Coupling quantum emitters in metal–insulator–metal heterostructure: Green tensor approach in the quasi-static limit

Coupling between quantum emitters (QEs) has been a topic extensively explored in recent years. Theoretical models based on the Lindblad master equation and mapping to cascaded quantum system has shed light to the chiral coupling phenomena from the aspect of microscopic quantum electrodynamics. Different from dissipative systems investigated in previous literature, we investigate the QE–QE coupling in Hermitian and pseudo-Hermitian systems by considering a multi-layered metal–insulator–amplifying metal heterostructure that represents the two kinds of system by adjusting the damping factor of the metallic layers. Our investigation is restricted in the quasi-static regime that gives qualitative conclusion without loss of simplicity. From the aspect of macroscopic quantum electrodynamics, the explanation of the coupling process is based on the dyadic Green’s function. We clearly reveal the different coupling characteristics of differently polarized transition dipole moments.