The Fermi liquid state of matter describes the normal phase of a plethora of strongly correlated materials, such for instance cuprates and iron-based superconductors. Also, it can be realized in cold atom platforms. Although there is much work on the static properties of these quantum fluids, such as quantum phase transitions and thermodynamic properties, there is still a lot to be understood in their dynamical properties. In this talk, I will show the existence of non-Hermitian singularities (called exceptional points) in the excitation spectrum of a class of Fermi liquids with multipolar interactions. We completely characterize this exceptional point, analyzing the Hilbert space structure and its topological properties. Experimental signatures are discussed in different set-ups: frequency- and momentum-dependent spectral functions, pump-probe spectroscopy, and the ac conductivity of Fermi liquids in a narrow slab. Furthermore, I will show some recent work on ultraf!
ast control of these non-hermitian fluctuations.
