Résumé:
This do ctoral work intends to take account of dynamical correlations in binary
mixtures of Bose-Ein stein condensates (BEC), comp osed of two distinct sp ecies.
In a p rel imi nary analysis, we consider a purely one-dimensional mixture, where the
anomalous (or off-diagonal) correlations are finite and do not requ ire any renormalization.
Their b ehavior, examined within a variational framework usin g a gau ssian density
op erator, corrob orate a preceding result assessing that the anomalous and non cond ensate
densities are of the same order and, therefore, any approach con sidering only non
condensate densities can only b e viabl e at very low temp erature (or zero temp erature) or
near the transition. This was demonstrated numerically by solving a set of self-consistent
equations. Furthermore, in a binary mixture, a set of unprecedented correlations app ears .
Indeed, b eside the intras p ecies correlations, we shed light on intersp ecies correlations,
which depict the entanglement b etween the sp ecies
In the vaste literature, we noticed that these effects are generally omitted owing
to the fact that, in many exp eriments, the entanglement b etween different sp ecies is
considered as marginal.
We show however in this work, that it n eed s not b e the case in a general context.
These effects are however quite tiny and cannot b e observed in situations where the
mean field is dominant. Hence, we considered situations where the mean -field is almost
zero. This fortunately happ ens for a binary system when the intersp ecies interactions are
attractive an d almost neutralize the interasp ecies ones. This lead s to self-b oun d states
named droplets which were indeed dis covered exp eri mentally.
We therefore fo cused on droplets in quasi-one dimensional geometries and exhibited
the dominant role of intersp ecies fluctuations. We showed that the droplet states are more
stable and therefore more easily ob servable when one includes intersp ecies correlations.
We also show that these effects add up to the LHY contributions extending th e b eyond
mean-field theory in the Bogoliub ov framework. This work was p erformed in a consistent
and metho dic way which led to original results published in journal of low temp erature
physics
