  A new generation of cold atom experiments trapping atomic mixtures in species
selective optical potentials opens up the intriguing possibility to create
systems in which different atoms live in different spatial dimensions. Inspired
by this, we investigate a mixed dimensional Bose polaron consisting of an
impurity particle moving in a two-dimensional (2D) layer immersed in a 3D
Bose-Einstein condensate (BEC), using a theory that includes the mixed
dimensional vacuum scattering between the impurity and the bosons exactly. We
show that similarly to the pure 3D case, this system exhibits a well-defined
polaron state for attractive boson-impurity interaction that evolves smoothly
into a mixed-dimensional dimer for strong attraction, as well as a well-defined
polaron state for weak repulsive interaction, which becomes over-damped for
strong interaction. We furthermore find that the properties of the polaron
depend only weakly on the gas parameter of the BEC as long as the Bogoliubov
theory remains a valid description for the BEC. This indicates that higher
order correlations between the impurity and the bosons are suppressed by the
mixed dimensional geometry in comparison to a pure 3D system, and that the
mixed dimensional polaron has universal properties in the unitarity limit of
the impurity-boson interaction.
