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            <title xml:lang="en">Spin mixture in Bose-Einstein condensate : Quantum droplet and coherent coupling</title>
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                <term xml:lang="en">Quantum fluctuations</term>
                <term xml:lang="en">Quantum droplet</term>
                <term xml:lang="en">Tunable interactions</term>
                <term xml:lang="en">Coherent coupling</term>
                <term xml:lang="en">Spin mixtures</term>
                <term xml:lang="en">Quantum gases</term>
                <term xml:lang="fr">Fluctuations quantiques</term>
                <term xml:lang="fr">Gouttelette quantique</term>
                <term xml:lang="fr">Interactions contrôlables</term>
                <term xml:lang="fr">Couplage cohérent</term>
                <term xml:lang="fr">Mélanges de spin</term>
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              <p>The high degree of control of ultracold atoms has made these systems ideal candidates to identify and measure the role of quantum fluctuations. For a Bose-Einstein condensate, quantum fluctuations cause quantum depletion and lead to the Lee-Huang-Yang (LHY) correction in the mean field equation of state. Recently, quantum droplets formation using spin mixtures has been theoretically predicted and observed experimentally. This doctoral thesis is part of these studies. We have theoretically studied the existence of quantum droplets in the beyond-mean-field crossover from one dimension to three dimensions. Experimentally, we use a quantum bosonic gas of potassium 39 which offers the possibility to tune interatomic interactions using Feshbach resonances. This manuscript presents two experimental studies where we explored coherently coupled spin mixtures whose intra spin interactions are repulsive and inter spin attractive. The first analysis shows the possibility of engineering an attractive three-body interaction with important consequences on the system dynamics. It originates from the spinor degree of freedom that is affected by a two-body mean-field shift of the driven transition frequency. We finally study in an experimental configuration where the mean field interactions are canceled, the beyond-mean-field equation of state of a coherently coupled two-component condensates. We show that the presence of the coupling changes the density dependence of the quantum fluctuations term with respect to the LHY term in the uncoupled case.</p>
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              <p>Le degré élevé de contrôle des atomes ultra-froids a fait de ces systèmes des candidats idéaux pour identifier et mesurer le rôle des fluctuations quantiques. Pour un condensat de Bose-Einstein, les fluctuations quantiques causent la déplétion quantique et conduisent à la correction de Lee-Huang-Yang (LHY) dans l'équation d'état de champ moyen. Récemment, la formation de gouttelette quantique à l'aide de mélange de condensats a été théoriquement prédit et observé expérimentalement. Cette thèse de doctorat s'inscrit dans la continuité de ces études. Nous avons théoriquement étudié l'existence de gouttelette quantique dans le croisement unidimensionnel à tridimensionnel pour le terme LHY. Expérimentalement, nous utilisons un gaz quantique bosonique de potassium 39 qui offre la possibilité de modifier les interactions interatomiques à l'aide de résonances de Feshbach. Ce manuscrit présente deux études expérimentales où nous avons exploré les mélanges de spin couplés de manière cohérente dont les interactions intra spin sont répulsives et inter spin attractives. La première analyse montre la possibilité d'engendrer une interaction attractive à trois corps importante ayant des conséquences importantes sur la dynamique du système. Cette interaction provient de l'affectation du degré de liberté du spineur par l'interaction à deux corps de champ-moyen. Nous étudions finalement dans une configuration expérimentale où les interactions de champ moyen sont annulées, l'équation d'état au-delà du champ moyen d'un condensat à deux composantes couplées de manière cohérente. Nous montrons que la présence du couplage change la dépendance en densité du terme des fluctuations quantiques par rapport au terme de LHY dans le cas non couplé.</p>
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