Appearance of objectivity for NV centers interacting with dynamically polarized nuclear environment

Quantum-to-classical transition still eludes a full understanding. Out of its multiple aspects, one has recently gained an increased attention - the appearance of objective world out of the quantum. One particular idea is that objectivity appears thanks to specific quantum state structures formation during the evolution, known as spectrum broadcast structures (SBS). Despite that quite some research was already performed on this strong and fundamental form of objectivity, the practical realization of SBS in a concrete physical medium has not been explicitly analyzed so far. In this work, we study the possibility to simulate objectivization process via SBS formation using widely studied nitrogen-vacancy centers in diamonds. Assuming achievable limits of dynamical polarization technique, we show that for high, but experimentally viable polarizations (p > 0.5) of nuclear spins and for magnetic fields lower than ≈20 G the state of the NV center and its nearest polarized environment approaches an SBS state reasonably well.