THE QUANTUM HEAT ENGINE AND HEAT-PUMP - AN IRREVERSIBLE THERMODYNAMICANALYSIS OF THE 3-LEVEL AMPLIFIER

The manifestations of the three laws of thermodynamics are explored in a model of an irreversible quantum heat engine. The engine is compose d of a three-level system simultaneously coupled to hot and cold heat baths, and driven by an oscillating external field. General quantum he at baths are considered, which are weakly coupled to the three-level s ystem. The work reservoir is modeled by a classical electro-magnetic f ield of arbitrary intensity, which is driving the three-level system. The first law of thermodynamics is related to the rate of change of en ergy obtained from the quantum master equation in the Heisenberg pictu re. The fluxes of the thermodynamic heat and work are then directly re lated to the expectation values of quantum observables. An analysis of the standard quantum master equation for the amplifier, first introdu ced by Lamb, is shown to be thermodynamically inconsistent when strong driving fields are used. A generalized master equation is rigorously derived, starting from the underlying quantum dynamics, which includes relaxation terms that explicitly depend upon the field. For weak fiel ds the generalized master equation reduces to the standard equation. I n very intense fields the amplifier splits into two heat engines. One engine accelerates as the field intensifies, while the other slows dow n and eventually switches direction to become a heat pump. The relativ e weight of the slower engine increases with the field intensity, lead ing to a maximum in power as a function of the field intensity. The am plifier is shown to go through four ''phases'' as the driving field is intensified, throughout all of which the second law of thermodynamics is generally satisfied. One phase corresponds to a ''refrigeration wi ndow'' which allows for the extraction of heat out of a cold bath of t emperatures down to the absolute zero. This window disappears at absol ute zero, which is conjectured to be a dynamical manifestation of the third law of thermodynamics. (C) 1996 American Institute of Physics.