Lasing and transport in a multi-level double quantum dot system coupled to a microwave oscillator

We study a system of two quantum dots, each with several discrete levels, which are coherently coupled to a microwave oscillator. They are attached to electronic leads and coupled to a phonon bath, both leading to inelastic processes. For a simpler system with a single level in each dot it has been shown that a population inversion can be created by electron tunneling, which in a resonance situation leads to lasing-type properties of the oscillator. In the multi-level system several resonance situations may arise, some of them relying on a sequence of tunneling processes which also involve non-resonant, inelastic transitions. The resulting photon number in the oscillator and the current-voltage characteristic are highly sensitive to these properties and accordingly can serve as a probe for microscopic details.