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

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.