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Rubidium II 1) The point on our experiment 2) Constriction of a magnetic guide and related topics

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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Rubidium II 1) The point on our experiment 2) Constriction of a magnetic guide and related topics

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  1. 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

  2. 1) The point on our experiment

  3. 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 F=3.109 atoms/s for P=2.10-8 mbar (Best compromise)

  4. INJECTOR 2D MOT Loading from a pre-cooled beam 150 mW per beam b’=15 G/cm d=-3G P<10-9 mbar P=10-7 mbar >1010 atoms/s Capture velocity of the injector MOT Low velocity atoms are filtered by the differential vacuum tube

  5. 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.

  6. 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

  7. Pushing beam 2D MOT INJECTOR P<10-9 mbar P=10-7 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 ?

  8. New setup MOPA & Fibers instead of slave + pinhole w+dw SLAVE1 MOPA1 100 mW fiber 1 2 mW 30 mW 100 mW fiber 2 MASTER 100 mW SLAVE2 MOPA2 2 mW fiber 3 30 mW w-dw 100 mW fiber 4

  9. y 2 x 1 « classical » restoring force for d < 0 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

  10. What about a 6 beams configuration ? l/4 + Mirror Under investigation ... Perhaps a 8 beams configuration ... later

  11. 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

  12. 2) Constriction of a magnetic guide and related topics

  13. 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:

  14. 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).

  15. 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

  16. 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 2D+1D trap, ...

  17. 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

  18. Tilt the guide: results

  19. 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

  20. 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.

  21. 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, ...

  22. What happens for interacting particles ? (2) weak interaction limit Chemical potential Thomas Fermi regime In the stationary regime and TF regime with f=108 atoms/s v0=5 cm/s na=10 500Hz à 10kHz en 5 cm Physical picture : the radial size increases so the effect of compression is all the more important.

  23. 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 ?

  24. A situation where those kinds of effects may have to be taken into account For trapped-atom interferometer in a magnetic microtrap

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