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Le procédé PACES

Description technique

Principe thermodynamique

Principe électrostatique

Contradiction avec le principe de Carnot ?

Les applications

Expérience 1

Expérience 2

Expérience 3

Illustration du principe thermodynamique par l'expérience de Joule

Illustration du principe électrostatique par l'expérience d'un groupe hollandais

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Illustration du principe électrostatique
par l'expérience d'un groupe hollandais


Electrostatic method

The technique used by the Dutch group both to cool and to trap molecules relies on the Stark shift of the energy levels induced by the interaction of the molecule's electric dipole moment with an electric field. Meijer told us that in the 1950s, John King of MIT had tried a similar electrostatic method to slow ammonia to make an ammonium maser, but he never got it to work. In the 1960s, Lennard Wharton of the University of Chicago tried the reverse technique to accelerate molecules, also without success. More recently, researchers from the Lawrence Berkeley National Laboratory and the University of California, Berkeley, have applied a similar technique to slow neutral atoms. 3 Bretislav Friedrich of Harvard points out that electric fields, unlike their magnetic counterparts, can be switched quickly on the time scale of molecular translation. The corresponding dynamics of electrical trapping exhibit different and, at this point, novel phenomena. The principle of the deceleration in time-varying electric fields is shown schematically in figure 1 .

Electric fields slow molecules

(a) A dipolar molecule (green) experiences a Stark shift as it enters the electric field (red lines) between electrodes.

(b) As the molecules near the center, those with dipoles antiparallel to the field are decelerated, as shown by the shorter velocity vector (blue).

(c) Electrodes are turned off when the dipole reaches the center, so that the molecule does not gain velocity as it leaves the field. Connections to a high voltage source are labeled by ±HV. (Adapted from ref. 4.)

A pulse of the molecules to be slowed travels toward a pair of electrodes. Those molecules having their electric dipoles, on average, oriented antiparallel to the electric field are attracted toward regions where the electric field intensity is low. An electric field is switched on just as the molecules approach the electrodes, putting a brake on the low-field-seeking molecules. These molecules must climb a potential hill as they move into the high-field region at the center of the electrodes, consequently losing kinetic energy.

Of course, if the field remained on, the molecules would lose potential energy (gaining back kinetic energy) as they moved out of the field. But the experimenters turn off the field when the pulse of molecules is near the center, preserving the slow speeds. The molecular pulse then heads toward a second pair of electrodes, where the cycle is repeated for a succession of stages (the Dutch experiment had 63 stages). The timing of the electric fields is critical, and only molecules in a chosen energy level will be in phase with the switching on and off of the field at each stage. Figure 2

Electric fields trap molecules

(a) As dipolar molecules (blue cloud) approach the trap, they face a steep gradient in the electric field (red lines), which slows those with dipoles opposite to the electric field, as sketched in the upper figure. Graph at bottom shows the potential energy as a function of position.

(b) Once molecules are in the cell, the field configuration (top) creates a potential well (bottom), trapping them inside. Energy is given in units of wavenumber. (Adapted from ref. 1.)

Because the electrostatic stages must be turned on and off sequentially, the electrostatic trapping method works only with pulses of molecules rather than with a steady stream. Meijer and company formed their pulse by expanding a gas containing 1% ammonia molecules and 99% xenon atoms through a cooled solenoid valve. Collisions with the heavy rare gas atoms removed much of the energy of the ammonia molecules, so that the molecular beam streaming through the valve had a mean translational speed of 280 m/s, with a fairly narrow velocity spread (about 15%).

Last year, the Dutch team used the Stark decelerator to slow molecules of metastable carbon monoxide, but did not trap them. 4 In June, the same group presented a mathematical description of the process, showing that the phase-space density can be kept constant in the deceleration process. 5

For the recent work on trapping, Meijer and his colleagues turned to deuterated ammonia molecules (ND 3)--the first molecule with more than two atoms to be trapped. (The deuterated version of ammonia was preferred because the normal version has a nonlinear Stark effect at the most convenient values of electric fields.) The particular state selected to be slowed was the upper inversion level in the vibrational ground state. About one-eighth of the ammonia molecules in each pulse were in this state.

To trap the slowed molecules, the Dutch researchers directed the pulse of molecules into an electrostatic trap. As the molecules approached the trap, the experimenters applied an inhomogeneous field, which got stronger the farther the molecules traveled into the trap, as seen in figure 2 .

It was like making the molecules travel uphill: Eventually most were stopped or even turned around. At that point, the electric field was changed to a symmetric configuration with a minimum at the center. By ionizing and detecting a small volume of the trapped molecules, the Dutch experimenters have determined the density to be 10 6/cm 3, and they estimate their volume to be about 0.25 cm 3. So far the team does not have a direct measurement of the temperature of the trap, but team members suspect it is appreciably less than the depth of the trap's potential well, or 350 mK, corresponding to a few tens of meters per second. (The maximum speed of molecules contained in the trap is 17 m/s.) Meijer adds that the temperature might be as low as 2 mK, corresponding to the narrow velocity spread of molecules loaded into the trap from the beam. The 1/ e decay time of the trapped species was 0.24 s.

Having demonstrated the promise of their new technique, the Dutch experimenters hope to improve it in several ways. Meijer thinks they can achieve trap densities of 10 9/cm 3by such measures as increasing the intensity of the beam, raising the electric field strength and adding more stages to handle higher initial velocities, and moving the trap closer to the end of the decelerator for more efficient loading. He thinks they can extend the trap lifetime by reducing the vacuum pressure. Furthermore, he plans to try evaporative cooling to further reduce temperatures. He and his coworkers have yet to devise ways to load the trap with successive pulses. The team has also been working on a storage ring for neutral molecules, based on their decelerator ideas. As Meijer remarked, "Every trick people played with charged particles, we can now do with dipole molecules ."


1. H. L. Bethlem, G. Berden, F. M. H. Crompvoets, R. T. Jongma, A. J. A. van Roij, G. Meijer, Nature 406 , 491 (2000).
2. For a review, see J. T. Bahns, P. L. Gould, W. C. Stwalley, Adv. At., Mol., and Opt. Phys. 42 , 171 (2000).
3. J. A. Maddi, T. P. Dinneen, H. Gould, Phys. Rev. A 60 , 3882 (1999).
4. H. L. Bethlem, G. Berden, G. Meijer, Phys. Rev. Lett. 83 , 1558 (1999).
5. H. L. Bethlem, G. Berden, A. J. A. van Roij, F. M. H. Crompvoets, G. Meijer, Phys. Rev. Lett. 84 , 5744 (2000).


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