Optimal non-invasive measurement of Full Counting Statistics by a single qubit

TL;DR

This paper proposes an optimal, non-invasive method to measure the full counting statistics of charge transport in mesoscopic devices using a qubit, enhancing precision and reducing back-action.

Contribution

It introduces a measurement scheme utilizing multiple couplings and Ramsey sequences to optimally determine FCS moments with near quantum-limited precision.

Findings

Optimal distribution of couplings and measurements enhances precision.

Including many additional couplings approaches the standard quantum limit.

The scheme reduces back-action in FCS measurements.

Abstract

The complete characterisation of the charge transport in a mesoscopic device is provided by the Full Counting Statistics (FCS) $P_t(m)$, describing the amount of charge $Q = me$ transmitted during the time $t$. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function $P_t(m)$ or its moments $\langle Q^n \rangle$ are rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $\chi(\lambda)$ and moments $\langle Q^n \rangle$, by a qubit with a set of different couplings $\lambda_j$, $j = 1,\dots,k,\dots k+p$, $k = \lceil n/2 \rceil$, $p \geq 0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths $\lambda_j$ and we find the optimal distribution for these couplings $\lambda_j$ as well as the optimal distribution $N_j$ of $N = \sum N_j$ measurements among the different couplings $\lambda_j$. We determine the precision scaling for the moments $\langle Q^n \rangle$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $p\gg 1$ are included in the measurement scheme.