Splitting Dynamics and Quantum Hydrodynamics of Bose-Einstein condensates

Since the realisation of the first Bose-Einstein condensate (BEC) a couple of decades ago, there have been intense works on the quantum gas field, aiming mostly at unravelling the quantum properties of matter at large scale and to experimentally mimic the behaviour of physical systems that cannot be directly explored. With the advent of the era of high frequency and big data processing, the hunt for better crypto-machines and more powerful computers has reinforced the interest for BECs. In this respect, the present project is devoted to examining two crucial problems with ultra-cold quantum gases. The first subproject will address the problem of matter-wave interferometry through a detailed study of the nonlinear dynamics of split ultra-cold atomic clouds. We expect to built appropriate theoretical tools, both analytical and numerical, useful for such an interferometry. The second subproject will be concerned with the study of instabilities as quantum hydrodynamic phenomena in spin-orbit coupled Bose-Einstein condensates.