. Dans-cette-optique, il seraitégalementseraitégalement intéressant de faire le lien avec des travaux théoriques qui ont traité de l'amortissement des phonons dans un potentiel aléatoire de faible amplitude

. Superfluidité-et-vitesse-du-son-dans-un-condensat-de-bose, Einstein Nous rappelons ici, d'une part, la valeur de la vitesse du son dans un condensat de Bose- Einstein gazeuxàgazeuxà partir de la description hydrodynamique de celui-ci, et, d'autre part

. La-quantité-c, (r) = µ ? V ext (r) L'´ equation précédente (5.15) est analoguè a l'´ equation de propagation d'une onde sonorè a la vitesse c(r) Ainsi elle définit une vitesse du son locale, c(r), dans le nuage atomique qui dépend de la position r. Les solutions de l'´ equation (5.15) dans le cas d'un système homogène (V ext = 0) sont des ondes sonores se propageantàpropageant`propageantà la vitesse c son = µ/m = gn 0 /m [133]

. Dans-le-cas, u cette condition n'est pas respectée l'´ equation de propagation linéarisée n'est pas valide. La présence d'interactions est ainsi nécessaire dans la description hydrodynamique du propageant sous la forme d

´. Il-a and . Suggéré, que la vitesse de propagation d'une onde sonore sous forme d'un pic de densité dans un condensat avec interactions fortes soit plus rapide que la vitesse déterminée par l'´ equation (5.16) Les barres d'erreur sur nos mesures expérimentales ne permettent pas de mettre enévidenceenévidence unécartàunécartunécart`unécartà l'´ equation (5.16). Cetté equation décrit très bien la propagation d'ondes sonores dans nos condensats allongés

W. Dans-l-'´-etude-précédente-réalisée-dans-le-groupe-de, Ketterle [20], une déviation entre les mesures et l'´ equation (5.16) a ´ eté observée aux faibles densités. CetécartCetécart est attribuéattribuéà la technique utilisée pour travailler avec de faibles densités atomiques qui consistè a ouvrir le pì ege radial. En effet, dans ce cas

. Au-contraire, 100 pour toutes les densités atomiques utilisées Le caractère 1D du pic de densité se propageant sur notre condensat n'´ evolue donc pas avec la densité atomique. Nous n'attendons donc pas de déviation par rapport aux prédictions [184] pour toute la gamme de densité que nous avons testées et c'est bien en accord avec ce que nous obtenons. Les travaux de Kavoulakis et Pethick [185] de propagation d'onde sonore dans un condensat 1D tendentàtendentà montrer que la dispersion dans le cas d'une forte perturbation du profil de densité devraitêtredevraitêtre importantè a cause de la présence des interactions. Le pic de densité devrait ainsi se distordre ou s'´ etaler lors de sa propagation. Cependant, nous n'observons pas un tel phénomène appara??treappara??tre clairement dans notre expérience 15 . Uné etude plus précise de l'´ evolution de la forme du pic de densité au cours de sa propagation est certainement nécessaire

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