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We theoretically investigate the characteristics of the electron transportthrough a two-dimensionala quantum dot system in the $xy$-plane coupled to aphoton cavity and a photon reservoir, the environment. The electron-photoncoupling, $g_{\gamma}$, and the cavity-reservoir coupling, $\kappa$, are tunedto study the system in the weak, $g_{\gamma} \leq \kappa$, and the strongcoupling regime, $g_{\gamma} > \kappa$. An enhancement of current is both seenwith increasing $g_{\gamma}$ and $\kappa$ in the weak coupling regime for both$x$- and $y$-polarization of the photon field. This is a direct consequence ofthe Purcell effect. The current enhancement is due to the contribution of thephoton replica states to the electron transport in which intraband transitionsplay an important role. The properties of the electron transport aredrastically changed in the strong coupling regime with an $x$-polarized photonfield in which the current is suppressed with increasing $g_{\gamma}$, but itis still increasing with $\kappa$. This behavior of the current is related tothe population of purely electronic states and depopulation of photon replicastates.

The interplay of electron-photon and cavity-environment coupling on the electron transport through a quantum dot system