Simulation of the dissipative dynamics of strongly interacting nitrogen-vacancy centers with tensor networks

Nitrogen-vacancy (NV) centers in diamond are a promising platform for highly sensitive quantum sensors for magnetic fields and other physical quantities. The quest for high sensitivity combined with high spatial resolution naturally leads to dense ensembles of NV centers and hence to strong, long-range interactions between them. Hence, simulating strongly interacting NVs becomes essential. However, obtaining the exact dynamics for a many-spin system is a challenging task due to the exponential scaling of the Hilbert space dimension, a problem that is exacerbated when the system is modeled as an open quantum system. In this work, we employ the matrix product density operator (MPDO) method to represent the many-body mixed state and to simulate the dynamics of an ensemble of NVs in the presence of strong long-range couplings due to dipole-dipole forces. We benchmark different time-evolution algorithms in terms of numerical accuracy and stability against time evolution based on exact numerical diagonalization. Subsequently, we simulate the dynamics in the strong-interaction regime and study the impact of decoherence on the accuracy of the MPDO method. Last, we investigate the dynamics of quantum Fisher information and show that for small distances below about 5 nm the resulting strong dipole-dipole interaction can improve the sensitivity for magnetic field sensing when the ensemble is driven by pulses of constant amplitude.