AC driven fractional quantum Hall systems: Uncovering unexpected features

Abstract

We investigate the challenges of reaching the quantum regime and generating minimal excitations in the fractional quantum Hall effect (FQHE) under AC driving. Using the unifying non-equilibrium perturbative (UNEP) approach, we analyze weak backscattering through a quantum point contact (QPC). In both two-terminal geometries and the "anyon collider" setup, the lower bound on photoassisted backscattering noise is set by the photoassisted current rather than the DC noise predicted by Levitov's theorem. This super-Poissonian character is confirmed within the Tomonaga-Luttinger liquid (TLL) framework, where Levitov's theorem is violated, challenging the conventional interpretation of "photoassisted" noise. In the two-terminal geometry, we show that when the QPC has a low scaling dimension, two challenges arise: first, achieving the expected power-law behavior in the DC regime, and second, maintaining the AC quantum regime, where the drive frequency exceeds the temperature, when the DC voltage component is resonant with that drive frequency. The validity of the UNEP relations imposes a lower bound on temperature and a persisting equilibrium contribution to backscattering noise. This forces us to choose a high enough scaling dimension, for which we find that it is rather the photoconductance, often overlooked, that might exhibit spikes at resonant DC voltages, providing a reliable probe of fractional charge. Moreover, we highlight that the zero-temperature limit, frequently assumed in prior studies, including X. G. Wen's foundational work, is inappropriate in this context. Our findings extend beyond the FQHE to coherent conductors and Josephson or phase-slip junctions strongly coupled to an ohmic environment under AC bias, with broader implications for quantum transport and minimal excitation engineering.