Quantum heat engine: A fully quantized model

Motivated by the growing interest in the nanophysics and the field of quantum thermodynamics [J. Gemmer, M. Michel, G. Mahler, Springer, 2005] we study a system consisting of two different 2-level atoms (spins) coupled to a quantum oscillator (resonator field mode), and each spin linked to a heat bath with different temperatures. We find that the energy gradient imposed on the system and the “coherent driving” of the two atoms achieved by the oscillator make this system act as a thermodynamic machine. We analyze the engine dynamics using the recently developed definitions of heat flux and power [E. Boukobza, D.J. Tannor, Phys. Rev. A. 74 (2006) 063823; H. Weimer, M.J. Henrich, F. Rempp, H. Schröder, G. Mahler, Eur. Phys. Lett. 83 (3) (2008) 30008]. The system can work as heat engine (laser) or a heat pump in a non-cyclic continuous mode. We characterize the properties of the resonator field. The concept of work and heat for this machine is discussed.