Laser induced $\mathcal{P}\mathcal{T}$-symmetry breaking in the fluctuations of electronic fluids

Electronic fluids can display exciting dynamical properties. In particular, due to Landau damping, the collective modes spectrum of an electronic system with multipolar interactions is non-hermitian, and can present non-hermitian degeneracies called $\mathit{\text{exceptional}}\mathit{\text{points}}$. In this work, we want to explore the dynamical properties of these degeneracies using laser control. We show that by using a light pulse, we can control the collective mode spectrum and tune a non-hermitian $\mathcal{P}\mathcal{T}$ phase transition in which two exceptional points anhilate each other. At this transition, the gap closes with a cubic root signature, what defines a third order exceptional point.