Abstract

Nonequilibrium dynamics is a paramount scenario for studying quantum systems. The emergence of new features with no equilibrium counterpart, such as dynamical quantum phase transition (DQPT), has attracted wide attention. In this paper, we depart from the well-known Ising model and showcase an experimentally accessible configuration of a negatively charged nitrogen-vacancy center that interacts with nearby carbon-13 nuclear spins. We provide insights into this system in the context of DQPT. We show that nuclear spins undergo DQPT by appropriately choosing the relation between the transverse and longitudinal components of an external magnetic field. Furthermore, we can steer the DQPT via a time-dependent longitudinal magnetic field and apply this control to enhance the estimation of the coupling strength between the nuclear spins. Moreover, we propose a quenched dynamics that originates from the rotation of the central electron spin, which controls the DQPT relying on the anisotropy of the hyperfine coupling.