Suppression of dephasing and phase lapses in the fractional quantum Hall regime

Abstract

A charge fluctuator which is electrostatically coupled to a conducting channel may fully dephase quantum transport through the latter. Here, we address the case where a quantum dot (QD), playing the role of a charge fluctuator, is tunnel-coupled to an additional channel. In the case where the latter may support fractional charge, distinct differences from the integer case arise: Abrupt phase lapses of the transmission through the conducting channel occur (which may or may not be equal to π). This is accompanied by a cusp-like suppression of the interferometer's visibility, yet no full dephasing. We interpret our findings in terms of the entanglement between the fluctuator and the conducting channels.PACS numbers: 71.10.Pm, 72.10.Fk, 73.63.Kv Interference between possible paths is a fundamental quantum mechanical phenomenon. Its realization via an electronic Mach-Zehnder interferometer (MZI) 1 and an electronic Fabry-Pérot interferometer 2 plays an important role in investigating basic physics phenomena such as the Aharonov-Bohm effect, action-free measurement, correlations among particles, and fractional statistics of Abelian and non-Abelian anyons. Understanding the degradation of quantum interference (dephasing) is crucial for nanoelectronic technologies, and is of profound importance for clarifying the elusive transition from a quantum behavior to a classical one. Dephasing of interferometry signal due to the interaction with a detector is intimately related to the entanglement between them. It is often associated with acquiring information about which path the interfering particle has taken. 3-6It is common practice to model the effect of an environment on a system through a bath of harmonic oscillators or a puddle of Fermi liquid coupled to the latter. However, recent developments in experimental techniques have made it possible to perform controlleddephasing experiments, where the dephasor consists of only few degrees of freedom, and can be controlled with high precision. This has introduced the need for models of dephasors that are non-Gaussian and fully quantum mechanical. An out-of-equilibrium detector capable of determining the path taken by the electron, and thereby destroying the interference signal, is a standard paradigm in mesoscopic physics. Recently it has been shown that the Friedel sum rule is a useful tool for analyzing dephasing induced by charge fluctuations 7 . Here we study a paradigmatic controlled-dephasing setup of a MZI interacting with a fluctuator, but with a twist: the fluctuator operates in the fractional quantum Hall regime. The fluctuator is realized by a quantum dot (QD) (cf. Fig. 1), which is electrostatically coupled to the upper arm of the MZI. Since the QD has two charging states ("empty" and "occupied"), the fluctuation pattern of the charge on it defines quantum telegraph noise. Consequently, the phase accumulated along the upper arm of the MZI fluctuates between two val-Schematics of the setup. A quantum dot (QD) (red solid puddle) is capacitively coupled (black wi...