Published November 15, 1988 | Version v1
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Study of the 2. order Doppler effect on the 40,5 GHz microwave hyperfine transition of the 2s1/2 fundamental level of 199Hg+ ions trapped in a RF trap

Creators

Description

We have studied the energy properties of 199Hg+ stored in an R.F. cylindrical trap in order to evaluate the 2. order Doppler effect on the resonance line at 40.5 GHz of the hyperfine transition of the fundamental level 2s1/2. The purpose of this study, both experimental and theoretical, is to improve the precision of 199 mercury ions atomic frequency standard. Besides, we wanted to give a general character to the issued results so as they could be applied to all kinds of ions, with an hyperfine structure, stored in an R.F. trap, quadrupole or cylindrical. We have established an analytical formalism, using physical parameters that can be measured experimentally, in order to estimate the mean kinetic energy of the stored ions, the 2. order Doppler effect being directly proportional to this quantity. The mean kinetic energy calculated by this way takes into account the contribution of slow macro-motion, supposed thermalized and that of rapid micromotion due to the confining field. We have assumed a thermalized charge density distribution in a confining pseudo potential taking also into account space charge effects. The above formalism also permits to evaluate the ion cloud central density as well as space charge potential. The results have been compared to those of numerical simulation methods for different trapping conditions showing a very good agreement. We have then carried out a numerical study of the confinement properties of an R.F. cylindrical trap pseudo potential so as to adjust this formalism to our experimental conditions. We have thus demonstrated that the effective potential of such a trap is quite different to that of a quadrupole one. We have also defined the condition of an approximate sphericity and harmonicity of the pseudo potential as well as the value of the corresponding theoretical secular frequency. We have deduced that higher density (about 25 %) can be achieved in an R.F. cylindrical trap than in a quadrupolar one for the same trapping parameters. The model has been applied to different experimental conditions measuring each time the necessary physical parameters which are the total ion number and the macro-motion secular frequency shifted by space charge. We have concluded that the temperature of an ion cloud of 2.106 199Hg+ ions trapped in a spherical pseudo potential of 40 kHz is 3300 ± 100 K in a residual vacuum of 10-8 Torr. The 2. order Doppler effect shift in this case is: Δf/f = - (5.44 ± 0.16) 10-12. We have also studied the collisional cooling of an ion cloud for the same trapping conditions using helium buffer gas. At helium pressure of 3.10-5 Torr we have measured a lowest temperature of 700 ± 60 K. The corresponding 2. order Doppler shift is: Δf/f = - (1.76 ± 0.11) 10-12. Finally, we have put in evidence the weak distortion of the pseudo potential well of an R.F. cylindrical trap due to the irregularities. (author)

Abstract (French)

On a etudie les proprietes energetiques des ions 199Hg+ pieges dans une trappe radiofrequence cylindrique afin d'evaluer le decalage du a l'effet Doppler du second ordre sur la raie de resonance a 40,5 GHz de la transition hyperfine du niveau fondamental 2s1/2. Cette etude, theorique et experimentale, a ete menee pour ameliorer la precision de l'etalon de frequence atomique a ion mercure 199. On a voulu, par ailleurs, donner un caractere general aux resultats deduits afin qu'ils puissent etre applicables a n'importe quel type d'ions possedant une structure hyperfine, confine dans une trappe radiofrequence quadrupolaire ou cylindrique. On a cree pour cela un formalisme analytique mettant en jeu des parametres physiques pouvant etre mesures experimentalement afin d'evaluer l'energie cinetique moyenne des ions confines, ce qui permet de connaitre l'effet Doppler du second ordre proportionnel a cette quantite. L'energie cinetique moyenne calculee tient compte aussi bien de la contribution du macromouvement lent, qu'on a suppose thermalise, que de celle du micromouvement rapide du au champ de confinement. On a considere un modele thermalise de la distribution des charges a l'interieur d'un pseudo potentiel de confinement, tout en tenant compte du potentiel d'interaction electrique entre les ions pieges (charge d'espace). Ce formalisme permet, en outre, d'estimer la densite centrale du nuage ionique forme, ainsi que le potentiel de la charge d'espace. Les resultats ont ete compares a des calculs numeriques de simulation, pour differentes conditions de confinement, montrant un tres bon accord. Une etude numerique a permis d'etudier les proprietes de confinement du pseudo potentiel cree a l'interieur d'une trappe radiofrequence cylindrique, afin d'adapter ce formalisme a nos conditions experimentales. On a demontre que le potentiel efficace de cette trappe est tres different de celui d'une trappe hyperboloide (quadrupolaire) radiofrequence. Les conditions de sphericite et d'harmonicite du pseudo potentiel ont ete definies, ainsi que la valeur de la frequence theorique seculaire resultante. On a aussi deduit que des densites plus elevees (environ 25 %) peuvent etre atteintes dans une trappe cylindrique pour les memes tensions de confinement. Le modele a ete applique a differentes conditions experimentales en mesurant, a chaque fois, les parametres physiques intervenant dans le formalisme, qui sont le nombre d'ions total et la frequence du macro mouvement seculaire deplacee par la charge d'espace. On en a deduit que la temperature d'un nuage de 2 millions d'ions 199Hg+ pieges dans un pseudo potentiel de frequence seculaire theorique 40 khz, est typiquement de 3300 ± 100 K dans un vide residuel de 10-8 Torr. Le deplacement du a l'effet Doppler du second ordre dans ce cas est: Δf/f = - (5.44 ± 0.16) 10-12. En utilisant l'helium comme gaz tampon, on a etudie le refroidissement collisionnel de ce nuage d'ions dans les memes conditions de confinement. La plus basse temperature mesuree est de 700 K pour une pression d'helium de 3.10-5 Torr. Le deplacement du a l'effet Doppler du second ordre est, dans ce cas: Δf/f = - (1.76 ± 0.11) 10-12. Finalement, on a mis en evidence la faible distorsion du pseudo potentiel due aux asymetries de la trappe cylindrique. Les irregularites sont partiellement compensees par la forme particuliere du potentiel efficace. (auteur)

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Additional details

Additional titles

Original title (French)
Etude de l'effet Doppler du 2e ordre sur la transition hyperfine micro-onde a 40,5 GHz du niveau fondamental 2s1/2 des ions 199Hg+ pieges dans une trappe radiofrequence

Publishing Information

Imprint Pagination
229 p.
Report number
FRNC-TH--13924

INIS

Country of Publication
France
Country of Input or Organization
France
INIS RN
54027972
Subject category
S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; S74: ATOMIC AND MOLECULAR PHYSICS;
Resource subtype / Literary indicator
Thesis
Descriptors DEI
ATOMIC CLOCKS; CHARGE DENSITY; CONFINEMENT; CYLINDRICAL CONFIGURATION; DOPPLER EFFECT; ENERGY-LEVEL TRANSITIONS; KINETIC ENERGY; OPTICAL PUMPING; OSCILLATORS; QUADRUPOLES; SPACE CHARGE; SPECTRA; THERMALIZATION; TRAPPING
Descriptors DEC
CONFIGURATION; ELECTRONIC EQUIPMENT; ENERGY; EQUIPMENT; MULTIPOLES; PUMPING; SLOWING-DOWN

Optional Information

Notes
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