Emission and absorption noise in the fractional quantum Hall effect

In this study, 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 (LL) and apply the non-equilibrium perturbative Keldysh formalism to derive our results. Our analysis shows that the non-symmetrized high-frequency noise reveals significant signatures of electron-electron interactions, which are critical for testing the principles of Luttinger liquid physics in FQHE edge states and potentially in other one-dimensional systems such as carbon nanotubes. Notably, we discover a difference in the emission and absorption components of the excess noise (defined as the difference between noise measured at finite voltage versus zero voltage) in an interacting system, contrasting with the non-interacting case where they are identical. Furthermore, we examine resonance features in the noise related to the Josephson frequency, which is proportional to the applied voltage, and assess the impact of the measurement point's distance from the backscattering site. While the majority of our analysis is conducted in the weak backscattering limit, we also provide a brief computation and discussion on the high-frequency noise within the tunneling regime.