Time-controlled charge injection in a quantum Hall fluid

We consider the injection of a controlled charge from a normal metal into an edge state of the fractional quantum Hall effect (FQHE), with a time-dependent voltage V(t). Using perturbative calculations in the tunneling limit, and a chiral Luttinger liquid model for the edge state, we show that the electronic correlations prevent the charge fluctuations from being divergent for a generic voltage pulse V(t). This is in strong contrast with the case of charge injection in a normal metal, where this divergence is present. We show that explicit formulas for the mean injected charge and its fluctuations can be obtained using an adiabatic approximation, and that nonperturbative results can be obtained for injection in an edge state of the FQHE with filling factor nu=1/3. Generalization to other correlated systems which can be described with the Luttinger liquid model, like metallic carbon nanotube, is given.