Bose polarons at finite temperature and strong coupling.

The temperature dependence of a mobile impurity in a dilute Bose gas, the Bose polaron, is investigated for wide a range of impurity-bath interactions. Using a diagrammatic resummation scheme designed to include scattering processes important at finite temperature $T$, we show that the phase transition of the environment to a Bose-Einstein condensate at the critical temperature $T_c$ leads to several non-trivial effects. The attractive polaron present at $T=0$ fragments into two quasiparticle states for finite temperature whenever $|a|\gtrsim a_B$, with $a$ and $a_B$ the impurity-boson and boson-boson scattering lengths. While the quasiparticle with higher energy disappears at $T_c$, the ground state quasiparticle remains well-defined across $T_c$. Its energy depends non-monotonically on temperature, featuring a minimum at $T_c$, after which it increases towards zero, and at $T\gg T_c$ the polaron eventually becomes overdamped due to strong scattering with thermally excited bosons.