Unified time-dependent perturbative relations applied to spectroscopy through photo-drag current

We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage $V_{dc}$, and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series (M. Kapfer et al, Science 2018). The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge $q$, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on $V_{dc}$ can reduce the current compared to its dc value, at the same $V_{dc}$, questioning the terminology "photo-assisted". Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction.