We investigate gain in microwave photonic cavities coupled to voltage-biased double quantum dot systems with an arbitrarily strong dot-lead coupling and with a Holstein-like light-matter interaction, by employing the diagrammatic Keldysh nonequilibrium Green's function approach. We compute out-of-equilibrium properties of the cavity: its transmission, phase response, mean photon number, power spectrum, and spectral function. We show that by the careful engineering of these hybrid light-matter systems, one can achieve a significant amplification of the optical signal with the voltage-biased electronic system serving as a gain medium. We also study the steady-state current across the device, identifying elastic and inelastic tunneling processes which involve the cavity mode. Our results show how recent advances in quantum electronics can be exploited to build hybrid light-matter systems that behave as microwave amplifiers and photon source devices. The diagrammatic Keldysh approach is primarily discussed for a cavity-coupled double quantum dot architecture, but it is generalizable to other hybrid light-matter systems.

Motivated by recent experiments on the generation of coherent light in engineered hybrid quantum systems, we investigate gain in a microwave photonic cavity coupled to quantum dot structures and develop concrete directions for achieving a giant amplification in photon transmission. We propose two architectures for scaling up the electronic gain medium: (i) N-double quantum dot systems and (ii) M-quantum dots arranged in series akin to a quantum cascade laser setup. In both setups, the fermionic reservoirs are voltage biased, and the quantum dots are coupled to a single-mode cavity. Optical amplification is explained based on a sum rule for the transmission function, and it is determined by an intricate competition between two different processes: charge-density response in the gain medium and cavity losses to input and output ports. The same design principle is also responsible for the corresponding giant amplification in other photonic observables, mean photon number, and emission spectrum, thereby realizing a quantum device that behaves as a giant microwave amplifier.