  The main technological obstacle hampering the dissemination of modern
optoelectronic devices operating with large light-matter coupling strength
${\Omega}$ is an in-depth comprehension of the carrier current extraction and
injection from and into strongly coupled light-matter states, the so-called
polaritonic states. The main challenge lies in modeling the interaction between
excitations of different nature, namely bosonic excitations (the plasmonic ISB
excitations) with fermionic excitations (the electrons within the extraction or
injection subband). In this work, we introduce a comprehensive quantum
framework that encompasses both the ISB plasmonic mode and the
extractor/injector mode, with a specific emphasis on accurately describing the
coherent nature of transport. This reveals inherent selection rules dictating
the interaction between the ISB plasmon and the extraction/injection subband.
To incorporate the dynamics of the system, this framework is combined to a
density matrix model and a quantum master equation which have the key property
to distinguish intra and intersubband mechanisms. These theoretical
developments are confronted to experimental photocurrent measurements from
midinfrared quantum cascade detectors (${\lambda}$ = 10 ${\mu}$m) embedded in
metal-semiconductor-metal microcavities, operating at the onset of the strong
light-matter coupling regime (2${\Omega}$ = 9.3 meV). We are able to reproduce
quantitatively the different features of the photocurrent spectra, notably the
relative amplitude evolution of the polaritonic peaks with respect to the
voltage bias applied to the structure. These results on extraction allow us to
elucidate the possibility to effectively inject electronic excitations into ISB
plasmonic states, and thus polaritonic states.
