| Abstract [eng] |
The thesis explores manifestations of topological phenomena in systems of driven quantum gases. The first part of the thesis studies Floquet-engineered phases, namely the time-space crystalline structures, elucidating the role of time in systems with synthetic dimensions. The concept of topological particle pumping in the temporal dimension is developed, and a realisation of a topologically nontrivial eight-dimensional quantum system is proposed, with an emphasis on the relation to the quantum Hall effect. Additionally, a perturbative theory of calculation of quasienergy spectra in the case of resonant periodic driving is worked out in the extended Floquet–Hilbert space. The second part of the thesis investigates topological defects in Bose–Einstein condensates subject to a continuous optical perturbation. An optical scheme for creation of unconventional, strongly localised vortices in a two-component condensate is presented, and their properties are studied. The localised vortex present in one of the components is treated as an impurity and is used to probe the superfluid nature of the condensate. |
