  We consider an impurity immersed in a Bose-Einstein condensate with tunable
boson-impurity interactions. Such a Bose polaron has recently been predicted to
exhibit an intriguing energy spectrum at finite temperature, where the
ground-state quasiparticle evenly splits into two branches as the temperature
is increased from zero [Guenther et al., Phys. Rev. Lett. 120, 050405 (2018)].
To investigate this theoretical prediction, we employ a recently developed
variational approach that systematically includes multi-body correlations
between the impurity and the finite-temperature medium, thus allowing us to go
beyond previous finite-temperature methods. Crucially, we find that the number
of quasiparticle branches is simply set by the number of hole excitations of
the thermal cloud, such that including up to one hole yields one splitting, two
holes yields two splittings, and so on. Moreover, this effect is independent of
the impurity mass. We thus expect that the exact ground-state quasiparticle
will evolve into a single broad peak for temperatures $T>0$, with a broadening
that scales as $T^{3/4}$ at low temperatures and sufficiently weak boson-boson
interactions. In the zero-temperature limit, we show that our calculated
ground-state polaron energy is in excellent agreement with recent quantum Monte
Carlo results and with experiments.
