Doppler-broadened quantum electromagnetically-induced-transparency heat engines

A nontraditional quantum heat engine based on electromagnetically induced transparency has recently been suggested and experimentally demonstrated in ultracold atoms. In more practical setups with warm atoms, thermal atomic motions might hamper this heat engine mechanism. We here show that a Doppler-broadened atomic sample can still behave like an engine. However, only photons emitted in the direction of the coupling laser have the same brightness as for the Doppler-free engine, while the larger the angular deviation of emission, the lower the brightness. Our results suggest that the lower brightness can be seen as an act of Doppler broadening as if the thermal occupation number of the reservoir serving as entropy sink is increased, and the quantum heat engines may be feasible in warm atomic interfaces.