  The Fermi-polaron problem of a mobile impurity interacting with fermionic
medium emerges in various contexts, ranging from the foundations of Landau's
Fermi-liquid theory to electron-exciton interaction in semiconductors, to
unusual properties of high-temperature superconductors. While classically the
medium provides only a dissipative environment to the impurity, quantum picture
of polaronic dressing is more intricate and arises from the interplay of few-
and many-body aspects of the problem. The conventional expectation for the
dynamics of Fermi polarons is that it is dissipative in character, and any
excess energy is rapidly emitted away from the impurity as particle-hole
excitations. Here we report a strikingly different type of polaron dynamics in
a one-dimensional system of the impurity interacting repulsively with the
fermions. When the total momentum of the system equals the Fermi momentum,
there emerges a sharp collective mode corresponding to long-lived oscillations
of the polaronic cloud surrounding the impurity. This mode can be observed
experimentally with ultracold atoms using Ramsey interferometry and
radio-frequency spectroscopy.
