Robust fermionic-mode entanglement of a nanoelectronic system in non-Markovian environments

TL;DR

This paper investigates the generation and dynamics of steady-state fermionic entanglement in nanoelectronic systems within non-Markovian environments, providing analytical insights into how finite temperature and spectral properties influence entanglement behavior.

Contribution

It offers an exact analytical framework linking non-Markovian dynamics with fermionic entanglement, including equivalence of different descriptions and effects of environment structure.

Findings

Steady-state fermionic entanglement can be achieved at finite temperature.

Different environmental spectral structures lead to various relaxation and memory states.

Analytical methods connect non-Markovian dynamics with entanglement evolution.

Abstract

A maximal steady-state fermionic entanglement of a nanoelectronic system is generated in finite temperature non-Markovian environments. The fermionic entanglement dynamics is presented by connecting the exact solution of the system with an appropriate definition of fermionic entanglement. We prove that the two understandings of the dissipationless non-Markovian dynamics, namely the bound state and the modified Laplace transformation are completely equivalent. For comparison, the steady-state entanglement is also studied in the wide-band limit and Born-Markovian approximation. When the environments have a finite band structure, we find that the system presents various kinds of relaxation processes. The final states can be: thermal or thermal-like states, quantum memory states and oscillating quantum memory states. Our study provide an analytical way to explore the non-Markovian entanglement dynamics of identical fermions in a realistic setting, i.e., finite temperature reservoirs with a cutoff spectrum.