Superkomputer KDM: Zastosowania

The project aims to perform an accurate theoretical study of the time coherence of ultra-cold atomic gases with dipolar interactions. The motivation for the research proposed is recent experimental discoveries of novel quantum phases in the system and the weakness of its present-day description.
Understanding of its phase dynamics and resulting coherence time is still poorly developed.

In previous works of PI, it was shown that phase dynamics of Bose-Einstein condensates with contact interactions depend on energy fluctuations present in the initial state: It is ballistic when fluctuations of energy are nonzero and diffusive in the conservative case. The time dependence of phase spreading turns out to be determined by mathematical properties of the dispersion relation of elementary excitations in the system. They are phonons that have linear dispersion relation on the lowest energy scale and quadratic otherwise (convex curve) in the case of contact interactions. On the other hand, it was shown under certain assumptions that the opposite behaviour of the dispersion relation of elementary excitations (concave curve) leads to exotic phase spreading where time dependence lies between diffusive and sub-diffusive behaviour. The dispersion relation of ultra-cold atomic gases might be concave or even contain the roton-like minimum when dipolar interactions dominate. Therefore, we expect a qualitative change in the phase dynamics and appearance of the non-trivial phase spreading in the system. Details of that change are not known apriori, and therefore a careful investigation is needed. While thinking about the phase coherence of ultra-cold atoms with dipolar interactions a series of natural questions arise: How phase spreading is affected by concave dispersion relation in general? How exotic is it? Can it have a diffusive character? How do thermal excitations, in particular roton excitations, affect phase dynamics? How phase spreading is changed in lower dimensions, e.g. in the 2D case? Finally, what is the relation, if there is any, between the nature of phase spreading and quantum phases of dipolar ultra-cold gases?

The project makes an attempt to answer the above questions and generalize our understanding of the phase dynamics behaviour in terms of mathematical properties of dispersion relation responsible for elementary excitations in the system.