Full counting statistics for boundary driven transport in presence of correlated gain and loss channels

TL;DR

This paper analyzes the full counting statistics of particle current in boundary driven fermionic lattices with engineered correlated gain and loss channels, revealing nonreciprocity and conditions for balanced gain-loss scenarios.

Contribution

It introduces a method to compute the cumulant generating function for current in such systems and explores the effects of correlated versus local gain-loss channels.

Findings

Correlated gain-loss channels lead to nonreciprocal current statistics.

Conditions for PT-symmetric balanced gain-loss scenarios are identified.

Correlated gain-loss channels significantly affect current fluctuations and nonreciprocity.

Abstract

One of the major advances of quantum technology is the engineering of complex quantum channels in lattice systems that paves the way for a variety of novel non-equilibrium phenomena. For a boundary driven lattice with such engineered quantum channels, the analysis of the full counting statistics of current across boundaries has received limited attention. In this work, we consider a boundary driven free fermionic lattice with carefully engineered correlated gain and loss channels and obtain the cumulant generating function of the steady-state particle current. We also discuss the limit for simplifying the correlated gain-loss channel to a local gain-loss channel and obtain the average current and its fluctuation in such cases. Generally, in the presence of gain-loss, the current statistics are different at the two ends of the lattice. Hence, for both local and correlated gain-loss, we devise the conditions for which the statistics can coincide, giving rise to a $\mathcal{PT}$ symmetric balanced gain-loss scenario. A striking difference between the correlated gain-loss and their local counterpart is the emergence of nonreciprocity in the system and we observe that it has a dramatic impact in the current as well as fluctuations. Our work therefore provides interesting insights about the importance of engineered dissipators in boundary driven systems.