Fermi-Bose mixture in mixed dimensions

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological $p_{x} + ip_{y}$ superfluid for identical fermions in two dimensions (2D). The expectations of reaching the critical temperature $T_c$ through p-wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes. Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background. Within the weak-coupling regime, we calculate the critical temperature $T_c$ for the fermionic pair formation, using Bethe-Salpeter formalism, and show that it is significantly boosted by higher-order diagramatic terms, such as phonon dressing and vertex corrections. We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p-wave superfluid is at reach with state-of-the-art experiments.Comment: 12 pages, 6 figures, 2 tables and supplementary materia

Tkachenko polarons in vortex lattices

We analyze the properties of impurities immersed in a vortex lattice formed by ultracold bosons in the mean field quantum Hall regime. In addition to the effects of a periodic lattice potential, the impurity is dressed by collective modes with parabolic dispersion (Tkachenko modes). We derive the effective polaron model, which contains a marginal impurity-phonon interaction. The polaron spectral function exhibits a Lorentzian broadening for arbitrarily small wave vectors even at zero temperature, in contrast with the result for optical or acoustic phonons. The anomalous damping of Tkachenko polarons could be detected experimentally using momentum-resolved spectroscopy.Comment: 10 pages, 2 figure

Free expansion of a Bose-Einstein condensate at the presence of a thermal cloud

We investigate numerically the free-fall expansion of a $^{87}$Rb atoms condensate at nonzero temperatures. The classical field approximation is used to separate the condensate and the thermal cloud during the expansion. We calculate the radial and axial widths of the expanding condensate and find clear evidence that the thermal component changes the dynamics of the condensate. Our results are confronted against the experimental data