Fermi-Edge Singularity in a Nonequilibrium System

We report exact nonperturbative results for the Fermi-edge singularity in the absorption spectrum of an out-of-equilibrium tunnel junction. We consider two metals with chemical potential difference V separated by a tunneling barrier containing a defect, which exists in one of two states. When it is in its excited state, tunneling through the otherwise impermeable barrier is possible. Our nonperturbative solution of this nonequilibrium many-body problem shows that, as well as extending below the equilibrium threshold, the line shape depends on the difference in the phase of the reflection amplitudes on the two sides of the barrier. These results have a surprisingly simple interpretation in terms of known results for the equilibrium case but with (in general complex-valued) combinations of elements of the scattering matrix replacing the equilibrium phase shifts.