Analytical results for the quantum non-Markovianity of spin ensembles undergoing pure dephasing dynamics

TL;DR

This paper provides exact analytical formulas to quantify the non-Markovian behavior of spin ensembles under pure dephasing, exploring how interaction range and environment size influence Markovianity.

Contribution

It derives exact formulas for non-Markovianity in spin ensembles with arbitrary size and interaction range, including the thermodynamic limit, and analyzes the role of initial states.

Findings

Non-Markovianity depends on interaction range and environment size.

In the thermodynamic limit, dynamics can be Markovian or non-Markovian based on interaction range.

Non-Markovianity can occur without entanglement between system and environment.

Abstract

We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with pairwise interactions. We derive exact formulas for the reduced dynamics of the system and for its non-Markovianity as assessed by the witness of Lorenzo \emph{et al.} [Phys.~Rev.~A \textbf{88}, 020102(R) (2013)]. The non-Markovianity is further investigated in the thermodynamic limit when the environment's size goes to infinity. In this limit and for finite-size systems, we find that the Markovian's character of the system's dynamics crucially depends on the range of the interactions. We also show that, when the system and its environment are initially in a separable state, the appearance of non-Markovianity is independent of the entanglement generation between the system and its environment.