Lindblad Formalism based on Fermion-to-Qubit mapping for Non-equilibrium Open-Quantum Systems

TL;DR

This paper introduces a new Lindblad master equation formalism for fermionic open quantum systems using fermion-to-qubit mapping, enabling analysis of non-equilibrium dynamics with practical applications to quantum sensors.

Contribution

It develops an alternative Lindblad formalism for fermionic systems via Jordan-Wigner transformation, facilitating broader analysis of non-equilibrium open quantum systems.

Findings

The formalism effectively models charge sensor effects on electron dynamics.

Probes induce dephasing, leading to entanglement sudden death and rebirth.

The system evolves to a statistical mixture in the long term.

Abstract

We present an alternative form of master equation, applicable on the analysis of non-equilibrium dynamics of fermionic open quantum systems. The formalism considers a general scenario, composed by a multipartite quantum system in contact with several reservoirs, each one with a specific chemical potential and in thermal equilibrium. With the help of Jordan-Wigner transformation, we perform a fermion-to-qubit mapping to derive a set of Lindblad superoperators that can be straightforwardly used on a wide range of physical setups.To illustrate our approach, we explore the effect of a charge sensor, acting as a probe, over the dynamics of electrons on coupled quantum molecules. The probe consists on a quantum dot attached to source and drain leads, that allows a current flow. The dynamics of populations, entanglement degree and purity show how the probe is behind the sudden deaths and rebirths of entanglement, at short times. Then, the evolution leads the system to an asymptotic state being a statistical mixture. Those are signatures that the probe induces dephasing, a process that destroys the coherence of the quantum system.