Executive Summary : | The project aims to explore quantum mixtures, specifically quantum and thermal fluctuations in coherently coupled Bose-Einstein condensates of dilute atomic gases. Atoms occupy two different hyperfine states and interact via inter- and intraspecies collisions and an external coherent-drive inducing transfer. The properties of these ultracold bosonic gases are studied within a mean-field framework suitable for zero temperature using analytical and numerical methods. The statics and dynamical properties of the system are described using a set of coupled Gross-Pitaevskii equations, which can be solved numerically. The thermal and beyond mean-field effects on these condensates at equilibrium are examined. The theoretical formalism is built based on the Hartree-Fock-Bogoliubov (HFB) theory with the Popov approximation, which computes quantum and thermal fluctuations. The dynamics are explored using the Stochastic Gross-Pitaevskii equation (SGPE), adapted for multicomponent condensates. The investigation of multicomponent condensates at finite temperatures is a more general open problem, numerically non-trivial, and challenging to obtain reasonable conclusions. A wide range of finite temperature models developed over the years to address single component condensates opens up the possibility, but careful and systematic investigation of the accuracy and limitations of these methods is necessary to describe the finite temperature effects in the multicomponent condensates of dilute atomic gases. |