Entanglement growth in the dark intervals of a locally monitored free-fermion chain

TL;DR

This paper investigates how entanglement entropy evolves in a monitored free-fermion chain, revealing volume law scaling due to dark intervals caused by superpoissonian jump distributions, with effects diminishing as more sites are monitored.

Contribution

It demonstrates the impact of dark intervals and jump distribution on entanglement growth, highlighting the transition from volume law to Zeno effect with increased monitoring.

Findings

Entanglement entropy grows to a volume law in monitored trajectories.

Dark intervals with superpoissonian jump distribution cause extensive entanglement.

Increasing monitored sites leads to the Zeno effect and area law scaling.

Abstract

We consider a free fermionic chain with monitoring of the particle density on a single site of the chain and study the entanglement dynamics of quantum jump trajectories. We show that the entanglement entropy grows in time towards a stationary state which display volume law scaling of the entropy, in stark contrast with both the unitary dynamics after a local quench and the no-click limit corresponding to full post-selection. We explain the extensive entanglement growth as a consequence of the peculiar distribution of quantum jumps in time, which display superpoissonian waiting time distribution characterised by a bunching of quantum jumps followed by long dark intervals where no-clicks are detected, akin to the distribution of fluorescence light in a driven atom. We show that the presence of dark intervals is the key feature to explain the effect and that by increasing the number of sites which are monitored the volume law scaling gives away to the Zeno effect and its associated area law.