We present a general theory of gain-modified emission dynamics between two quantum emitters (two level systems) in a linear gain medium, demonstrating how gain modifies the usual radiative decay rates and interemitter coupling and decay rates, from purely lossy systems. We derive a Born-Markov master equation that shows explicitly how gain modifies the usual rates appearing for two emitters in a loss-only medium and introduces new gain terms. We then present Bloch equations in the bare state basis as well as a dressed-state basis (using superradiant and subradiant states). As an application of the theory, we show calculations for a fully three-dimensional metal dimer in a gain-compensated medium containing two quantum emitters and show explicit solutions in terms of the quasinormal modes, which easily allows one to obtain all the relevant decay rates. We study the modified decay dynamics, gain excited pumping, as well as the entanglement entropy and spectral emission. We also demonstrate how a breakdown of the weak excitation approximation in the presence of gain requires a careful treatment beyond a linear response, which yields nontrivial incoherent coupling terms that typically are not included in dipole-dipole coupling models and heuristic gain pumping models.

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• Plasmonics
• Quantum optics