We report on developing a quantum description for surface lattice resonances (SLR) using a basis of quasi-normal modes (QNM) in the coupled dipole approximation (CDA) and its application to the strong-coupling regime (SC) with individual quantum emitters.<br/>Metal nanoparticles (MNP) significantly enhance the electromagnetic field in their vicinity, allowing them to interact with quantum emitters strongly. However, due to dissipative processes, this effect is counterbalanced by the very short lifetime of their local surface plasmon (LSP) modes. SLRs are long-lived collective resonances arising when MNPs are ordered on an array with lattice constant matching the wavelength of the incoming light field. The significant increase in the SLR lifetime with respect to individual LSP modes opens the way toward SC.<br/>QNMs solve the Helmholtz equation for an arbitrary dissipative medium with a complex-valued dielectric permittivity. The Ohmic dissipation and open boundary conditions imply that the QNMs have a finite lifetime. They form a basis for expanding the electromagnetic field. Their limited lifetime allows them to efficiently model dissipative processes with a reasonably small, discrete basis. In this contribution, we propose to use the QNMs basis to build collective lattice resonances from a purely quantum point of view. In this first approach, we match the formalism with the classical theory of SLRs in the CDA by taking the dipole limit for each QNM supported by the individual particles. In this limit, we partially ignore the internal structure of the nanoparticles, and the interaction between distinct nanoparticles reduces to dipole-dipole interactions mediated by the background EM field. We apply the equations of motion for the SLR modes to the case of strong coupling with an individual dipole emitter and show how the SLR modes are affected by their strong coupling with an individual quantum emitter.

Quantum dynamics of single emitters strongly coupled with collective lattice resonance: Quasi-normal modes in the coupled-dipole approximation

ACS Spring 2022

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