## Non-conventional many-body phases in ultracold dipolar systems

### Aleksey Fedorov

The problem of revealing and describing novel macroscopic quantum states characterized by exotic and non-conventional properties has the fundamental importance for modern physics. Such states offer fascinating prospects for potential applications in quantum information processing, quantum simulation, and material research. In the present Thesis we develop a theory for describing non-conventional phases of ultracold dipolar gases. The related systems of large-spin atoms, polar molecules, and dipolar excitons in semiconductors are actively studied in experiments. We put the main emphasis on revealing the role of the long-range character of the dipole-dipole interaction. We consider the effect of rotonization for a 2D weakly interacting gas of tilted dipolar bosons in a homogeneous layer, and demonstrate that in contrast to the case of perpendicular dipoles, in a wide range of tilting angles the condensate depletion remains small even when the roton minimum is extremely close to zero. We predict the effect of rotonization for a weakly correlated Bose gas of dipolar excitons in a semiconductor layer and calculate the stability diagram. According to our estimates, the threshold of the roton instability for a bose-condensed exciton gas with the roton-maxon spectrum is achievable experimentally in semiconductor layers. We then consider p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scat- tering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. For short-range interacting atoms in deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create p-wave superfluids with sizable transition temperatures. For fermionic polar molecules, due to a long-range character of the dipole-dipole interaction the effect of the suppression of the scattering amplitude is absent. It is shown that for microwave-dressed polar molecules a stable topological p+ip superfluid may emerge in the 2D lattice at realistic temperatures. Finally, we discuss another interesting novel superfluid of fermionic polar molecules. It is expected in a bilayer system, where dipoles are oriented perpendicularly to the layers and in opposite directions in different layers. We demonstrate the emergence of interlayer superfluid pairing. In contrast to the already known s-wave interlayer superfluid, when all dipoles are parallel to each other, in our case the s-wave pairing is suppressed and there can be p-wave or higher partial wave superfluids.

Directeurs de thèse: Georgy Shlyapnikov

Jury: Christophe Texier, Mikhail Baranov, Paolo Pedri, Andrey Varlamov