  Recent breakthroughs in quantum-dot circuit-quantum-electrodynamics
(circuit-QED) systems are important both from a fundamental perspective and
from the point of view of quantum photonic devices. However, understanding the
applications of such setups as potential thermoelectric diodes and transistors
has been missing. In this paper, via the Keldysh nonequilibrium Green's
function approach, we show that cavity-coupled double quantum-dots can serve as
excellent quantum thermoelectric diodes and transistors. Using an enhanced
perturbation approach based on polaron-transformations, we find non-monotonic
dependences of thermoelectric transport properties on the electron-photon
interaction. Strong light-matter interaction leads to pronounced rectification
effects for both charge and heat, as well as thermal transistor effects in the
linear transport regime, which opens up a cutting-edge frontier for quantum
thermoelectric devices.
