Driven quantum circuits and conductors: A unifying perturbative approach

International audienceWe 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 nonperturbative 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 Vdc, and the out-of-equilibrium dc current which encodes the effects of interactions. 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. We have derived similar relations for noise (I. Safi, arXiv:1401.5950) which have been exploited, recently, to determine the fractional charge in the fractional quantum Hall effect (FQHE) within the Jain series [M. Kapfer et al., Science (2019)]. The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates rectification exploited here to propose methods to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-Gaussian source of noise. We also apply the theory to the Tomonaga-Luttinger liquid (TLL), showing a counterintuitive feature: A Lorentzian pulse superimposed on Vdc can reduce the current compared to its dc value, at the same Vdc, questioning the terminology “photoassisted.” 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