Exact Entanglement Dynamics of Two Spins in Finite Baths

TL;DR

This paper provides an exact analysis of how two-spin entanglement evolves in finite spin baths, revealing how non-Markovian effects influence dephasing and entanglement, and proposing methods to mitigate entanglement loss.

Contribution

It offers an exact solution for non-Markovian spin dephasing dynamics and explores strategies to preserve entanglement in finite spin environments.

Findings

Non-Markovianity increases dephasing rate with nearest neighbor interactions.

Three-body interactions can reduce entanglement degradation.

Reset operations help maintain steady-state entanglement.

Abstract

We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest neighbour interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions.