DYNAMICAL CORRELATION IN BINARY MIXTURES OF BOSE–EINSTEIN CONDENSATES (BECs)

This work intends to take account of dynamical correlations in binary mixtures of Bose–Einstein condensates (BECs), composed of two distinct species. In a preliminary analysis, we consider a purely one-dimensional mixture, where the anomalous (or off-diagonal) correlations are finite and do not require any renormalization.

Their behavior, examined within a variational framework using a gaussian density operator, corroborates a previous result indicating that the anomalous and noncondensate densities are of the same order and, therefore, any approach considering only noncondensate densities can only be viable at very low temperature (or zero temperature) 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 appears. Indeed, in addition to intraspecies correlations, we shed light on interspecies correlations, which depict the entanglement between the species.

In the vast literature, we noticed that these effects are generally omitted owing to the fact that, in many experiments, the entanglement between different species is considered to be marginal.

However, in this work, we show that this needs not be the case in a general context. These effects are, however, quite tiny and cannot be observed in situations where the mean field is dominant. Hence, we considered situations where the mean field is almost zero. This fortunately happens for a binary system when the interspecies interactions are attractive and almost neutralize the intraspecies ones. This leads to self-bound states named droplets, which were indeed discovered experimentally.

Based on a semi-classical approach, we determine variationally analytic expressions for both the anomalous and the noncondensate densities for one-, two- and three-dimensional systems. The anomalous averages and the noncondensate densities for a 1D homogeneous bose mixture are computed numerically.