Four main results have been achieved during the execution of the action.
First, we have put forward a framework that allows to coherently understand how particles behave in the presence of position-space, momentum-space, and phase-space Berry curvatures. In deriving this framework, we have clearly separated the adiabatic transformation, and the semiclassical approximation. This has allowed for an elegant understanding of the spin-orbit coupling problem in general.
Second, we have described a non-Abelian counterpart of the universal intrinsic spin Hall effect. Loosely speaking, this means that particles move as if the magnetic field was pointing in all directions at once. We have quantified the strength of such an omnidirectional spin Hall effect by calculating the corresponding conductivity for fermions and non-condensed bosons, showing the viability of the observation of this effect.
Third, we have reported a system where two qualitatively different kinds of superfluidity are present. In particular, spinor Bose gases subject to a quadratic Zeeman effect exhibit coexisting superfluidity and spin superfluidity. As an illustration, we have proposed an experimentally accessible stationary state, where the two types of supercurrents counterflow and cancel each other, thus resulting in no mass transport. We have verified the robustness of these findings, and have found that the time scale for coherent (superfluid) dynamics is separated from that of the slower incoherent dynamics by one order of magnitude.
Finally, we have discovered a collective mode corresponding to the spin Hall effect. In particular, in response to a displacement of the center of mass of a two-dimensional harmonically trapped gas of identical atoms with Rashba spin-orbit coupling, spin-dipole moment oscillations occur. We have determined the properties of these oscillations exactly and have found that their amplitude strongly depends on the spin-orbit-coupling strength and the quantum statistics of the particles.
All these results have been disseminated through peer-reviewed publications and presented at international conferences and seminars. These publications are also freely accessible on the arXiv repository.
Popularizing these results and science in general has resulted in multiple articles in the local press, several national radio appearances, as well as an international workshop Ultracold@Vilnius with a popular science talk attended by several hundred students.
