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 . 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 . 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 . 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 . 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.
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