Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment

TL;DR

This paper derives analytical tools to analyze non-Markovian quantum dynamics of one and two qubits interacting with environments modeled by quadratic fermionic Hamiltonians, with specific insights into Ising model environments.

Contribution

It provides explicit Kraus decompositions and criteria for non-positivity of intermediate maps in non-Markovian quantum processes involving quadratic fermionic baths.

Findings

Derived analytical Kraus decomposition for quadratic fermionic environments.

Established criteria for detecting non-Markovianity in such systems.

Analyzed sources of non-Markovianity in Ising model environments.

Abstract

We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.