Symmetrized and non-symmetrized noise from weak measurements in mesoscopic circuits

Abstract

Generalized quantum measurement schemes are described by positive operator-valued measures going beyond the projection postulate, which predicts the instantaneous collapse of the systems wave function. This allows to take the noninvasive limit and investigate the correlations of such weak measurements which enables the observation of non-commuting observables within the same system. We propose a scheme in which the detector is coupled to the measured system for a finite time, as it is the case in many real setups. This leads to non-Markovian effects appearing by memory functions which are related to symmetric and antisymmetric correlators of the detector variables [12]. We investigate these functions addressing the role of equilibrium and non-equilibrium detectors and how they differ from and could realize the standard Markovian measurement respectively. The latter scheme leads to the symmetrized operator order (aka Keldysh ordering), which is widely used in quantum measurement discussions. We show that the non-Markovian measurement scheme yields information beyond the standard approach, allowing e.g. for the proof of the non classical nature of a system (quasiprobability statistics) by second-order correlation functions [13].We further propose setups in mesoscopic electronic circuits to realise those concepts. One possibility is to use two double quantum dots coupled to a common quantum system. The detectors cross correlations are read out and by tuning the dot parameters, it is possible to explore the non-Markovian nature of the measurement setup.