Signature of Liouvillian exceptional point in stationary current noise*

Open quantum systems coupled to thermal reservoirs naturally exhibit non-Hermitian physics; their time evolution can be described by quantum master equations characterized by Liouvillian superoperators, accounting for both free Hamiltonian evolution and dissipation due to coupling to the reservoirs, the latter being inherently non-Hermitian. An interesting feature of non-Hermitian physics is the presence of exceptional points (EPs), which can also be found in dissipative open quantum systems as Liouvillian EPs. At an EP, the operator exhibits a singularity where eigenvalues and corresponding eigenvectors coincide, rendering the operator non-diagonalizable and only transformable into the Jordan block form. In the present study, we consider a quantum thermal machine, consisting of two interacting quantum dots attached to two electrodes, whose Liouvillian has an EP. By focusing on the steady state electronic current noise between the electrodes, we show that the Jordan block structure at the Liouvillian EP leads to a super-Lorentzian line shape of the current noise spectrum.