction ofthermal beam one can tolerate ?
A situation where those kinds of effects may have to be taken into account
For trapped-atom interferometer in a magnetic microtrap
