Spin decoherence in inhomogeneous media

A Green’s function formalism for describing the decoherence of a ‘central spin’ in inhomogeneous media is developed. By embedding the ‘central spin’ in a background medium and performing real-cavity, local-field corrections on the macroscopic fields at the location of the ‘central spin’ one can show that the Green’s function splits up into two main contributions, a contribution that is related to the bulk properties of the background medium and a contribution that is related inhomogeneities within the background medium. As an example, the coherence time of a shallow NV center in diamond close to a planar interface, both in the absence and presence of surface spins, is computed. It is found that the coherence time of the NV center increases as it moves away from the interface and, at distances greater than ≈1 nm, the interaction with the interface is negligible with the main source of decoherence coming from the interaction with the surface spins. Above ≈50 nm the interaction with the surface spins is also negligible and one recovers the bulk coherence time.