Entanglement of nitrogen-vacancy-center ensembles with initial squeezing

Abstract

In this paper, we investigate entanglement of an experimental system of two nitrogen-vacancy-center ensembles which are initially squeezed under the one-axis twisting Hamiltonian. We take into account three scenarios in which initial squeezing and entanglement are mediated by phonons or photons: (a) the phonon-squeezed photon-entangled scenario, (b) the phonon-squeezed phonon-entangled scenario, and (c) the photon-squeezed photon-entangled scenario. For our investigation, we employ the Tavis-Cummings model, which includes dissipative decoherence of the collective spin ensemble, and analyze the system both for a relatively small number of spins and in the limit of a large number of spins using the approach of a quantum master equation. Although evidence in the literature on idealized coupled oscillator systems and coupled quantum kicked tops suggests that initial squeezing can enhance entanglement, we find that, in the realistic system studied in this paper, initial squeezing can improve entanglement overall when the field mode interacts in a particular manner with the two spin ensembles. Our analysis using the Holstein-Primakoff transformation and Wigner characteristic function in the rotating frame of reference shows that the entanglement enhancement is a subtle consequence of the way in which the dissipative decoherence rotates the state of the collective spin ensemble such that enhancement depends on the time-evolved rotated states between the presence and absence of initial squeezing.