Profondeur de pi`ege

ae

′f

F’=2 F’=3 F’=4 F’=5

F = 3 1 3/4 5/12 0

F = 4 0 1/4 7/12 1

Tab. B.2: Rapports de branchement en ´emission spontan´ee de la raie D2

entre l’´etat excit´ee

′

et un ´etat fondamental f.

B.2 Profondeur de pi`ege

Le paragraphe 1.3.2 donne l’expression du potentiel dipolaire dans le cas d’un atomes `a deux

niveaux :

U0 = ¹

4^kBTD

s0

δ/Γ ^(B.2)

L’atome de C´esium ´etant un atome `a plusieurs niveaux, chaque transition va contribuer au

potentiel dipolaire. Pour ´eviter les cycles d’absorption/´emission spontan´ee, la fr´equence laser est

choisie loin d’une r´esonance, typiquement de quelques nanom`etres (soit quelques centaines de

GHz). `A cette ´echelle, les ´ecarts d’´energie entre les niveaux hyperfins (de l’ordre de la centaine

de MHz) sont n´egligeable, et l’on peut consid´erer que le d´esaccord est le mˆeme pour toutes les

transitions de la raie D2.

Dans le cas d’une polarisation π, les niveaux d’´energie hyperfins restent d´eg´en´er´es, et le

potentiel dipolaire total est obtenu par la somme des contributions de la raie D2 :

U0 = ¹

4^kBTD

X

e

s0wf e

′

δ/Γ ^(B.3a)

U0 = ¹

4^kBTD

2

3

s0

δ/Γ ^(B.3b)

U0 = ¹

4^kBTD

s0

δef f/Γ ^(B.3c)

avec

δef f = ³

2^{δ (B.4)}

L’expression du potentiel dipolaire pour l’atome `a deux niveaux reste donc valable, en

rempla¸cant le d´esaccord δ par un d´esaccord effectif δef f.

Notons que ce r´esultat n’est pas valable pour les d´esaccords trop importants, pour lesquels

la contribution de la raie D1 n’est plus n´egligeable. Le d´esaccord effectif prend alors pour

expression :

1

δ

_{ef f}

⁼

1

3δ

_D1

+ ²

3δ

_D2

(B.5)

L’´ecart en longueur d’onde entre les raies D1 et D2 du C´esium est de 42 nm. Les d´esaccords

par rapport `a la raieD2 les plus importants utilis´es dans ce travail ´etant typiquement de 5 nm,

la contribution de la raie D1 est bien n´egligeable.

De plus, dans le cas o`u la polarisation est σ

±

, un terme s’ajoute pour tenir compte de

l’ellipticit´e de la polarisation. Le lecteur pourra consulter [75] pour de plus amples informations.

Dans le cas du travail pr´esent´e ici, la polarisation du laser est rectiligne, et la direction du

champ magn´etique r´esiduel est inconnue. Nous choisissons donc de prendre l’expression donn´ee

par l’´equation (B.3c), faute de mieux.

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