Entanglement generation between Unruh–DeWitt detectors in the de Sitter spacetime — Analysis with complex scalar fields

We investigate the entanglement generation or harvesting between two identical, comoving Unruh–DeWitt detectors in the cosmological de Sitter spacetime. The detectors are assumed to be unentangled initially. They are individually coupled to a complex scalar field, which eventually leads to coupling between themselves. Two kinds of complex scalar fields are investigated here — conformally invariant and massless minimally coupled. By tracing out the degrees of freedom corresponding to the scalar, we construct the reduced density matrix for the two detectors, whose eigenvalues characterise transition probabilities between the energy levels of the detectors. We have computed the negativity, quantifying the degree of entanglement generated at late times between the two detectors. The similarities and differences of these results between the aforementioned two kinds of scalar fields have been discussed. We also compare our results with the existing result of the real scalar field, and point out the qualitative differences. In particular, we emphasise that entanglement harvesting is more resilient in scenarios involving complex fields and nonlinear couplings.