Emission and absorption noise in the fractional quantum Hall effect

We compute the high-frequency emission and absorption noise in a fractional quantum Hall effect (FQHE) sample at arbitrary temperature. We model the edges of the FQHE as chiral Luttinger liquids, and we use the nonequilibrium perturbative Keldysh formalism. We find that the nonsymmetrized high-frequency noise contains important signatures of the electron-electron interactions that can be used to test the Luttinger liquid physics, not only in FQHE edge states but possibly also in other one-dimensional systems such as carbon nanotubes. In particular, we find that the emission and absorption components of the excess noise (defined as the difference between the noise at finite voltage and at zero voltage) are different in an interacting system, as opposed to the noninteracting case when they are identical. We study the resonance features which appear in the noise at the Josephson frequency (proportional to the applied voltage), and we also analyze the effect of the distance between the measurement point and the backscattering site. Most of our analysis is performed in the weak-backscattering limit, but we also compute and discuss briefly the high-frequency noise in the tunneling regime.