Mixed-dimensional Bose polaron

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 overdamped 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, which led us to speculate that the mixed-dimensional polaron has universal properties in the unitarity limit of the impurity-boson interaction.

Figure 1

Sketch of the system: 2D impurity particle (blue) immersed in a 3D Bose-Einstein condensate (red).

Figure 2

Diagrams used in the ladder approximation for the impurity. A solid line represents an impurity propagator, a dashed line denotes a boson propagator, and a dotted line denotes a boson emitted or absorbed by the BEC. (a) The polaron self-energy given by the sum of the diagrams ${\mathrm{\Sigma }}_0$ and ${\mathrm{\Sigma }}_1$. (b) The $\mathcal{T}$ matrix giving the scattering between the impurity and a boson.

Figure 3

The quasiparticle energy for zero momentum as a function of the inverse Fermi-Bose interaction strength.

Figure 4

The quasiparticle residue for zero momentum as a function of the inverse Fermi-Bose interaction strength.

Figure 5

The effective mass for zero momentum as a function of the inverse Fermi-Bose interaction strength.

Figure 6

The spectral function of the zero-momentum polaron as a function of frequency and inverse Fermi-Bose interaction strength.