Open classical and quantum systems with effective parity-time (PT) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and non-reciprocaldevices. And yet, the microscopic origin of such effective, non-Hermitian models is not well understood. Here, we show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot-circuit-QED (DQD-circuit QED) set-up, which can be controllably tuned to the PT-symmetric point. This effective Hamiltonian, derived from a microscopic model for the set-up, governs the dynamics of two coupled circuit-QED cavities with a voltage-biased DQD in one of them. Our analysis also reveals the effect of quantum fluctuations on the PT symmetric system. The PT-transition is, then, observed both in the dynamics of cavity observables as well as via an input-output experiment. As a simple application of the PT-transition in this set-up, we show that loss-induced enhancement of amplification and lasing can be observed in the coupled cavities. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system with a gain medium in quantum regime, as well as its potential applications for quantum technology.
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 (N-DQD), (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.