## Abstract

Mixed-dimensional systems are mixtures of quantum gases of different species in which one or more species live in restricted spatial dimensions. Mixtures of three-dimensional Bose and Fermi superfluids have been recently realised [1]. One-dimensional and two-dimensional systems can be obtained by imposing an optical lattice on the three-dimensional gas, and mixed-dimensional systems can be realised by means of species-selective optical lattices [2]. The interplay of the interactions between the different species in the mixture and the restricted dimensionality can lead to interesting physics. In this talk I report some of our recent work regarding systems that consist of 2D layers of spin-polarized fermions (40K for example) immersed in a 3D Bose-Einstein condensate (7Li for example). In the first part of my talk, I will describe how a single layer of non-interacting fermi gas immersed in a 3D BEC constitutes a very promising system to realise a px + i py superfluid [3]. The originally non-interacting fermions can attract each other via an induced interaction mediated by the bosons, and the resulting p-wave pairing can be analysed by a Berezinskii-Kosterlitz-Thouless theory which takes the retardation effects fully into account. In the second part, I will explained how the induced interaction between the fermions can be directly detected in experiment by considering two layers of fermions in a 3D BEC [4]. We theoretically determine this induced interaction between two layers of fermions separated by a distance for all the strengths of the Bose-Fermi interactions. Furthermore, we propose an experiment to detect the presence of induced inter-layer interaction through the dipole oscillations of the 2D Fermi gas. An experiment has been planned by our experimental collaborators to test our theoretical predictions. Finally, if time permits, I will discuss the induced p-wave superfluidity in a 3D-3D Bose-Fermi mixture. From the experimental point of view, such a system perhaps has a greater potential to achieve non-conventional superfluid pairing in cold atomic gases.

[1] I. Ferrier-Barbut et al.,
Science, 345, 6200 (2014).

[2] L. J. LeBlanc and J. H.
Thywissen, Phys. Rev. A 75, 053612 (2007).

[3] Z. Wu and G. M. Bruun, Phys.
Rev. Lett. 117, 245302 (2016).

[4] D. Suchet, Z.
Wu, F. Chevy and G. M. Bruun, Phys. Rev. A 95, 043643 (2017).