Driven strongly correlated quantum circuits and Hall edge states: Unified photoassisted noise and revisited minimal excitations

Abstract

We study the photoassisted shot noise (PASN) generated by time-dependent (TD) or random sources and transmission amplitudes. We show that it obeys a perturbative nonequilibrium (NEQ) fluctuation relation (FR) that fully extends the lateral-band transmission picture in terms of many-body correlated states. This FR holds in NEQ strongly correlated systems such as the integer or fractional quantum Hall regime as well as in quantum circuits formed by a normal or a Josephson junction (JJ) strongly coupled to an electromagnetic environment, with a possible temperature bias. We then show that the PASN is universally super-Poissonian, giving an alternative to a theorem by L. Levitov et al. which states that an ac voltage increases the noise. We show that this theorem is restricted to a linear dc current and that it does not apply to a nonlinear SIS (superconductor-insulatorsuperconductor) junction. Then we characterize minimal excitations in nonlinear conductors as those which ensure a Poissonian PASN, and show that these can carry a nontrivial charge value in the fractional quantum Hall regime. We also propose methods for shot noise spectroscopy and for a robust determination of the fractional charge which complement those we have proposed previously and that have been implemented experimentally