Exact entanglement dynamics of two spins in finite baths

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-neighbor 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.

Automated summary

We investigate the effects of two-spin entanglement buildup and decay through phase interactions in a finite environment of surrounding spins. We find that non-Markovian dephasing caused by the spin environment can be solved exactly and compared to a Markovian treatment based on collision models. In two case studies, we demonstrate that non-Markovianity accelerates dephasing and degrades entanglement, but additional three-body interactions and random reset operations can mitigate this degradation.