Emission and absorption noise in the fractional quantum Hall effect

Abstract

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 we use the non-equilibrium perturbative Keldysh formalism. We find that the non-symmetrized 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 non-interacting 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.

26 pages, 11 figures

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• AC conductance and non-symmetrized noise at finite frequency in quantum wires and carbon nanotubes
• Perturbative fluctuation dissipation relation for non-equilibrium finite frequency noise in quantum circuits
• Determination of tunneling charge via current measurements
• Multiple quasiparticle Hall spectroscopy investigated with a resonant detector
• Neutral modes edge state dynamics through quantum point contacts
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• Spectral noise for edge states at filling factor $\nu =5/2$
• Microwave photons emitted by fractionally charged quasiparticles
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• Fluctuation dissipation relations for strongly correlated out-of-equilibrium circuits
• Unified time-dependent perturbative relations applied to spectroscopy through photo-drag current
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• Non-equilibrium quantum transport through a dissipative resonant level
• Phase-Coherent Dynamics of Quantum Devices With Local Interactions
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• Finite frequency noise for Laughlin state investigated by a resonant circuit